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16 Dec, 2024 | AI ML DS - How To Get Started?
16 Dec, 2024
Artificial Intelligence (AI), Machine Learning (ML), and Data Science (DS) are three interrelated fields in computer science and statistics. AI focuses on creating intelligent systems, ML enables computers to learn from data and make predictions, and DS leverages data to extract insights and drive decision-making. These three fields often overlap and complement each other in solving real-world problems and advancing technology.Data ScienceData Science combines statistical and computational tools to process and analyze large amounts of data. DS practitioners use their insights from data to inform decisions, predict trends, and improve the effectiveness of processes.Prerequisites for Data ScienceMaths for Data Science Statistics for Data Science Linear Algebra for Data ScienceCalculus for Data Science Important LibrariesPandas Tutorial NumPy Tutorial Data Analysis Data Cleaning Handling Missing Data Outlier Detection Exploratory Data Analysis (EDA)Statistical Analysis Time Series Analysis Data Visualization Data Visualization using Matplotlib Data Visualization using Seaborn Data Visualization using Plotly Data Visualization using BokehPower BI Tutorial Tableau TutorialMachine Learning Machine Learning is a subset of AI focused on building systems that learn from data, identify patterns, and make decisions with minimal human intervention. ML algorithms improve their performance as the amount of data they're exposed to increases.Supervised Machine Learning In supervised machine learning, the model is trained on the label data to predict outcomes for new or unseen data. Linear Regression Logistic Regression Support Vector Machine (SVM)Decision Trees Random Forest Naive Bayes K-Nearest Neighbour (KNN) XGBoost Semi-Supervised Learning uses a small amount of labeled data and a large amount of unlabeled data to improve learning accuracy.Unsupervised Machine Learning In unsupervised machine learning, the model learns patters and structures from unlabeled data without defined output labels. K-Means Clustering Hierarchical Clustering DBSCANPrincipal Component Analysis (PCA) Independent Component Analysis (ICA)Gaussian Mixture Models (GMM)t-SNE (t-Distributed Stochastic Neighbor Embedding)Reinforcement Learning In reinforcement learning, agent learns to make decisions by interacting with an environment and receiving rewards or penalties based on its actions. Q Learning SARSA (State-Action-Reward-State-Action)REINFORCE AlgorithmActor-Critic MethodProximal Policy Optimization (PPO)To learn more about machine learning, you can follow this tutorial: Machine Learning Tutorial Deep Learning Deep learning is a specialized area within ML. Deep learning uses neural networks with many layers (deep neural networks) to automatically learn features and representations from large datasets. Perceptron Multi-Layer Perceptron Artificial Neural Network Convolutional Neural Networks (CNNs)Recurrent Neural Networks (RNNs)Long Short-Term Memory Networks (LSTMs)Generative Adversarial Networks (GANs)To learn more about deep learning, you can follow this tutorial: Deep Learning Tutorial Artificial Intelligence (AI) Artificial Intelligence refers to the capability of a machine to imitate intelligent human behavior. It encompasses a broad range of technologies that enable machines to perceive, comprehend, act, and learn. Search Algorithms Optimization AlgorithmsAdversarial Search AlgorithmsConstraint Satisfaction ProblemsKnowledge Representation Reasoning Planning Uncertain Knowledge Robotics To learn more, you can follow these tutorials: Artificial Intelligence Tutorial Computer Vision Tutorial Natural Language Processing Tutorial Generative AI Tutorial | Data Science & ML/AI ML DS - How To Get Started? | https://www.geeksforgeeks.org/ai-ml-ds/?ref=outindfooter | Data Science & ML | AI ML DS - How To Get Started? | Data Science & ML, AI ML DS - How To Get Started? | GeeksforGeeks | [0.0216117352, -0.00712580839, -0.0099926712, 0.0149821155, 0.0442985445, -0.0183589496, 0.0137623204, 0.000607743917, 0.0213498585, 0.0115639325, 0.0256777201, -0.0496187806, 0.0396398939, -0.0259395968, -0.0346780159, 0.0085936971, 0.0150923794, 0.00681569101, 0.0074566, -0.0549390167, 0.00183141546, -0.00158246013, -0.0470000133, 0.0170357823, -0.0102752224, 0.0175871011, 0.00985484105, 0.00270318985, -0.0485161431, 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16 Apr, 2024 | AI ML DS - Projects
16 Apr, 2024
Welcome to the "Projects Series: Artificial Intelligence, Machine Learning, and Data Science"! This series is designed to dive deep into the transformative world of AI, machine learning, and data science through practical, hands-on projects. Whether you're a budding enthusiast eager to explore the fundamentals or a seasoned professional looking to expand your skill set, this series offers a comprehensive exploration of the latest technologies and methodologies. Each segment—Artificial Intelligence, Machine Learning, and Data Science—focuses on specific tools, applications, and real-world scenarios to equip you with the knowledge and skills necessary to lead and innovate in this dynamic field. Join us as we unravel the complexities of these technologies and harness their power to solve some of the most challenging problems facing industries today.
In this article, we are going to discuss the series of Projects which is used in Artificial Intelligence, Machine Learning, and Data Science domains.
Here we will start with Data analysis, Data Visualization, Machine Learning, NLP, Deep Learning, Computer Vision, AI and Generative AI Projects.
Table of Content
Data Analysis ProjectsData Visualization ProjectsMachine Learning Projects NLP Projects - Deep Learning Projects - Computer Vision Projects AI ProjectsData Analysis ProjectsThis article offers a comprehensive guide on various data analyst projects. The article aims to provide valuable insights and ideas for individuals interested in pursuing projects related to data analysis. These projects are designed to enhance data analytics skills, offering practical experience in handling real-world data and deriving meaningful insights.
The article begins by emphasizing the importance of hands-on experience in data analysis and the value it brings to aspiring data analysts. It then proceeds to showcase a diverse range of project ideas, catering to different domains and levels of expertise. Each project idea is accompanied by a brief description, highlighting the skills that can be acquired or enhanced through its completion.
The project ideas cover various aspects of data analysis, including data visualization, predictive modeling, machine learning, and industry-specific applications. For instance, one project idea focuses on creating interactive dashboards to visualize and explore data trends, while another involves building a recommendation system using collaborative filtering techniques.
The article also emphasizes the importance of working with real-world datasets, providing links to data sources and suggesting tools and technologies commonly used in data analysis, such as Excel, SQL, and programming languages like Python or R. Additionally, it encourages readers to explore data storytelling, where data-driven narratives are crafted to convey insights effectively to stakeholders.
By undertaking these projects, individuals can strengthen their data manipulation, critical thinking, and problem-solving skills. They gain exposure to various data analysis techniques, learn to communicate insights effectively, and develop a portfolio that showcases their analytical capabilities. These projects serve as a stepping stone for aspiring data analysts, enabling them to apply their knowledge in practical scenarios and build a solid foundation for their career.
Data Visualization ProjectsThis article will explain you the idea of Data Visualization Projects, here you will get an idea of Projects. The article begins by emphasizing the importance of data visualization and its role in extracting insights from data. It highlights how effective visualization techniques can simplify complex data, reveal patterns and trends, and facilitate better decision-making. By undertaking these projects, individuals can gain practical experience in translating data into visually appealing and informative representations.
Machine Learning Projects The article begins by emphasizing the importance of hands-on experience in machine learning and the advantages it brings. It then proceeds to showcase a diverse array of project ideas, each designed to help readers apply their machine learning knowledge in a practical manner. The projects are categorized based on difficulty levels, ensuring that beginners, intermediate learners, and advanced practitioners can find suitable challenges.
The project ideas cover various domains and techniques in machine learning. For instance, one project idea focuses on building a spam filter using natural language processing techniques, while another involves creating a recommendation system for personalized movie suggestions. The article also includes projects related to image classification, sentiment analysis, time series prediction, and game-playing agents.
NLP ProjectsThe article begins by emphasizing the significance of NLP and its wide range of applications. It highlights the impact of NLP in various domains, including information retrieval, sentiment analysis, machine translation, and language-driven virtual assistants. By undertaking these projects, individuals can gain practical experience in applying NLP techniques and contributing to the advancement of human-computer interaction.
The project ideas presented in the article cater to different levels of expertise, ensuring that beginners, intermediate learners, and advanced practitioners can find suitable challenges. The projects cover various aspects of NLP, such as text classification, named entity recognition, sentiment analysis, machine translation, question answering, and language generation.
Deep Learning ProjectsThis article that offers a comprehensive list of deep learning projects. The article aims to provide valuable insights and ideas for individuals interested in pursuing projects related to deep learning, a powerful branch of machine learning. These projects cover a range of topics and applications, allowing readers to enhance their skills and gain practical experience in this exciting field.
The project ideas presented in the article cater to different levels of expertise, ensuring that beginners, intermediate learners, and advanced practitioners can find suitable challenges. The projects cover a diverse range of domains, including computer vision, natural language processing, healthcare, finance, and autonomous systems.
Each project idea is accompanied by a concise description, providing a clear understanding of the task and the skills that can be acquired or improved upon. The article emphasizes the practical nature of these projects, encouraging readers to work with popular deep learning frameworks such as TensorFlow, PyTorch, and Keras. It provides links to relevant tutorials, datasets, and resources that can aid in the development process.
Computer Vision Projects This article that offers a comprehensive list of computer vision projects. The article aims to provide valuable insights and ideas for individuals interested in pursuing projects related to computer vision, a fascinating field that focuses on understanding and interpreting visual information. These projects cover a range of topics, allowing individuals to enhance their skills in image and video processing, object detection, recognition, and analysis.
The project ideas presented in the article cater to different levels of expertise, ensuring that beginners, intermediate learners, and advanced practitioners can find suitable challenges. The projects cover various aspects of computer vision, including image classification, object detection, image segmentation, facial recognition, and video analysis.
AI ProjectsIn this Project Article, you will learn the ideas of some AI Details Project Ideas, The article begins by emphasizing the significance of AI and its growing impact on various industries. It highlights the potential of AI to revolutionize fields such as healthcare, finance, transportation, and robotics. By undertaking these projects, individuals can gain hands-on experience in applying AI techniques, solving real-world problems, and contributing to the advancement of intelligent systems. Each project idea is accompanied by a concise description, providing a clear understanding of the task and the skills that can be acquired or improved upon. The article emphasizes the practical nature of these projects, encouraging readers to work with popular AI frameworks, libraries, and tools. It provides links to relevant tutorials, datasets, and resources that can aid in the development process. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects | https://www.geeksforgeeks.org/ai-ml-ds-projects/?ref=lbp | Data Science & ML | AI ML DS - Projects | Data Science & ML, AI ML DS - Projects, AI ML DS - How To Get Started? | GeeksforGeeks | [-0.0295599792, 0.00724923285, -0.0242954865, -0.00294544082, 0.0394696109, -0.00705568539, 0.0126474481, 0.0033906, 0.0171729401, 0.0233664587, 0.0342614241, -0.0552630834, 0.0670589209, -0.0194392055, -0.0347681642, -0.030911291, -0.00757298479, -0.0181019679, 0.021916613, -0.0445088819, -0.00915655494, -0.000995889772, -0.0471270531, 0.00843867, 0.00490906788, 0.0187072437, -0.00560935773, 0.00283459085, -0.0311928149, 0.0327130444, 0.0190732237, -0.0257875621, 0.0238591265, -0.0599645264, -0.0288561694, -0.00895245094, 0.00116040511, 0.0233101547, -0.00597885763, 0.0192280617, 0.030854987, -0.00667562848, 0.0148925986, 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21 Mar, 2025 | 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]
21 Mar, 2025
Artificial intelligence (AI) is the branch of computer science that aims to create intelligent agents, which are systems that can reason, learn and act autonomously. This involves developing algorithms and techniques that enable machines to perform tasks that typically require human intelligence such as understanding and responding to natural language, recognizing objects in images, making autonomous decisions and solving complex problems.
This article gives you an insight into Thirty Best Artificial Intelligence Projects that will help you learn how things work. While working on these ideas, you can find it easy to implement them in different fields of work.
Best Artificial Intelligence Project Ideas [2025]
Here are the list of top 30+ projects that you need to build in 2025:
1. Chatbots
As a beginner, you can start by creating chatbots. You’re recommended to start by creating a simple version. Several chatbots are available on almost every company website. You can check them out and identify the basic structure and can build your very own chatbots with a similar kind of structure.
Create Your Own Rule-Based Chatbot Using NLP
Once you have completed try creating one. Also try working on different niche chatbots. Artificial Intelligence gives you the freedom to open up your wings and helps you put your ideas into action.
2. Fake News Detection System
In the era of social media and digital communication the spread of fake news has become a significant concern. Using artificial intelligence you can create a Fake News Detection System that identifies and flags unreliable or fabricated news articles. This project involves working with Natural Language Processing (NLP) techniques to preprocess textual data, extract meaningful features and classify news as real or fake. By training machine learning models like Logistic Regression, Random Forest or advanced models like LSTM and BERT. You can achieve high accuracy in detecting fake news.
Fake News Detection Model using TensorFlow in Python
This project not only strengthens your NLP skills but also makes a real-world impact by combating misinformation. It’s a project that appeals to industries focused on media, cybersecurity and public safety offering immense career potential.
3. Stock Market Predictor
If you are good at numbers then this one is pretty much for you. Have you come across a stock market predictor before? If not do check them out. They are known for their accuracy based on mathematical assumptions and present circumstances. You can even get to know whether your predictor works or not within no time by keeping stock prediction cycles small. There is a massive value and demand for such systems. This project will help you to make a career in finance if mathematics is your cup of tea.
Stock Market Prediction using Machine Learning in Python
4. Sentiment Predictor
Consumer behavior is something that every online business is targeting. To know how a consumer reacts to a post will better the chances of them buying a product. Artificial Intelligence can be used to identify the sentiments of consumers. You can come up with a sentiment predictor that can help analyze in what state of mind the consumer is. This project will help you create an impression among Tier-I companies. Almost every online business has started implementing this. Now is the time to showcase your skill by implementing this project and grabbing hold of the opportunity.
Sentiment Analysis with an Recurrent Neural Networks (RNN)
5. Flower Classification Using AI
A great project for novices who want to explore computer vision and artificial intelligence is flower classification. You can develop a system that uses AI to categorize flowers according to their distinct characteristics like size, color and shape. Working with image datasets, preparing the data and applying methods like convolutional neural networks (CNNs) are all part of this research in order to get reliable findings. It is an excellent place to start for people who want to work on more complex image recognition systems including retinal scanning or facial recognition.
Flower Recognition using CNN
6. Human Activity Recognition System
You would have already come across stuff like smart-watches, bands, etc. Did you know that they use artificial intelligence to attain accuracy in determining your heartbeat and the number of calories you have lost based on the walking you have done? An activity recognition system would be a good project. Analyze how the product works and build your very own smart activity recognition system with a similar kind of structure. You’ll get to learn what algorithms are used in such applications and let us tell you that you’ll enjoy the process. Initially, start with a simple algorithm; once done, do go for a complex one. There is considerable scope for such devices, so do give it a try.
Human Activity Recognition with OpenCV
7. Wine Quality Analyzer
Using a particular set of data you can determine the quality of the wine. You might be aware of the fact that the older the wine, the better it becomes. Several considerations are to be taken into account before validating the quality of the wine. The pH content, percentage of alcohol and amount of acidity are some of the few criteria to be taken into consideration.
Using artificial intelligence you can test these factors and conclude which one is the best wine. The same thing is implemented for testing the fertility of the soil by architectures using AI. You can initially start with wine to get an unobstructed exposure to how the algorithm works. You’ll find that there are more than 4000 odd sets of data that you have to consider. This project will surely hone your AI skills.
Wine Quality Prediciton using Machine Learning
8. Object Detector
Have you heard of the term deep neural network? Neural networks are used by top-notch companies to carry out a different set of operations like face recognition, translation, etc. The object detector is somewhat similar to the flower classification system yet a little complex. It helps you detect a particular object with the help of artificial intelligence. If you are looking to make more of an impact with your project then this smart object detection is the one for you.
Object detection is the same method that artificially intelligent robots implement. Virtual Reality and 3D augmentation also work on the same principle. Make the best use of this opportunity to learn and to upgrade such a skill.
Detect an object with OpenCV-Python
9. Recommender Engine
Have you wonder while watching a video or a show on YouTube or Netflix how similar videos pop up based on your preferences? How about creating an engine that can do the same task? Based on the behavioral and implicit activity, algorithm can decide on your preferences and show similar content. Instead of binge-watching you could build your very own recommender engine. To start with you can use your browsing history. Both behavioral data and implicit data is required. It definitely will turn heads around.
When it comes to job opportunities recommender engine developers are in demand. With several training institutes going digital everyone is looking for an AI developer to come up with a recommendation system on their websites.
Recommendation System in Python
10. Sales Predictor
Supermarkets are a place where there is a surplus amount of products. How they manage to keep track of the sales of every product is beyond our imagination. That is where a sales predictor comes in handy. It helps you monitor stocks that come in daily and products that are sold out. Sales Predictor will turn out to be one of the project. You have to come up with an algorithm on how many products are being sold daily and predict the sales of that product on a weekly or monthly basis.
The sales predictor is definitely a project that would create a better first impression. If you find it simple try a sophisticated algorithm and check whether it works. You’ll get to learn what algorithms are used in such applications and let me tell you’ll enjoy the process. Almost every online grocery store has started implementing this. Do give it a try.
Sales Forecast Prediction – Python
11. Image Caption Generator
The Image Caption Generator is an interesting AI project where you can generate captions for images using deep learning. The model learns to describe images by analyzing their content and associating words with various visual elements. You can create an image caption generator using Convolutional Neural Networks (CNNs) combined with Recurrent Neural Networks (RNNs) or LSTMs. This project will help improve your skills in computer vision and NLP.
Image Caption Generator using Deep Learning
12. Predicting Fuel Efficiency
Predicting the fuel efficiency of vehicles is an essential application of AI in the automotive industry. By using machine learning algorithms you can predict the fuel efficiency of vehicles based on various factors such as engine type, weight, fuel type and other vehicle specifications. The project involves data preprocessing, feature selection and training a model to predict fuel efficiency accurately. It provides real-world value in the context of improving vehicle design and environmental sustainability.
Predict Fuel Efficiency Using Tensorflow in Python
13. Detecting Spam Emails
Spam email detection is a critical problem in email systems. By applying NLP techniques you can build a model that detects spam emails by analyzing the content, sender and other metadata of the email. Machine learning models such as Naive Bayes, Support Vector Machines (SVM) or advanced neural networks like LSTM can be trained to classify emails as spam or legitimate. This project will allow you to improve your understanding of text classification, NLP and machine learning algorithms.
Detecting Spam Emails Using Tensorflow in Python
14. Language Translation
Language translation is a powerful application of AI that enables real-time translation between different languages. You can build a machine translation model using transformer-based architectures which relies on attention mechanisms to translate text. This project involves training on large parallel datasets containing pairs of translated sentences and can be extended to different languages. Working on this project will enhance your understanding of sequence-to-sequence models, attention mechanisms and transformer networks.
Machine Translation with Transformer in Python
15. Text Summarization
Text summarization helps condense lengthy documents into concise summaries while retaining essential information. There are two types of summarization methods: extractive and abstractive. In the extractive method you select key sentences directly from the text while in the abstractive method the model generates a summary using new phrases. Using NLP techniques and deep learning models like BERT or GPT you can build an effective text summarizer. This project is useful in applications where large volumes of text need to be condensed such as news articles or research papers.
Text Summarization in NLP
16. Hate Speech Detection
Hate speech detection aims to automatically identify offensive and harmful content online. This is particularly important in social media and online platforms to prevent cyberbullying and promote healthy online discussions. By training a model on datasets containing labeled examples of hate speech and non-hate speech you can build an AI system that classifies text as harmful or safe. Techniques such as deep learning and NLP are ideal for this task. The project will enhance your skills in text classification and sentiment analysis.
Hate Speech Detection using Deep Learning
17. Text Autocorrector
Text autocorrection is a common feature in word processors and mobile keyboards. In this project you can build an AI-powered autocorrect system that suggests spelling corrections for words typed by users. You can implement this using NLP techniques like spell checking algorithms, n-grams and deep learning-based approaches such as sequence-to-sequence models. With this project you will learn how to handle text input, perform error correction and improve user experience through NLP applications.
Autocorrector Feature Using NLP In Python
18. Recognize Car License Plate from a video
License plate recognition is a real-world application of computer vision. In this project you can build a system that detects and reads car license plates in real-time from video streams. Using object detection techniques like YOLO (You Only Look Once) or Faster R-CNN combined with Optical Character Recognition (OCR) you can identify license plates. This project is widely applicable in surveillance, toll collection systems and law enforcement allowing you to apply your skills in both computer vision and real-time processing.
Detect and Recognize Car License Plate from a video in real time
19. Age Detection
Age detection through facial features is a popular application in security and personalized services. By analyzing facial images you can predict a person’s age group like child, adult and senior or we can give a range of their age. This AI project can be built using CNNs that extract facial features and map them to corresponding age labels. You can use OpenCV to process and analyze the images and deep learning to train the model. The project helps you gain expertise in facial recognition and age estimation.
Age Detection using Deep Learning in OpenCV
20. Text Generation
Text generation is an exciting field in AI where a model generates new text based on given input. You can create a text generator using Gated Recurrent Unit (GRU) networks which are a type of RNN. These networks can generate coherent sentences by learning from large text dataset. The project will involve training a language model, fine-tuning it on specific data and using it to generate text based on user input. Text generation has numerous applications including chatbots, creative writing and content creation.
Text Generation using Gated Recurrent Unit Networks
21. Lung Cancer Detection
Lung cancer detection through medical imaging is an essential application of AI that can aid in early diagnosis. By using Convolutional Neural Networks (CNNs) you can build a system that analyzes X-ray or CT scan images to detect signs of lung cancer. The project requires working with medical image datasets, preprocessing images and training the model to identify cancerous lesions or abnormalities in the lungs. This project will sharpen your skills in image processing, medical AI applications and CNNs.
Lung Cancer Detection using Convolutional Neural Network (CNN)
22. Recipe Recommendation System
A recipe recommendation system suggests recipes based on available ingredients or dietary preferences. You can build this AI system by analyzing data on various recipes and matching them to user preferences like dietary restrictions, taste and preparation time. Collaborative filtering and content-based recommendation methods can be used in this project. By working on this you’ll gain experience in recommender systems and data analysis.
Recipe Recommendation System Using Python
23. Personalized Voice Assistant
A personalized voice assistant is an AI-powered system that responds to voice commands, performs tasks and provides information. You can build your voice assistant using Python and libraries like SpeechRecognition, pyttsx3 for text-to-speech and NLP models for command processing. The system can perform tasks such as setting reminders, sending messages or playing music based on user commands. This project provides hands-on experience with speech recognition, NLP and virtual assistant design.
Voice Assistant using python
24. Inventory Demand Forecasting
Demand forecasting is crucial for businesses to manage their inventory efficiently and avoid stockouts or overstocking. In this project you can build a machine learning model using historical sales data to predict future demand for products. By analyzing patterns in past sales, seasonal trends and other factors like promotions or economic conditions the model will help businesses optimize stock levels and make data-driven decisions. This project will improve your skills in data analysis, forecasting and machine learning making it a valuable tool for inventory management and business operations.
Inventory Demand Forecasting using Machine Learning – Python
25. Speech Recognition
Speech recognition is a transformative technology that converts human speech into text enabling the development of voice-based applications like virtual assistants and transcription services. In this project you can build a speech recognition model for real-time voice-to-text conversion. The project involves several steps starting with collecting audio data, followed by preprocessing the speech signals such as noise reduction and feature extraction. Once the data is ready, you can apply machine learning algorithms to recognize speech patterns and transcribe them into text.
Speech Recognition in Python using Google Speech API
This project will provide you with valuable experience in speech processing, deep learning and NLP and can be applied in areas such as voice assistants, transcription services and accessibility tools.
26. Credit Card Fraud Detection
Credit card fraud detection is a critical challenge in the financial services industry helping to protect users and organizations from financial losses. In this project you can build an AI model that identifies fraudulent transactions by analyzing historical transaction data such as transaction amounts, location, time and user behavior. By using machine learning models like decision trees, logistic regression or neural networks the system can detect patterns of unusual or suspicious activity that may indicate fraud.
Credit Card Fraud Detection
This project will enhance your skills in classification models, anomaly detection and feature engineering providing a valuable foundation for working with financial data and building predictive systems for real-world applications.
27. IPL Score Prediction
In this project you can build a model to predict the scores of cricket matches specifically the Indian Premier League (IPL). The model will use historical match data, player performance, weather conditions and other relevant factors to predict the final score of a match. By applying deep learning techniques or time series analysis you can train the model to understand patterns in past games and predict future outcomes. This project allows you to dive deep into sports analytics that enhance your data analysis skills and gain practical experience in predictive modeling
IPL Score Prediction using Deep Learning
28. Loan Eligibility Prediction
Predicting loan eligibility is a crucial application of machine learning in the finance industry helping lenders make informed decisions and streamline the loan approval process. By developing a machine learning model you can predict whether an individual is eligible for a loan based on various financial factors, such as income, credit score, existing debts, loan amount and employment history. You will train a machine learning model such as logistic regression, decision trees or random forests to classify individuals as either eligible or ineligible for a loan.
Loan Eligibility Prediction using Machine Learning Models in Python
This project not only helps you understand the mechanics of machine learning algorithms but also teaches you the importance of handling financial data and making predictions in real-world applications.
29. Reviews Analysis
Reviews analysis is a powerful tool for businesses to gain insights from customer feedback and improve their products or services. By building an AI system you can automatically analyze large volumes of reviews and classify them into sentiment categories such as positive, negative or neutral. Using Natural Language Processing (NLP) and sentiment analysis techniques you can process and understand customer opinions at scale. Machine learning algorithms like Naive Bayes, SVM or LSTM are used to categorize the sentiment. Beyond sentiment classification you can extract key insights such as recurring customer complaints or features that are highly appreciated which can guide business decisions.
Flipkart Reviews Sentiment Analysis using Python
30. Sign Language Recognition System
Sign language recognition system helps bridge communication gaps for the hearing impaired by converting sign language gestures into text or speech. In this project you can use deep learning models along with pose estimation techniques to recognize hand gestures. The system involves training a model on labeled datasets of various sign language gestures and learning to identify the gestures accurately. You can implement a real-time recognition system that processes video feeds, detects gestures and outputs the corresponding text or speech.
Sign Language Recognition System using TensorFlow in Python
This project will give you valuable experience in computer vision, deep learning and real-time systems while also contributing to an impactful and inclusive application.
31. Text Detection and Extraction
Text detection and extraction from images or documents is a powerful application that can be achieved using Optical Character Recognition (OCR). In this project you will use OpenCV to preprocess images such as removing noise or adjusting contrast and then apply Tesseract OCR to detect and extract text from scanned documents or images. The system will automatically recognize characters and output the extracted text for further processing such as data analysis or storage.
Text Detection and Extraction using OpenCV and OCR
This project will enhance your skills in image processing, OCR technology and text recognition while providing a practical tool for automating text extraction from various image formats. It’s a useful project for applications in document management, digitization and text analysis.
32. Next Sentence Prediction
Next sentence prediction predicts the next sentence based on the context of a given preceding sentence. This task involves determining whether a particular sentence logically follows the one before it which requires the model to understand context, coherence and relationships between sentences. By using transformer-based models like BERT you can train the system to make these predictions effectively. Working on it will help you enhance your skills in using state-of-the-art NLP models and exploring how they can be applied to real-world tasks such as document classification, text summarization and conversational AI.
Next Sentence Prediction using BERT
Working on AI projects not only enhances your technical skills but also provides you with the opportunity to apply machine learning and deep learning techniques to real-world problems. Whether it’s building a chatbot, detecting fraudulent transactions or creating a speech recognition system these projects equip you with valuable experience in data analysis, model training and problem-solving. As you explore various domains like NLP, computer vision and predictive modeling you’ll be better prepared to tackle complex challenges and make meaningful contributions to the ever-evolving field of artificial intelligence. Keep experimenting with new ideas, stay curious and let these projects be the stepping stones to your success in the AI industry.
FAQs – Best Artificial Intelligence Project Ideas
What are some popular AI project ideas for beginners?
Beginners can start with projects like chatbots, recommendation systems, sentiment analysis, and image recognition to build foundational AI skills.
Which tools are commonly used in AI projects?
Popular tools include Python, TensorFlow, Keras, PyTorch, OpenCV, and Scikit-Learn, depending on the project type (e.g., NLP, computer vision, machine learning).
What skills are needed for AI projects?
Core skills include programming (Python), understanding of machine learning algorithms, data analysis, and familiarity with AI libraries.
How can I make my AI project impactful?
Focus on solving real-world problems and choose projects with practical applications, like predictive analytics, fraud detection, or automation.
Can AI projects be deployed in real environments?
Yes, AI projects can be deployed using cloud services like AWS, Azure, or Google Cloud for scalability and real-world usage. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated] | https://www.geeksforgeeks.org/10-best-artificial-intelligence-project-ideas-to-kick-start-your-career/ | Data Science & ML | 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated] | Data Science & ML, AI ML DS - Projects, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], AI ML DS - How To Get Started? | GeeksforGeeks | [-0.027088685, -0.0110250954, -0.0211968962, 0.0133818109, 0.0290119834, 0.0173232146, 0.0099754082, 0.00881736726, 0.0226732306, 0.0174044799, 0.00679248804, -0.0414186, 0.0358112417, -0.00394817581, -0.0239463989, 0.00567507977, 0.0194767658, -0.0129551636, 0.00350459875, -0.0554776303, -0.0112418048, -0.0238786768, -0.065825507, 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27 Sep, 2024 | Does Artificial Intelligence Require Coding?
27 Sep, 2024
As artificial intelligence (AI) continues to make headlines and permeate various industries, a common question arises: Does AI require coding? This inquiry can lead to a deeper exploration of what AI entails, who can work with it, and how accessible it is for individuals with varying levels of technical expertise. In this blog post, we'll unpack the relationship between AI and coding, considering both the traditional approaches and the emerging no-code/low-code alternatives.Table of ContentUnderstanding AI: A Brief OverviewTraditional AI Development: The Role of Coding1. Coding as the Foundation2. The Need for a Strong Math and Statistics BackgroundThe Rise of No-Code and Low-Code Solutions1. No-Code Platforms2. Low-Code PlatformsWho Can Work with AI?1. Data Scientists and Engineers2. Business Analysts and Domain Experts3. Enthusiasts and HobbyistsThe Future of AI DevelopmentConclusionUnderstanding AI: A Brief OverviewArtificial intelligence encompasses a range of technologies designed to simulate human intelligence. This includes machine learning (ML), natural language processing (NLP), computer vision, and robotics, among others. These technologies rely on algorithms, data, and models to learn from patterns, make decisions, and perform tasks.Traditional AI Development: The Role of Coding1. Coding as the FoundationIn traditional AI development, coding is indeed a fundamental skill. Most AI models are built using programming languages such as Python, R, or Java. Here's why coding is essential:Algorithm Implementation: To create and optimize algorithms that drive AI, developers need to write code. This involves implementing mathematical models and leveraging libraries such as TensorFlow, PyTorch, or Scikit-learn.Data Handling: Working with data is a critical aspect of AI. Coding skills enable developers to preprocess, clean, and manipulate datasets to ensure they are suitable for training models.Customization: Businesses often have unique needs that require tailored solutions. Coding allows developers to customize AI models and workflows to fit specific requirements.2. The Need for a Strong Math and Statistics BackgroundIn addition to coding, a solid understanding of mathematics and statistics is crucial for AI development. Concepts such as linear algebra, calculus, probability, and statistical analysis underpin many AI algorithms. Therefore, aspiring AI developers typically need both coding skills and a robust mathematical foundation.The Rise of No-Code and Low-Code SolutionsAs the demand for AI solutions grows, so does the need for accessibility. Enter no-code and low-code platforms, which are designed to democratize AI development:1. No-Code PlatformsNo-code platforms enable users to create AI models without writing any code. These platforms typically provide a user-friendly interface with drag-and-drop features, allowing individuals to build and deploy models intuitively. Examples include:Google AutoML: Offers tools for training custom ML models without requiring deep coding expertise.Teachable Machine: A simple way for anyone to create machine learning models using images, sounds, or poses.2. Low-Code PlatformsLow-code platforms offer a middle ground, allowing users to create applications with minimal coding. They often provide pre-built components and templates while still allowing for customization through coding when needed. Examples include:Microsoft Power Apps: Enables users to build applications that incorporate AI capabilities, often with minimal coding.DataRobot: A platform that allows data scientists and business analysts to create and deploy machine learning models efficiently.Who Can Work with AI?1. Data Scientists and EngineersTraditionally, data scientists and engineers are the primary users of AI technologies. Their expertise in coding, mathematics, and statistics enables them to create complex models and analyze data effectively.2. Business Analysts and Domain ExpertsWith the advent of no-code and low-code solutions, professionals without a technical background can now work with AI. Business analysts and domain experts can leverage these platforms to harness AI for their specific needs, making data-driven decisions without needing extensive coding skills.3. Enthusiasts and HobbyistsFor those interested in AI but lacking formal training, no-code tools provide an entry point. These individuals can experiment with AI technologies, build projects, and learn about the underlying concepts without the barrier of coding.The Future of AI DevelopmentThe evolution of AI development is indicative of a broader trend toward accessibility. While coding will always be important, especially for complex and customized solutions, the rise of no-code and low-code platforms signifies a shift. This democratization of AI opens doors for a wider range of people to engage with the technology, fostering innovation and collaboration across various sectors.ConclusionIn summary, while traditional AI development relies heavily on coding and technical expertise, the landscape is changing. No-code and low-code platforms are making AI accessible to a broader audience, allowing individuals from diverse backgrounds to harness the power of AI. Whether you're a seasoned developer or a curious beginner, there are now numerous pathways to explore and engage with artificial intelligence. Embrace the tools that best suit your skills and interests, and start your AI journey today! | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding? | https://www.geeksforgeeks.org/does-artificial-intelligence-require-coding/?ref=ml_lbp | Data Science & ML | Does Artificial Intelligence Require Coding? | AI ML DS - Projects, Data Science & ML, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding? | GeeksforGeeks | [-0.0142713934, -0.0131636346, -0.00917857792, 0.0116386665, 0.0113437437, -0.000349996204, 0.0299238898, -0.00846644677, 0.00630847411, 0.0340672, 0.0214358643, -0.0290607, 0.0266006123, -0.00561072957, -0.0290607, 0.0176090579, 0.00263452507, -0.00253202138, -0.00510720257, -0.0498923324, 0.0149619449, 0.00413971115, -0.0276652109, 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17 May, 2020 | Artificial Intelligence – Boon or Bane
17 May, 2020
Artificial Intelligence is a branch of computer science that deals with the development of machines that can perform tasks that require human intelligence like speech recognition, language translation, and decision making. Artificial Intelligence is said to be the simulation of human intelligence in machines that are programmed to think and perform tasks like humans. There are various real-life applications of Artificial Intelligence they are as follows:
1. Gaming: In strategic games like Chess the machine is programmed such that it can generate its moves and also study the moves of its opponents and decide which movie to be made next.
2. Speech Recognition: Some systems can recognize the language spoken by humans and respond in the same way by grasping the accent, grammar, etc. These types of speech recognition systems are present in our smartphones and home devices. Some examples of speech recognition systems are Google Now, Google Assistant, and Amazon Alexa.
3. Handwriting Recognition: Handwriting Text Recognition system in the machine enables it to read handwriting and transform into editable text.
4. Robotics: Robotics is a branch of science and engineering which deals with construction, design, and programming of robots. Robots are the most sophisticated and complex inventions of humans to date. Robots are capable of carrying out a series of a complex tasks. They are efficient in their tasks as they can multitask as well and save time doing so. They have vast memory space and can adjust to their environment.
With the growth in AI, there is a debate that whether AI is a boon or a bane. Some factors support AI to be a boon as well as a bane.
Factors that support AI to be a Boon:
Ease in Availability: Machines do not require refreshment like humans and can work for a longer period. They are capable of performing tasks and work continuously and produce quality output.
Daily Usage: Currently the most widely used machine in our daily life is a smartphone, which results knowingly and unknowingly using the benefits of AI. A few examples that demonstrate the use of AI in our daily life are speech recognition system used in our search engine on our smartphones, GPS used for navigation and fingerprint recognition and face recognition system in our smartphone for security.
Performing Complex Tasks: For a human performing tedious task is time-consuming. AI algorithms are developed to perform complex tasks. Machines are capable of performing multiple tasks at a particular period and function faster than humans.
Virtual Assistants: Virtual assistants communicate with various users, thus resulting in less use of manpower. As machines do not have emotions they perform more logically and efficiently and thus arrive at the right decision.
AI as a Bane:
Incurs High Cost: With the use of AI the productivity enhances and efficient results are obtained but huge costs are incurred in the process as machines are very complex and complicated in their training. And machines require regular maintenance at a particular point of time thus resulting in bigger costs to incur.
Lack of Experience: Humans depend upon their experience and perform accordingly in the future whereas do not have experience. Machines act according to the algorithm that is set for its functioning. They do not react with the environment and this what creates the difference between machines and humans.
Unemployment: The growing concern in the global economy today is that will AI completely take over human jobs. To enhance the productivity enterprises are adopting AI-based technologies that are now replacing human jobs and making us more dependent on machines. This would lead to a major loss in the ability of thinking and result in creativity and ideas.
AI will grow further in the future and shape our lives. It has its advantages and disadvantages. It has the factors that support it be a boon or bane. But still, there is a debate whether it will be a boon or a bane. We’ll come to know in the future whether it proves to be boon or bane. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane | https://www.geeksforgeeks.org/artificial-intelligence-boon-or-bane/?ref=ml_lbp | Data Science & ML | Artificial Intelligence – Boon or Bane | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding? | GeeksforGeeks | [-0.0252266917, -0.0178738572, -0.00776865939, -0.0161973592, 0.0128047578, -0.00359391258, 0.00292067276, -0.0172006171, 0.0147056701, 0.0327115357, 0.00234478875, -0.0143492492, 0.0301241819, -0.000709954475, -0.0445130318, 0.0285664909, 0.0342428274, 0.0067588, -0.0247514639, -0.022045305, 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05 Apr, 2024 | Artificial Intelligence Examples
05 Apr, 2024
Artificial intelligence (AI) has emerged as a transformative force, transforming industries and reshaping the way we interact with technology in our daily lives. With the ability to analyze vast amounts of data, learn from patterns, and make autonomous decisions, AI is driving innovation in a variety of industries. At its core, AI refers to the development of computer systems that can perform tasks that typically require human intelligence. This encompasses a wide range of capabilities, including natural language processing, machine learning, computer vision, and robotics. By leveraging algorithms and data, AI enables machines to learn from experience, adapt to new inputs, and perform tasks with a level of efficiency and accuracy that was once thought to be exclusive to human cognition.
The rapid advancements in AI technology have paved the way for a myriad of applications across various domains. Virtual assistants like Siri, Alexa, and Google Assistant have become ubiquitous, revolutionizing the way we interact with our devices and access information. These AI-driven assistants can understand natural language commands, answer queries, and perform tasks such as setting reminders or controlling smart home devices, making everyday life more convenient and efficient.
In industries such as healthcare, AI is driving transformative changes in diagnostics, treatment planning, and patient care. AI algorithms can analyze complex medical imaging data to assist healthcare professionals in diagnosing diseases, detecting anomalies, and predicting patient outcomes with greater accuracy and speed. This not only enhances the quality of healthcare delivery but also improves patient outcomes and reduces healthcare costs.
Artificial Intelligence Examples in Real Life Moreover, AI-powered recommendation systems are revolutionizing the way we discover content, products, and services. Platforms like Netflix, Amazon, and Spotify leverage AI algorithms to analyze user preferences and behavior, offering personalized recommendations that cater to individual tastes and preferences. This not only enhances user satisfaction but also drives customer engagement and loyalty.
As AI continues to evolve and mature, its impact is extending into new frontiers, including autonomous vehicles, agricultural automation, financial trading, and gaming. With the proliferation of big data, advancements in computing power, and breakthroughs in algorithm development, the possibilities for AI-driven innovation are virtually limitless.
However, along with its immense potential, AI also raises important ethical, societal, and regulatory considerations. Issues such as data privacy, algorithmic bias, and the impact of automation on jobs require careful attention and thoughtful solutions to ensure that AI technologies are developed and deployed responsibly and ethically.
Strong Artificial Intelligence Examples Let’s explore 15 compelling examples of AI applications that are having the biggest impact:
1. Virtual Assistants: Virtual assistants like Siri, Alexa, and Google Assistant have become ubiquitous, leveraging AI algorithms to understand natural language commands, provide information, and perform tasks such as setting reminders or sending messages.
2. Recommendation Systems: AI-powered recommendation engines drive platforms like Netflix, Amazon, and Spotify, offering personalized content, product suggestions, and music playlists based on user preferences and behavior.
3. Autonomous Vehicles: AI technologies, including deep learning and computer vision, enable self-driving cars to perceive their surroundings, navigate roads, and make driving decisions, paving the way for safer and more efficient transportation systems.
4. Healthcare Diagnostics: AI algorithms analyze medical images such as X-rays and MRIs, assisting healthcare professionals in diagnosing diseases, detecting abnormalities, and planning treatment strategies with greater accuracy and efficiency.
5. Natural Language Processing (NLP): NLP algorithms power language-related tasks like sentiment analysis, language translation, and chatbots, facilitating seamless communication between humans and machines across various applications.
6. Fraud Detection: AI-driven fraud detection systems analyze patterns and anomalies in financial transactions to identify potential fraudulent activities, safeguarding against unauthorized access and financial losses.
7. Image Recognition: AI algorithms, particularly convolutional neural networks (CNNs), enable precise image recognition and object detection in applications ranging from security surveillance to medical imaging and industrial quality control.
8. Chatbots: AI-powered chatbots engage in natural language conversations with users, providing customer support, answering queries, and automating tasks such as booking appointments or processing orders.
9. Smart Home Devices: AI-driven smart home devices such as thermostats, security cameras, and lighting systems use machine learning algorithms to adapt to user preferences, optimize energy usage, and enhance comfort and security.
10. Financial Trading: AI algorithms analyze vast amounts of financial data to identify market trends, predict stock price movements, and execute trades at optimal times, contributing to more informed investment decisions and improved trading strategies.
11. Language Translation: AI-powered language translation services like Google Translate leverage deep learning models to accurately translate text and speech between multiple languages, breaking down language barriers and facilitating cross-cultural communication.
12. Content Creation: AI algorithms can generate content, such as news articles, marketing copy, and even music compositions, based on data inputs and patterns, streamlining content creation processes and expanding creative possibilities.
13. Personalized Advertising: AI-driven advertising platforms use machine learning algorithms to analyze user behavior and preferences, delivering targeted ads that are more relevant and engaging to individual users, enhancing advertising effectiveness.
14. Agricultural Automation: AI technologies are being deployed in agriculture for tasks such as crop monitoring, pest detection, and yield prediction, enabling farmers to optimize crop production, reduce resource waste, and improve sustainability.
15. Gaming: AI-powered gaming systems employ techniques like reinforcement learning to create intelligent non-player characters (NPCs), generate dynamic game environments, and provide personalized gaming experiences, enhancing player engagement and immersion.
ConclusionIn conclusion, these 15 examples underscore the transformative potential of artificial intelligence across a diverse range of industries and applications. As AI continues to evolve and advance, we can expect further innovations that will shape the future of technology and redefine the way we live, work, and interact with the world around us | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples | https://www.geeksforgeeks.org/artificial-intelligence-examples/?ref=ml_lbp | Data Science & ML | Artificial Intelligence Examples | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding? | GeeksforGeeks | [-0.0251428504, 0.0192642696, -0.0143124918, -0.0100028561, 0.0253546908, 0.0160469376, 0.0317496322, 0.0027456549, 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05 Jun, 2023 | Agents in Artificial Intelligence
05 Jun, 2023
In artificial intelligence, an agent is a computer program or system that is designed to perceive its environment, make decisions and take actions to achieve a specific goal or set of goals. The agent operates autonomously, meaning it is not directly controlled by a human operator.
Agents can be classified into different types based on their characteristics, such as whether they are reactive or proactive, whether they have a fixed or dynamic environment, and whether they are single or multi-agent systems.
Reactive agents are those that respond to immediate stimuli from their environment and take actions based on those stimuli. Proactive agents, on the other hand, take initiative and plan ahead to achieve their goals. The environment in which an agent operates can also be fixed or dynamic. Fixed environments have a static set of rules that do not change, while dynamic environments are constantly changing and require agents to adapt to new situations.
Multi-agent systems involve multiple agents working together to achieve a common goal. These agents may have to coordinate their actions and communicate with each other to achieve their objectives. Agents are used in a variety of applications, including robotics, gaming, and intelligent systems. They can be implemented using different programming languages and techniques, including machine learning and natural language processing.
Artificial intelligence is defined as the study of rational agents. A rational agent could be anything that makes decisions, such as a person, firm, machine, or software. It carries out an action with the best outcome after considering past and current percepts(agent’s perceptual inputs at a given instance). An AI system is composed of an agent and its environment. The agents act in their environment. The environment may contain other agents.
An agent is anything that can be viewed as:
Perceiving its environment through sensors and
Acting upon that environment through actuators
Note: Every agent can perceive its own actions (but not always the effects).
Interaction of Agents with the Environment
Structure of an AI Agent
To understand the structure of Intelligent Agents, we should be familiar with Architecture and Agent programs. Architecture is the machinery that the agent executes on. It is a device with sensors and actuators, for example, a robotic car, a camera, and a PC. An agent program is an implementation of an agent function. An agent function is a map from the percept sequence(history of all that an agent has perceived to date) to an action.
Agent = Architecture + Agent Program
There are many examples of agents in artificial intelligence. Here are a few:
Intelligent personal assistants: These are agents that are designed to help users with various tasks, such as scheduling appointments, sending messages, and setting reminders. Examples of intelligent personal assistants include Siri, Alexa, and Google Assistant.
Autonomous robots: These are agents that are designed to operate autonomously in the physical world. They can perform tasks such as cleaning, sorting, and delivering goods. Examples of autonomous robots include the Roomba vacuum cleaner and the Amazon delivery robot.
Gaming agents: These are agents that are designed to play games, either against human opponents or other agents. Examples of gaming agents include chess-playing agents and poker-playing agents.
Fraud detection agents: These are agents that are designed to detect fraudulent behavior in financial transactions. They can analyze patterns of behavior to identify suspicious activity and alert authorities. Examples of fraud detection agents include those used by banks and credit card companies.
Traffic management agents: These are agents that are designed to manage traffic flow in cities. They can monitor traffic patterns, adjust traffic lights, and reroute vehicles to minimize congestion. Examples of traffic management agents include those used in smart cities around the world.
A software agent has Keystrokes, file contents, received network packages that act as sensors and displays on the screen, files, and sent network packets acting as actuators.
A Human-agent has eyes, ears, and other organs which act as sensors, and hands, legs, mouth, and other body parts act as actuators.
A Robotic agent has Cameras and infrared range finders which act as sensors and various motors act as actuators.
Characteristics of an Agent
Types of Agents
Agents can be grouped into five classes based on their degree of perceived intelligence and capability :
Simple Reflex Agents
Model-Based Reflex Agents
Goal-Based Agents
Utility-Based Agents
Learning Agent
Multi-agent systems
Hierarchical agents
Simple Reflex Agents
Simple reflex agents ignore the rest of the percept history and act only on the basis of the current percept. Percept history is the history of all that an agent has perceived to date. The agent function is based on the condition-action rule. A condition-action rule is a rule that maps a state i.e., a condition to an action. If the condition is true, then the action is taken, else not. This agent function only succeeds when the environment is fully observable. For simple reflex agents operating in partially observable environments, infinite loops are often unavoidable. It may be possible to escape from infinite loops if the agent can randomize its actions.
Problems with Simple reflex agents are :
Very limited intelligence.
No knowledge of non-perceptual parts of the state.
Usually too big to generate and store.
If there occurs any change in the environment, then the collection of rules needs to be updated.
Simple Reflex Agents
Model-Based Reflex Agents
It works by finding a rule whose condition matches the current situation. A model-based agent can handle partially observable environments by the use of a model about the world. The agent has to keep track of the internal state which is adjusted by each percept and that depends on the percept history. The current state is stored inside the agent which maintains some kind of structure describing the part of the world which cannot be seen.
Updating the state requires information about:
How the world evolves independently from the agent?
How do the agent’s actions affect the world?
Model-Based Reflex Agents
Goal-Based Agents
These kinds of agents take decisions based on how far they are currently from their goal(description of desirable situations). Their every action is intended to reduce their distance from the goal. This allows the agent a way to choose among multiple possibilities, selecting the one which reaches a goal state. The knowledge that supports its decisions is represented explicitly and can be modified, which makes these agents more flexible. They usually require search and planning. The goal-based agent’s behavior can easily be changed.
Goal-Based Agents
Utility-Based Agents
The agents which are developed having their end uses as building blocks are called utility-based agents. When there are multiple possible alternatives, then to decide which one is best, utility-based agents are used. They choose actions based on a preference (utility) for each state. Sometimes achieving the desired goal is not enough. We may look for a quicker, safer, cheaper trip to reach a destination. Agent happiness should be taken into consideration. Utility describes how “happy” the agent is. Because of the uncertainty in the world, a utility agent chooses the action that maximizes the expected utility. A utility function maps a state onto a real number which describes the associated degree of happiness.
Utility-Based Agents
Learning Agent
A learning agent in AI is the type of agent that can learn from its past experiences or it has learning capabilities. It starts to act with basic knowledge and then is able to act and adapt automatically through learning. A learning agent has mainly four conceptual components, which are:
Learning element: It is responsible for making improvements by learning from the environment.
Critic: The learning element takes feedback from critics which describes how well the agent is doing with respect to a fixed performance standard.
Performance element: It is responsible for selecting external action.
Problem Generator: This component is responsible for suggesting actions that will lead to new and informative experiences.
Learning Agent
Multi-Agent Systems
These agents interact with other agents to achieve a common goal. They may have to coordinate their actions and communicate with each other to achieve their objective.
A multi-agent system (MAS) is a system composed of multiple interacting agents that are designed to work together to achieve a common goal. These agents may be autonomous or semi-autonomous and are capable of perceiving their environment, making decisions, and taking action to achieve the common objective.
MAS can be used in a variety of applications, including transportation systems, robotics, and social networks. They can help improve efficiency, reduce costs, and increase flexibility in complex systems. MAS can be classified into different types based on their characteristics, such as whether the agents have the same or different goals, whether the agents are cooperative or competitive, and whether the agents are homogeneous or heterogeneous.
In a homogeneous MAS, all the agents have the same capabilities, goals, and behaviors.
In contrast, in a heterogeneous MAS, the agents have different capabilities, goals, and behaviors.
This can make coordination more challenging but can also lead to more flexible and robust systems.
Cooperative MAS involves agents working together to achieve a common goal, while competitive MAS involves agents working against each other to achieve their own goals. In some cases, MAS can also involve both cooperative and competitive behavior, where agents must balance their own interests with the interests of the group.
MAS can be implemented using different techniques, such as game theory, machine learning, and agent-based modeling. Game theory is used to analyze strategic interactions between agents and predict their behavior. Machine learning is used to train agents to improve their decision-making capabilities over time. Agent-based modeling is used to simulate complex systems and study the interactions between agents.
Overall, multi-agent systems are a powerful tool in artificial intelligence that can help solve complex problems and improve efficiency in a variety of applications.
Hierarchical Agents
These agents are organized into a hierarchy, with high-level agents overseeing the behavior of lower-level agents. The high-level agents provide goals and constraints, while the low-level agents carry out specific tasks. Hierarchical agents are useful in complex environments with many tasks and sub-tasks.
Hierarchical agents are agents that are organized into a hierarchy, with high-level agents overseeing the behavior of lower-level agents. The high-level agents provide goals and constraints, while the low-level agents carry out specific tasks. This structure allows for more efficient and organized decision-making in complex environments.
Hierarchical agents can be implemented in a variety of applications, including robotics, manufacturing, and transportation systems. They are particularly useful in environments where there are many tasks and sub-tasks that need to be coordinated and prioritized.
In a hierarchical agent system, the high-level agents are responsible for setting goals and constraints for the lower-level agents. These goals and constraints are typically based on the overall objective of the system. For example, in a manufacturing system, the high-level agents might set production targets for the lower-level agents based on customer demand.
The low-level agents are responsible for carrying out specific tasks to achieve the goals set by the high-level agents. These tasks may be relatively simple or more complex, depending on the specific application. For example, in a transportation system, low-level agents might be responsible for managing traffic flow at specific intersections.
Hierarchical agents can be organized into different levels, depending on the complexity of the system. In a simple system, there may be only two levels: high-level agents and low-level agents. In a more complex system, there may be multiple levels, with intermediate-level agents responsible for coordinating the activities of lower-level agents.
One advantage of hierarchical agents is that they allow for more efficient use of resources. By organizing agents into a hierarchy, it is possible to allocate tasks to the agents that are best suited to carry them out, while avoiding duplication of effort. This can lead to faster, more efficient decision-making and better overall performance of the system.
Overall, hierarchical agents are a powerful tool in artificial intelligence that can help solve complex problems and improve efficiency in a variety of applications.
Uses of Agents
Agents are used in a wide range of applications in artificial intelligence, including:
Robotics: Agents can be used to control robots and automate tasks in manufacturing, transportation, and other industries.
Smart homes and buildings: Agents can be used to control heating, lighting, and other systems in smart homes and buildings, optimizing energy use and improving comfort.
Transportation systems: Agents can be used to manage traffic flow, optimize routes for autonomous vehicles, and improve logistics and supply chain management.
Healthcare: Agents can be used to monitor patients, provide personalized treatment plans, and optimize healthcare resource allocation.
Finance: Agents can be used for automated trading, fraud detection, and risk management in the financial industry.
Games: Agents can be used to create intelligent opponents in games and simulations, providing a more challenging and realistic experience for players.
Natural language processing: Agents can be used for language translation, question answering, and chatbots that can communicate with users in natural language.
Cybersecurity: Agents can be used for intrusion detection, malware analysis, and network security.
Environmental monitoring: Agents can be used to monitor and manage natural resources, track climate change, and improve environmental sustainability.
Social media: Agents can be used to analyze social media data, identify trends and patterns, and provide personalized recommendations to users.
Overall, agents are a versatile and powerful tool in artificial intelligence that can help solve a wide range of problems in different fields. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence | https://www.geeksforgeeks.org/agents-artificial-intelligence/?ref=ml_lbp | Data Science & ML | Agents in Artificial Intelligence | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding? | GeeksforGeeks | [-0.019728167, -0.0236827191, -0.0219284445, -0.0255261958, 0.0377020575, 0.0271764044, 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27 Feb, 2025 | Transformers in Machine Learning
27 Feb, 2025
Transformer is a neural network architecture used for performing machine learning tasks particularly in natural language processing (NLP) and computer vision. In 2017 Vaswani et al. published a paper ” Attention is All You Need” in which the transformers architecture was introduced. The article explores the architecture, workings and applications of transformers.
Need For Transformers Model in Machine Learning Transformer Architecture is a model that uses self-attention to transform one whole sentence into a single sentence. This is useful where older models work step by step and it helps overcome the challenges seen in models like RNNs and LSTMs. Traditional models like RNNs (Recurrent Neural Networks) suffer from the vanishing gradient problem which leads to long-term memory loss. RNNs process text sequentially meaning they analyze words one at a time.
For example, in the sentence: “XYZ went to France in 2019 when there were no cases of COVID and there he met the president of that country” the word “that country” refers to “France”.
However RNN would struggle to link “that country” to “France” since it processes each word in sequence leading to losing context over long sentences. This limitation prevents RNNs from understanding the full meaning of the sentence.
While adding more memory cells in LSTMs (Long Short-Term Memory networks) helped address the vanishing gradient issue they still process words one by one. This sequential processing means LSTMs can’t analyze an entire sentence at once.
For instance the word “point” has different meanings in these two sentences:
“The needle has a sharp point.” (Point = Tip)“It is not polite to point at people.” (Point = Gesture)Traditional models struggle with this context dependence, whereas, Transformer model through its self-attention mechanism, processes the entire sentence in parallel addressing these issues and making it significantly more effective at understanding context.
Architecture and Working of Transformers 1. Positional Encoding Unlike RNNs transformers lack an inherent understanding of word order since they process data in parallel. To solve this Positional Encodings are added to token embeddings providing information about the position of each token within a sequence.
2. Position-wise Feed-Forward NetworksThe Feed-Forward Networks consist of two linear transformations with a ReLU activation. It is applied independently to each position in the sequence.
Mathematically:
[Tex]\text{FFN}(x) = \max(0, xW_1 + b_1)W_2 + b_2[/Tex]
This transformation helps refine the encoded representation at each position.
3. Attention Mechanism The attention mechanism allows transformers to determine which words in a sentence are most relevant to each other. This is done using a scaled dot-product attention approach:
1. Each word in a sequence is mapped to three vectors:
Query (Q)Key (K)Value (V)2. Attention scores are computed as: [Tex]\text{Attention}(Q, K, V) = \text{softmax} \left( \frac{QK^T}{\sqrt{d_k}} \right) V[/Tex]
3. These scores determine how much attention each word should pay to others.
Multi-Head AttentionInstead of using a single attention mechanism transformers apply multi-head attention where multiple attention layers run in parallel. This enables the model to capture different types of relationships within the input.
4. Encoder-Decoder Architecture The encoder-decoder structure is key to transformer models. The encoder processes the input sequence into a vector, while the decoder converts this vector back into a sequence. Each encoder and decoder layer includes self-attention and feed-forward layers. In the decoder, an encoder-decoder attention layer is added to focus on relevant parts of the input.
For example, a French sentence “Je suis étudiant” is translated into “I am a student” in English.
The encoder consists of multiple layers (typically 6 layers). Each layer has two main components:
Self-Attention Mechanism – Helps the model understand word relationships.Feed-Forward Neural Network – Further transforms the representation.The decoder also consists of 6 layers, but with an additional encoder-decoder attention mechanism. This allows the decoder to focus on relevant parts of the input sentence while generating output.
For instance in the sentence “The cat didn’t chase the mouse, because it was not hungry”, the word ‘it’ refers to ‘cat’. The self-attention mechanism helps the model correctly associate ‘it’ with ‘cat’ ensuring an accurate understanding of sentence structure.
Applications of TransformersSome of the applications of transformers are:
NLP Tasks: Transformers are used for machine translation, text summarization, named entity recognition and sentiment analysis.Speech Recognition: They process audio signals to convert speech into transcribed text.Computer Vision: Transformers are applied to image classification, object detection, and image generation.Recommendation Systems: They provide personalized recommendations based on user preferences.Text and Music Generation: Transformers are used for generating text (e.g., articles) and composing music.Transformers have redefined deep learning across NLP, computer vision, and beyond. With advancements like BERT, GPT and Vision Transformers (ViTs) they continue to push the boundaries of AI and language understanding and multimodal learning. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning | https://www.geeksforgeeks.org/getting-started-with-transformers/?ref=lbp | Data Science & ML | Transformers in Machine Learning | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Transformers in Machine Learning, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding? | GeeksforGeeks | [-0.0189541597, 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28 Dec, 2024 | Difference Between Encoder and Decoder
28 Dec, 2024
Combinational Logic is the concept in which two or more input states define one or more output states. The Encoder and Decoder are combinational logic circuits. In which we implement combinational logic with the help of boolean algebra. To encode something is to convert in piece of information into a form of code that is not so clearly understood and the device which performs this operation is termed as Encoder.
A decoder, on the other hand, performs the reverse operation, converting encoded data back into its original form. Encoders are used in data compression and signal processing, while decoders are essential in communication systems for interpreting received signals.
What is Encoder?
An Encoder is a device that converts the active data signal into a coded message format or it is a device that converts analogue signal to digital signals. It is a combinational circuit, that converts binary information in the form of 2N input lines into N output lines which represent N bit code for the input. When an input signal is applied to an encoder the logic circuitry involved within it converts that particular input into coded binary output.
To decode is to perform the reverse operation: converting a code back into an unambiguous form code and the device which performs this operation is termed a Decoder.
Advantages & Disadvantages of Encoder
Encoders provide highly accurate and repeatable position feedback for precise control in various applications. They can measure the linear and rotary motion with the high resolution enabling exceptional accuracy in the positioning tasks.
Encoders used in the wide range of industries from themanufacturing and robotics to healthcare and aerospace. Their ability to work in the diverse environments and integrate it with the various control systems makes them versatile for the motion control applications.
Encoders can be affected by the dust, debris, vibration and electromagnetic interference potentially leading to the measurement errors. This sensitivity may require the additional protective measures or frequent maintenance in the harsh industrial environments.
High-precision encoders can be expensive, especially for applications requiring extreme accuracy or specialized features. Their integration may increase system complexity, requiring careful calibration and specialized knowledge for proper installation and maintenance
What is Decoder?
A decoder is also a combinational circuit as an encoder but its operation is exactly reverse as that of the encoder. A decoder is a device that generates the original signal as output from the coded input signal and converts n lines of input into 2n lines of output. An AND gate can be used as the basic decoding element because it produces a high output only when all inputs are high.
Advantages & Disadvantages of Decoder
Decoders efficiently convert encoded information into a more usable format, enabling systems to interpret and process complex data streams. This capability is crucial in applications like digital communications, memory addressing, and signal processing.
By reducing the number of control lines needed, decoders help simplify circuit designs and reduce overall system complexity. This leads to more compact and efficient hardware implementations, particularly in digital systems and computer architecture.
Decoders introduce a small delay as they process and convert signals, which can impact system performance in high-speed applications. This delay may become significant in time-critical operations or when cascading multiple decoders.
As active components, decoders require power to operate, which can contribute to overall system power consumption. In battery-powered or energy-efficient designs, this additional power requirement may be a consideration, especially for large or complex decoding operations.
Importance of Encoders and Decoders
Encoders and decoders are very important tools in how computers handle information. An encoder takes information and changes it into a special format that’s easier to send or store. A decoder does the opposite – it takes that special format and turns it back into the original information. Think of them like a secret code. The encoder writes the message in code, and the decoder reads the code to understand the message. This is useful because sometimes the coded version is smaller or safer to send.
For example when you send a picture online, an encoder might make the file smaller so it sends faster. Then, a decoder on the other end turns it back into a picture you can see. Without encoders and decoders, many things we do with computers and phones would be much harder or slower.
Difference Between Encoder and Decoder
Encoder
Decoder
Encoder circuit basically converts the applied information signal into a coded digital bit stream.
Decoder performs reverse operation and recovers the original information signal from the coded bits.
In case of encoder, the applied signal is the active signal input.
Decoder accepts coded binary data as its input.
The number of inputs accepted by an encoder is 2n.
The number of input accepted by decoder is only n inputs.
The output lines for an encoder is n.
The output lines of an decoder is 2n.
The encoder generates coded data bits as its output.
The decoder generates an active output signal in response to the coded data bits.
The operation performed is simple.
The operation performed is complex.
The encoder circuit is installed at the transmitting end.
The decoder circuit is installed at the receiving side.
OR gate is the basic logic element used in it.
AND gate along with NOT gate is the basic logic element used in it.
It is used in E-mail, video encoders etc.
It is used in Microprocessors, memory chips etc.
Types of Encoders and Decoders
Linear encoders and decoders are used most often. They change information in a way that keeps the same pattern as the original. If you put in a little, you get a little out. If you put in a lot, you get a lot out.
Nonlinear encoders and decoders are not used as much, but they can do more things. They change information in a way that doesn’t follow the same pattern as the original. What comes out might be very different from what goes in, even if the change is small.
Applications of Encoder and Decoder
Applications of Encoders
Encoders change data into a form that can be sent over long distances. They help phones, computers, and other devices share information across the world by turning messages into special codes that travel easily.
In robots and machines, encoders turn physical movement into electrical signals. These signals tell the robot or machine its exact position, speed, and direction, helping it move accurately and do its job well.
Encoders help computers find specific information in their memory quickly. They work like a librarian, turning a request into a code that points directly to where the information is stored.
Encoders in sensors change real-world measurements into digital signals. This helps measure things like how far something has moved or how fast it’s turning, which is useful in many machines and devices.
In keyboards and other input devices, encoders change our actions (like pressing keys) into a language computers understand. This lets us type, click, and give commands to our devices easily.
Applications of Decoders
Decoders change computer code into visible numbers, letters, or pictures. They’re used in digital clocks, electronic signs, and screens to show information we can read and understand.
Decoders in devices like TV boxes or internet routers turn incoming signals back into pictures, sound, or data. This is how we can watch TV shows or browse websites sent from far away.
In computer systems, decoders help find and read the right information from memory. They’re like a guide that takes a code and uses it to find and bring back the exact data needed.
Decoders figure out what different signals mean, like the beeps when you press phone buttons. They turn these signals into instructions that devices can follow or understand.
In factories and smart homes, decoders help machines understand commands. They turn simple signals into actions, letting us control complex equipment with ease.
Examples of encoders and decoders
1. Encoder: A tool that changes computer numbers into a signal that can be sent. For instance, it might take the numbers that make up a picture on your computer and turn them into a signal that can be sent over the internet.
2. Decoder: A tool that changes a signal back into computer numbers. Following the previous example, it would take the signal sent over the internet and turn it back into numbers that your computer can show as a picture.
3. Binary encoder: A special encoder that uses simple math rules to change 1s and 0s into a signal. It takes the basic computer language (which is just 1s and 0s) and turns it into a signal that can be sent or stored more easily.
4. Binary decoder: A special decoder that uses simple math rules to change a signal back into 1s and 0s. It takes the signal and turns it back into the basic computer language of 1s and 0s that your computer can understand and use.
Conclusion
The Encoders and decoders are essential in the modern technology. The Encoders convert information into the machine friendly codes while the decoders translate these codes back into a usable data. They work behind the scenes in our phones, computers and many other devices. These tools make it possible for the humans and machines to communicate effectively and enabling everything from digital displays to robot control. The encoders and decoders help bridge the gap between the human understanding and machine processing playing the crucial role in world.
Frequently Asked Questions on Encoder and Decoder – FAQ’s
Where might we see encoders and decoders in my daily life?
You use them without knowing it in many devices! They’re in your TV remote, helping it send signals to your TV. They are also in the computer keyboard and turning your key presses into data the computer can use.
Why encoders and decoders are important in technology?
They help different parts of the system talk to each other. Encoders and decoders act like the translators making sure information can be shared and understood between the humans, machines and different types of devices.
Can you give example of how an encoder and decoder work together?
When you send the text message an encoder in your phone changes your words into the signal that can be sent. When it reaches your friends phone a decoder changes that signal back into the readable text on their screen. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder | https://www.geeksforgeeks.org/difference-between-encoder-and-decoder/ | Data Science & ML | Difference Between Encoder and Decoder | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Transformers in Machine Learning, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder | 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04 Jan, 2023 | Python OpenCV – Pose Estimation
04 Jan, 2023
What is Pose Estimation?
Pose estimation is a computer vision technique that is used to predict the configuration of the body(POSE) from an image. The reason for its importance is the abundance of applications that can benefit from technology.
Human pose estimation localizes body key points to accurately recognize the postures of individuals given an image. These estimations are performed in either 3D or 2D.
The main process of human pose estimation includes two basic steps: i) localizing human body joints/key points ii) grouping those joints into valid human pose configuration
In the first step, the main focus is on finding the location of each key points of human beings. E.g. Head, shoulder, arm, hand, knee, ankle. The second step is grouping those joints into valid human pose configuration which determines the pairwise terms between body parts.
Fig(b) represents detecting the key points and Fig(a) represents grouping of key points
What is OpenCV ?
OpenCV Python is a library of Python bindings designed to solve computer vision problems. It mainly focuses on image processing, video capture and analysis including features like face detection and object detection.
Use of OpenCV in python :
OpenCV Python is nothing but a wrapper class for the original C++ library to be used with Python. Using this, all the OpenCV array structures gets converted to/from NumPy arrays. This makes it easier to integrate it with other libraries which use NumPy. For example, libraries such as SciPy and Matplotlib.
To know more about OpenCV, https://opencv.org/about/
Datasets you can use:
In datasets selection, COCO and MPII are default picks in recent cases. Especially, COCO is a famous dataset by its property of having very wide human poses and an enormous number of images. LSP and FLIC datasets are also used next to COCO and MPII.
http://cocodataset.org/#keypoints-2018
http://human-pose.mpi-inf.mpg.de/
http://www.robots.ox.ac.uk/~vgg/data/pose_evaluation/
You can download the model weight files using the scripts provided at this location.
Code for Human Pose Estimation in OpenCV
In this section, we will see how to load the trained models in OpenCV and check the outputs. We will discuss code for only single person pose estimation to keep things simple. These outputs can be used to find the pose for every person in a frame if multiple people are present. We will cover the multiple-person case in a future post.
First, download the code and model files from below. There are separate files for Image and Video inputs. Please go through the README file if you encounter any difficulty in running the code.
Step 1: Download Model Weights
Use the getModels.sh file provided with the code to download all the model weights to the respective folders. Note that the configuration proto files are already present in the folders.
Python3
sudo chmod a+x getModels.sh
./getModels.sh
Check the folders to ensure that the model binaries (.caffemodel files) have been downloaded. If you are not able to run the above script, then you can download the model by clicking here for the MPII model and here for COCO model.
Step 2: Load Network
We are using models trained on Caffe Deep Learning Framework. Caffe models have 2 files –
prototxt file which specifies the architecture of the neural network — how the different layers are arranged etc.
caffemodel file which stores the weights of the trained model
We will use these two files to load the network into memory.
Python3
# Specify the paths for the 2 files
protoFile = "pose/mpi/pose_deploy_linevec_faster_4_stages.prototxt"
weightsFile = "pose/mpi/pose_iter_160000.caffemodel"
# Read the network into Memory
net = cv2.dnn.readNetFromCaffe(protoFile, weightsFile)
Step 3: Read Image and Prepare Input to the Network
The input frame that we read using OpenCV should be converted to an input blob (like Caffe) so that it can be fed to the network. This is done using the blobFromImage function which converts the image from OpenCV format to Caffe blob format.
The parameters are to be provided in the blobFromImage function. First, we normalize the pixel values to be in (0,1). Then we specify the dimensions of the image. Next, the Mean value to be subtracted, which is (0,0,0). There is no need to swap the R and B channels since both OpenCV and Caffe use RGB format.
Python3
# Read image
frame = cv2.imread("single.jpg")
# Specify the input image dimensions
inWidth = 368
inHeight = 368
# Prepare the frame to be fed to the network
inpBlob = cv2.dnn.blobFromImage(
frame, 1.0 / 255, (inWidth, inHeight), (0, 0, 0), swapRB=False, crop=False)
# Set the prepared object as the input blob of the network
net.setInput(inpBlob)
Step 4: Make Predictions and Parse Key points
Python3
output = net.forward()
The output is a 4D matrix :
The first dimension being the image ID ()in case you pass more than one image to the network).
The second dimension indicates the index of a key point. The model produces Confidence Maps and Part Affinity maps which are all concatenated. For COCO model it consists of 57 parts — 18 key point confidence Maps + 1 background + 19*2 Part Affinity Maps. Similarly, for MPII, it produces 44 points. We will be using only the first few points which correspond to Key points.
The third dimension is the height of the output map.
The fourth dimension is the width of the output map.
Once the key points are detected, we just plot them on the image.
Python3
H = out.shape[2]
W = out.shape[3]
# Empty list to store the detected keypoints
points = []
for i in range(len()):
# confidence map of corresponding body's part.
probMap = output[0, i, :, :]
# Find global maxima of the probMap.
minVal, prob, minLoc, point = cv2.minMaxLoc(probMap)
# Scale the point to fit on the original image
x = (frameWidth * point[0]) / W
y = (frameHeight * point[1]) / H
if prob > threshold:
cv2.circle(frame, (int(x), int(y)), 15, (0, 255, 255),
thickness=-1, lineType=cv.FILLED)
cv2.putText(frame, "{}".format(i), (int(x), int(
y)), cv2.FONT_HERSHEY_SIMPLEX, 1.4, (0, 0, 255), 3, lineType=cv2.LINE_AA)
# Add the point to the list if the probability is greater than the threshold
points.append((int(x), int(y)))
else:
points.append(None)
cv2.imshow("Output-Keypoints", frame)
cv2.waitKey(0)
cv2.destroyAllWindows()
Fig(a) shows the key points plotted using COCO model. Fig(b) shows the key points plotted using MPII model.
Step 5: Draw Skeleton
This figure shows the skeleton formed by all the key points joined
Python3
for pair in POSE_PAIRS:
partA = pair[0]
partB = pair[1]
if points[partA] and points[partB]:
cv2.line(frameCopy, points[partA], points[partB], (0, 255, 0), 3)
We found that COCO model is 1.5 times slower than the MPI model.
Applications of Pose Estimation :
Sign languages to help disabled people.
Human tracking
Gaming
Video surveillance
Advanced Driver Assistance Systems (ADAS)
Action recognition
REFERENCES:
https://github.com/CMU-Perceptual-Computing-Lab/openpose
https://learnopencv.com/deep-learning-based-human-pose-estimation-using-opencv-cpp-python/
https://ieeexplore.ieee.org/document/9144178 | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Python OpenCV – Pose Estimation | https://www.geeksforgeeks.org/python-opencv-pose-estimation/?ref=lbp | Data Science & ML | Python OpenCV – Pose Estimation | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Transformers in Machine Learning, Python OpenCV – Pose Estimation, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder | 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03 Jan, 2023 | Camera Calibration with Python – OpenCV
03 Jan, 2023
Prerequisites: OpenCV
A camera is an integral part of several domains like robotics, space exploration, etc camera is playing a major role. It helps to capture each and every moment and helpful for many analyses. In order to use the camera as a visual sensor, we should know the parameters of the camera. Camera Calibration is nothing but estimating the parameters of a camera, parameters about the camera are required to determine an accurate relationship between a 3D point in the real world and its corresponding 2D projection (pixel) in the image captured by that calibrated camera.
We need to consider both internal parameters like focal length, optical center, and radial distortion coefficients of the lens etc., and external parameters like rotation and translation of the camera with respect to some real world coordinate system.
Required libraries:
OpenCV library in python is a computer vision library, mostly used for image processing, video processing, and analysis, facial recognition and detection, etc.
Numpy is a general-purpose array-processing package. It provides a high-performance multidimensional array object and tools for working with these arrays.
Camera Calibration can be done in a step-by-step approach:
Step 1: First define real world coordinates of 3D points using known size of checkerboard pattern.
Step 2: Different viewpoints of check-board image is captured.
Step 3: findChessboardCorners() is a method in OpenCV and used to find pixel coordinates (u, v) for each 3D point in different images
Step 4: Then calibrateCamera() method is used to find camera parameters.
It will take our calculated (threedpoints, twodpoints, grayColor.shape[::-1], None, None) as parameters and returns list having elements as Camera matrix, Distortion coefficient, Rotation Vectors, and Translation Vectors.
Camera Matrix helps to transform 3D objects points to 2D image points and the Distortion Coefficient returns the position of the camera in the world, with the values of Rotation and Translation vectors
Below is the complete program of the above approach:
Python3
# Import required modules
import cv2
import numpy as np
import os
import glob
# Define the dimensions of checkerboard
CHECKERBOARD = (6, 9)
# stop the iteration when specified
# accuracy, epsilon, is reached or
# specified number of iterations are completed.
criteria = (cv2.TERM_CRITERIA_EPS +
cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
# Vector for 3D points
threedpoints = []
# Vector for 2D points
twodpoints = []
# 3D points real world coordinates
objectp3d = np.zeros((1, CHECKERBOARD[0]
* CHECKERBOARD[1],
3), np.float32)
objectp3d[0, :, :2] = np.mgrid[0:CHECKERBOARD[0],
0:CHECKERBOARD[1]].T.reshape(-1, 2)
prev_img_shape = None
# Extracting path of individual image stored
# in a given directory. Since no path is
# specified, it will take current directory
# jpg files alone
images = glob.glob('*.jpg')
for filename in images:
image = cv2.imread(filename)
grayColor = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
# Find the chess board corners
# If desired number of corners are
# found in the image then ret = true
ret, corners = cv2.findChessboardCorners(
grayColor, CHECKERBOARD,
cv2.CALIB_CB_ADAPTIVE_THRESH
+ cv2.CALIB_CB_FAST_CHECK +
cv2.CALIB_CB_NORMALIZE_IMAGE)
# If desired number of corners can be detected then,
# refine the pixel coordinates and display
# them on the images of checker board
if ret == True:
threedpoints.append(objectp3d)
# Refining pixel coordinates
# for given 2d points.
corners2 = cv2.cornerSubPix(
grayColor, corners, (11, 11), (-1, -1), criteria)
twodpoints.append(corners2)
# Draw and display the corners
image = cv2.drawChessboardCorners(image,
CHECKERBOARD,
corners2, ret)
cv2.imshow('img', image)
cv2.waitKey(0)
cv2.destroyAllWindows()
h, w = image.shape[:2]
# Perform camera calibration by
# passing the value of above found out 3D points (threedpoints)
# and its corresponding pixel coordinates of the
# detected corners (twodpoints)
ret, matrix, distortion, r_vecs, t_vecs = cv2.calibrateCamera(
threedpoints, twodpoints, grayColor.shape[::-1], None, None)
# Displaying required output
print(" Camera matrix:")
print(matrix)
print("\n Distortion coefficient:")
print(distortion)
print("\n Rotation Vectors:")
print(r_vecs)
print("\n Translation Vectors:")
print(t_vecs)
Input:
Output:
Camera matrix:
[[ 36.26378216 0. 125.68539168]
[ 0. 36.76607372 142.49821147]
[ 0. 0. 1. ]]
Distortion coefficient:
[[-1.25491812e-03 9.89269357e-05 -2.89077718e-03 4.52760939e-04
-3.29964245e-06]]
Rotation Vectors:
[array([[-0.05767492],
[ 0.03549497],
[ 1.50906953]]), array([[-0.09301982],
[-0.01034321],
[ 3.07733805]]), array([[-0.02175332],
[ 0.05611105],
[-0.07308161]])]
Translation Vectors:
[array([[ 4.63047351],
[-3.74281386],
[ 1.64238108]]), array([[2.31648737],
[3.98801521],
[1.64584622]]), array([[-3.17548808],
[-3.46022466],
[ 1.68200157]])] | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV | https://www.geeksforgeeks.org/camera-calibration-with-python-opencv/?ref=lbp | Data Science & ML | Camera Calibration with Python – OpenCV | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder | 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28 Jan, 2025 | NumPy Introduction
28 Jan, 2025
NumPy(Numerical Python) is a fundamental library for Python numerical computing. It provides efficient multi-dimensional array objects and various mathematical functions for handling large datasets making it a critical tool for professionals in fields that require heavy computation.
Table of Content
Key Features of NumPyInstalling NumPy in PythonCreating NumPy Arrays NumPy Array IndexingNumPy Basic OperationsNumPy ufuncsNumPy Sorting ArraysKey Features of NumPyNumPy has various features that make it popular over lists.
N-Dimensional Arrays: NumPy’s core feature is ndarray, a powerful N-dimensional array object that supports homogeneous data types.Arrays with High Performance: Arrays are stored in contiguous memory locations, enabling faster computations than Python lists (Please see Numpy Array vs Python List for details).Broadcasting: This allows element-wise computations between arrays of different shapes. It simplifies operations on arrays of various shapes by automatically aligning their dimensions without creating new data. Vectorization: Eliminates the need for explicit Python loops by applying operations directly on entire arrays. Linear algebra: NumPy contains routines for linear algebra operations, such as matrix multiplication, decompositions, and determinants.Installing NumPy in PythonTo begin using NumPy, you need to install it first. This can be done through pip command:
pip install numpy
Once installed, import the library with the alias np
import numpy as np
Creating NumPy Arrays Using ndarray : The array object is called ndarray. NumPy arrays are created using the array() function.Example:
Python
import numpy as np
# Creating a 1D array
x = np.array([1, 2, 3])
# Creating a 2D array
y = np.array([[1, 2], [3, 4]])
# Creating a 3D array
z = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
print(x)
print(y)
print(z)
Output[1 2 3]
[[1 2]
[3 4]]
[[[1 2]
[3 4]]
[[5 6]
[7 8]]]
Using Numpy Functions: NumPy provides convenient methods to create arrays initialized with specific values like zeros and ones:Example:
Python
import numpy as np
a1_zeros = np.zeros((3, 3))
a2_ones = np.ones((2, 2))
a3_range = np.arange(0, 10, 2)
print(a1_zeros)
print(a2_ones)
print(a3_range)
Output[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
[[1. 1.]
[1. 1.]]
[0 2 4 6 8]
You can also refer to this article – Different ways to create numpy arrays NumPy Array IndexingKnowing the basics of NumPy array indexing is important for analyzing and manipulating the array object.
Basic Indexing: Basic indexing in NumPy allows you to access elements of an array using indices.Example:
Python
import numpy as np
# Create a 1D array
arr1d = np.array([10, 20, 30, 40, 50])
# Single element access
print("Single element access:", arr1d[2])
# Negative indexing
print("Negative indexing:", arr1d[-1])
# Create a 2D array
arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
# Multidimensional array access
print("Multidimensional array access:", arr2d[1, 0])
OutputSingle element access: 30
Negative indexing: 50
Multidimensional array access: 4
Slicing: Just like lists in Python, NumPy arrays can be sliced. As arrays can be multidimensional, you need to specify a slice for each dimension of the array.Example:
Python
import numpy as np
arr = np.array([[1, 2, 3], [4, 5, 6]])
#elements from index 1 to 3
print("Range of Elements:",arr[1:4])
#all rows, second column
print("Multidimensional Slicing:", arr[:, 1])
OutputRange of Elements: [[4 5 6]]
Multidimensional Slicing: [2 5]
Advanced Indexing: Advanced Indexing in NumPy provides more powerful and flexible ways to access and manipulate array elements. Example:
Python
import numpy as np
arr = np.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
# Integer array indexing
indices = np.array([1, 3, 5])
print ("Integer array indexing:", arr[indices])
# boolean array indexing
cond = arr > 0
print ("\nElements greater than 0:\n", arr[cond])
OutputElements at indices (0, 3), (1, 2), (2, 1),(3, 0):
[4. 6. 0. 3.]
Elements greater than 0:
[2. 4. 4. 6. 2.6 7. 8. 3. 4. 2. ]
NumPy Basic OperationsElement-wise operations in NumPy allow you to perform mathematical operations on each element of an array individually, without the need for explicit loops.
Element-wise Operations: We can perform arithmetic operations like addition, subtraction, multiplication, and division directly on NumPy arrays.Example:
Python
import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
# Addition
add = x + y
print("Addition:",add)
# Subtraction
subtract = x - y
print("substration:",subtract)
# Multiplication
multiply = x * y
print("multiplication:",multiply)
# Division
divide = x / y
print("division:", divide)
OutputAddition: [5 7 9]
substration: [-3 -3 -3]
multiplication: [ 4 10 18]
division: [0.25 0.4 0.5 ]
Unary Operation: These operations are applied to each individual element in the array, without the need for multiple arrays (as in binary operations). Example:
Python
import numpy as np
# Example array with both positive and negative values
arr = np.array([-3, -1, 0, 1, 3])
# Applying a unary operation: absolute value
result = np.absolute(arr)
print("Absolute value:", result)
OutputAbsolute value: [3 1 0 1 3]
Binary Operators: Numpy Binary Operations apply to the array elementwise and a new array is created. We can use all basic arithmetic operators like +, -, /, etc. In the case of +=, -=, = operators, the existing array is modified.Example:
Python
import numpy as np
# Two example arrays
arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])
# Applying a binary operation: addition
result = np.add(arr1, arr2)
print("Array 1:", arr1)
print("Array 2:", arr2)
print("Addition Result:", result)
OutputArray 1: [1 2 3]
Array 2: [4 5 6]
Addition Result: [5 7 9]
NumPy ufuncsNumPy provides familiar mathematical functions such as sin, cos, exp, etc. These functions also operate elementwise on an array, producing an array as output.
Example:
Python
import numpy as np
# create an array of sine values
a = np.array([0, np.pi/2, np.pi])
print ("Sine values of array elements:", np.sin(a))
# exponential values
a = np.array([0, 1, 2, 3])
print ("Exponent of array elements:", np.exp(a))
# square root of array values
print ("Square root of array elements:", np.sqrt(a))
Output:
Sine values of array elements: [ 0.00000000e+00 1.00000000e+00 1.22464680e-16]
Exponent of array elements: [ 1. 2.71828183 7.3890561 20.08553692]
Square root of array elements: [ 0. 1. 1.41421356 1.73205081]NumPy Sorting ArraysWe can use a simple np.sort() method for sorting Python NumPy arrays.
Example:
Python
import numpy as np
# set alias names for dtypes
dtypes = [('name', 'S10'), ('grad_year', int), ('cgpa', float)]
# Values to be put in array
values = [('Hrithik', 2009, 8.5), ('Ajay', 2008, 8.7),
('Pankaj', 2008, 7.9), ('Aakash', 2009, 9.0)]
# Creating array
arr = np.array(values, dtype = dtypes)
print ("\nArray sorted by names:\n",
np.sort(arr, order = 'name'))
print ("Array sorted by graduation year and then cgpa:\n",
np.sort(arr, order = ['grad_year', 'cgpa']))
OutputArray sorted by names:
[(b'Aakash', 2009, 9. ) (b'Ajay', 2008, 8.7) (b'Hrithik', 2009, 8.5)
(b'Pankaj', 2008, 7.9)]
Array sorted by graduation year and then cgpa:
[(b'Pankaj', 2008, 7.9) (b'Ajay',...Read More:
Python LibrariesNumPy TutorialPython NumpyNumPy Introduction – FAQsWhat is the Basic Function of NumPy?The basic function of NumPy is to provide an efficient array structure (called ndarray) for storing and manipulating dense data buffers in a contiguous block of memory. NumPy arrays support vectorized operations, broadcasting, and various mathematical functions that are essential for scientific computing.
What is the First Entry in NumPy?In NumPy, the first entry in an array can be accessed by indexing, similar to how lists are indexed in Python. For a one-dimensional array, you access the first entry with an index of 0:
import numpy as np
arr = np.array([10, 20, 30, 40])
first_entry = arr[0]
print(first_entry) # Output: 10For multi-dimensional arrays, you can access elements using a tuple of indices:
matrix = np.array([[1, 2], [3, 4]])
first_entry = matrix[0, 0]
print(first_entry) # Output: 1What are NumPy Commands?NumPy commands refer to the functions and methods available in the NumPy library that operate on arrays. Here are a few commonly used NumPy commands:
np.array(): Create an array.np.arange(): Return evenly spaced values within a given interval.np.zeros(), np.ones(), np.full(): Create new arrays filled with zeros, ones, or a specified value, respectively.np.dot(): Dot product of two arrays.np.reshape(): Gives a new shape to an array without changing its data.np.mean(), np.median(), np.std(): Compute the mean, median, and standard deviation of array elements.np.linalg.inv(): Compute the (multiplicative) inverse of a matrix.These commands and many others make NumPy a versatile tool for numerical computing in Python | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction | https://www.geeksforgeeks.org/numpy-in-python-set-1-introduction/ | Data Science & ML | NumPy Introduction | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy Introduction | GeeksforGeeks | [-0.0240740646, -0.0107943062, -0.00477278838, 0.0296573266, 0.00796665438, -0.0140121859, 0.0148046492, 0.0134838773, 0.0107522821, 0.0315304212, -0.0188390054, -0.00452364283, -0.00323889218, -0.0142283123, 0.00169899256, 0.0352285802, 0.00556825288, 0.0066458825, -0.0314583778, 0.0107883029, 0.0328031629, -0.00207121, -0.0416163132, -0.0129555687, -0.0320347138, 0.0102599943, 0.0188269988, -0.00168248289, 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02 Sep, 2020 | How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?
02 Sep, 2020
In this article, we will discuss how to compute the eigenvalues and right eigenvectors of a given square array using NumPy library.
Example:
Suppose we have a matrix as:
[[1,2],
[2,3]]
Eigenvalue we get from this matrix or square array is:
[-0.23606798 4.23606798]
Eigenvectors of this matrix are:
[[-0.85065081 -0.52573111],
[ 0.52573111 -0.85065081]]
To know how they are calculated mathematically see this Calculation of EigenValues and EigenVectors. In the below examples, we have used numpy.linalg.eig() to find eigenvalues and eigenvectors for the given square array.
Syntax: numpy.linalg.eig()
Parameter: An square array.
Return: It will return two values first is eigenvalues and second is eigenvectors.
Example 1:
Python3
# importing numpy library
import numpy as np
# create numpy 2d-array
m = np.array([[1, 2],
[2, 3]])
print("Printing the Original square array:\n",
m)
# finding eigenvalues and eigenvectors
w, v = np.linalg.eig(m)
# printing eigen values
print("Printing the Eigen values of the given square array:\n",
w)
# printing eigen vectors
print("Printing Right eigenvectors of the given square array:\n"
v)
Output:
Printing the Original square array:
[[1 2]
[2 3]]
Printing the Eigen values of the given square array:
[-0.23606798 4.23606798]
Printing Right eigenvectors of the given square array:
[[-0.85065081 -0.52573111]
[ 0.52573111 -0.85065081]]
Example 2:
Python3
# importing numpy library
import numpy as np
# create numpy 2d-array
m = np.array([[1, 2, 3],
[2, 3, 4],
[4, 5, 6]])
print("Printing the Original square array:\n",
m)
# finding eigenvalues and eigenvectors
w, v = np.linalg.eig(m)
# printing eigen values
print("Printing the Eigen values of the given square array:\n",
w)
# printing eigen vectors
print("Printing Right eigenvectors of the given square array:\n",
v)
Output:
Printing the Original square array:
[[1 2 3]
[2 3 4]
[4 5 6]]
Printing the Eigen values of the given square array:
[ 1.08309519e+01 -8.30951895e-01 1.01486082e-16]
Printing Right eigenvectors of the given square array:
[[ 0.34416959 0.72770285 0.40824829]
[ 0.49532111 0.27580256 -0.81649658]
[ 0.79762415 -0.62799801 0.40824829]] | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY? | https://www.geeksforgeeks.org/how-to-compute-the-eigenvalues-and-right-eigenvectors-of-a-given-square-array-using-numpy/?ref=lbp | Data Science & ML | How to compute the eigenvalues and right eigenvectors of a given square array using NumPY? | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy Introduction | GeeksforGeeks | [-0.0261749066, -0.0136226658, -0.0119665377, 0.0107143428, -0.00377930515, 0.00105843262, 0.049279917, 0.0147233848, 0.000732761051, 0.0136327641, -0.0329004042, -0.0423726514, 0.00390048535, -0.0276492648, 0.0334861092, 0.0105628679, 0.00115436688, 0.0336476825, -0.0217114389, 0.0362328589, 0.00838162564, -0.034455549, -0.030840341, -0.0370609201, -0.0411204547, -0.0119968327, 0.00490022125, 0.0066396608, -0.0374648534, -0.0181770194, 0.0248015318, -0.00330215832, -0.0154605638, -0.00096754753, 0.0119362418, -0.0338496491, 0.00120485865, -0.0143396482, -0.00254983176, -0.00290579838, 0.00103760476, 0.00434986176, 0.00216988148, 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02 Jan, 2025 | Ordinary Least Squares (OLS) using statsmodels
02 Jan, 2025
In this article, we will use Python’s statsmodels module to implement Ordinary Least Squares ( OLS ) method of linear regression.
Introduction :
A linear regression model establishes the relation between a dependent variable( y ) and at least one independent variable( x ) as : [Tex] \hat{y}=b_1x+b_0 [/Tex]
In OLS method, we have to choose the values of [Tex] b_1 [/Tex] and [Tex] b_0 [/Tex] such that, the total sum of squares of the difference between the calculated and observed values of y, is minimised.
Formula for OLS:
Where, [Tex] \hat{y_i} [/Tex] = predicted value for the ith observation [Tex] y_i [/Tex] = actual value for the ith observation [Tex] \epsilon_i [/Tex] = error/residual for the ith observation n = total number of observations
To get the values of [Tex] b_0 [/Tex] and [Tex] b_1 [/Tex] which minimise S, we can take a partial derivative for each coefficient and equate it to zero.
Modules used :
statsmodels : provides classes and functions for the estimation of many different statistical models. pip install statsmodels pandas : library used for data manipulation and analysis. NumPy : core library for array computing. Matplotlib : a comprehensive library used for creating static and interactive graphs and visualisations. Approach :
First we define the variables x and y . In the example below, the variables are read from a csv file using pandas . The file used in the example can be downloaded here. Next, We need to add the constant [Tex] b_0 [/Tex] to the equation using the add_constant() method. The OLS() function of the statsmodels.api module is used to perform OLS regression. It returns an OLS object. Then fit() method is called on this object for fitting the regression line to the data. The summary() method is used to obtain a table which gives an extensive description about the regression results Syntax : statsmodels.api.OLS(y, x) Parameters :
y : the variable which is dependent on x x : the independent variable Code:
Python
import statsmodels.api as sm
import pandas as pd
# reading data from the csv
data = pd.read_csv('train.csv')
# defining the variables
x = data['x'].tolist()
y = data['y'].tolist()
# adding the constant term
x = sm.add_constant(x)
# performing the regression
# and fitting the model
result = sm.OLS(y, x).fit()
# printing the summary table
print(result.summary())
Output :
OLS Regression Results ==============================================================================Dep. Variable: y R-squared: 0.989Model: OLS Adj. R-squared: 0.989Method: Least Squares F-statistic: 2.709e+04Date: Fri, 26 Jun 2020 Prob (F-statistic): 1.33e-294Time: 15:55:38 Log-Likelihood: -757.98No. Observations: 300 AIC: 1520.Df Residuals: 298 BIC: 1527.Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975]------------------------------------------------------------------------------const -0.4618 0.360 -1.284 0.200 -1.169 0.246x1 1.0143 0.006 164.598 0.000 1.002 1.026==============================================================================Omnibus: 1.034 Durbin-Watson: 2.006Prob(Omnibus): 0.596 Jarque-Bera (JB): 0.825Skew: 0.117 Prob(JB): 0.662Kurtosis: 3.104 Cond. No. 120.==============================================================================Warnings:[1] Standard Errors assume that the covariance matrix of the errors is correctly specified. Description of some of the terms in the table :
R-squared : the coefficient of determination. It is the proportion of the variance in the dependent variable that is predictable/explained Adj. R-squared : Adjusted R-squared is the modified form of R-squared adjusted for the number of independent variables in the model. Value of adj. R-squared increases, when we include extra variables which actually improve the model. F-statistic : the ratio of mean squared error of the model to the mean squared error of residuals. It determines the overall significance of the model. coef : the coefficients of the independent variables and the constant term in the equation. t : the value of t-statistic. It is the ratio of the difference between the estimated and hypothesized value of a parameter, to the standard error Predicting values: From the results table, we note the coefficient of x and the constant term. These values are substituted in the original equation and the regression line is plotted using matplotlib . Code:
Python
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
# reading data from the csv
data = pd.read_csv('train.csv')
# plotting the original values
x = data['x'].tolist()
y = data['y'].tolist()
plt.scatter(x, y)
# finding the maximum and minimum
# values of x, to get the
# range of data
max_x = data['x'].max()
min_x = data['x'].min()
# range of values for plotting
# the regression line
x = np.arange(min_x, max_x, 1)
# the substituted equation
y = 1.0143 * x - 0.4618
# plotting the regression line
plt.plot(y, 'r')
plt.show()
Output:
Link to Dataset:Train.csv : click here. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels | https://www.geeksforgeeks.org/ordinary-least-squares-ols-using-statsmodels/?ref=lbp | Data Science & ML | Ordinary Least Squares (OLS) using statsmodels | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Ordinary Least Squares (OLS) using statsmodels, Agents in Artificial Intelligence, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy Introduction | GeeksforGeeks | [-0.0274255797, -0.00377619406, -0.00555644091, 0.000429243693, 0.000418818177, -0.0415755212, 0.0408622734, 0.00779397227, -0.0189701263, 0.0166578181, -0.0303245913, -0.00315497699, 0.0262291618, -0.00612013787, 0.00315497699, 0.0152083123, 0.0142304702, 0.0212824345, 0.0117283463, 0.00292633474, 0.00673560286, -0.0410003215, 0.00393725047, 0.0178542361, -0.0166923311, -0.00817360543, -0.00939303078, 0.0164967626, -0.00649977, -0.00791476481, 0.0421967395, 0.00667808251, -0.0101638, -0.0283689089, -0.00345408148, -0.0158640407, 0.0212249141, -0.0118721472, -0.0468213558, 0.0537467748, 0.00889260601, 0.019683376, 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20 May, 2019 | Stacking in Machine Learning
20 May, 2019
Stacking is a way to ensemble multiple classifications or regression model. There are many ways to ensemble models, the widely known models are Bagging or Boosting. Bagging allows multiple similar models with high variance are averaged to decrease variance. Boosting builds multiple incremental models to decrease the bias, while keeping variance small.
Stacking (sometimes called Stacked Generalization) is a different paradigm. The point of stacking is to explore a space of different models for the same problem. The idea is that you can attack a learning problem with different types of models which are capable to learn some part of the problem, but not the whole space of the problem. So, you can build multiple different learners and you use them to build an intermediate prediction, one prediction for each learned model. Then you add a new model which learns from the intermediate predictions the same target.
This final model is said to be stacked on the top of the others, hence the name. Thus, you might improve your overall performance, and often you end up with a model which is better than any individual intermediate model. Notice however, that it does not give you any guarantee, as is often the case with any machine learning technique.
How stacking works?
We split the training data into K-folds just like K-fold cross-validation.
A base model is fitted on the K-1 parts and predictions are made for Kth part.
We do for each part of the training data.
The base model is then fitted on the whole train data set to calculate its performance on the test set.
We repeat the last 3 steps for other base models.
Predictions from the train set are used as features for the second level model.
Second level model is used to make a prediction on the test set.
Blending –
Blending is a similar approach to stacking.
The train set is split into training and validation sets.
We train the base models on the training set.
We make predictions only on the validation set and the test set.
The validation predictions are used as features to build a new model.
This model is used to make final predictions on the test set using the prediction values as features. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning | https://www.geeksforgeeks.org/stacking-in-machine-learning/?ref=lbp | Data Science & ML | Stacking in Machine Learning | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Ordinary Least Squares (OLS) using statsmodels, Agents in Artificial Intelligence, Stacking in Machine Learning, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy Introduction | GeeksforGeeks | [-0.0661502406, 0.00606634794, -0.0305741131, -0.00697963731, 0.016790472, -0.0153994616, -0.00861302, 0.000746877398, -0.0334123336, 0.00612957589, 0.0124839609, -0.020387426, 0.0198394526, -2.09386926e-05, -0.0304336064, 0.00344239781, 0.0250241254, 0.0056869816, 0.0287475344, -0.0287756361, 0.0170012303, -0.0233380515, -0.0370092914, 0.0274127275, 0.0240405817, -0.00721498486, 0.0155540183, -0.0234364066, -0.0932398066, 0.0544882417, 0.00154732272, -0.00159123086, -0.000869381067, -0.00359168556, -0.0163970534, 0.0100883329, 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27 Jan, 2025 | ML | Naive Bayes Scratch Implementation using Python
27 Jan, 2025
Naive Bayes is a probabilistic machine learning algorithms based on the Bayes Theorem. It is a simple yet powerful algorithm because of its understanding, simplicity and ease of implementation. It is popular method for classification applications such as spam filtering and text classification. In this article we will learn about Naive Bayes Classifier From Scratch in Python.
Naive Bayes Scratch Implementation using PythonHere we are implementing a Naive Bayes Algorithm using Gaussian distributions. It performs all the necessary steps from data preparation and model training to testing and evaluation.
1. Importing LibrariesImporting necessary libraries:
math: for mathematical operationsrandom: for random number generationpandas: for data manipulationnumpy: for scientific computing
Python
import math
import random
import pandas as pd
import numpy as np
2. Encode ClassThe encode_class function converts class labels in the dataset into numeric values. It assigns a unique numeric identifier to each class.
Python
def encode_class(mydata):
classes = []
for i in range(len(mydata)):
if mydata[i][-1] not in classes:
classes.append(mydata[i][-1])
for i in range(len(classes)):
for j in range(len(mydata)):
if mydata[j][-1] == classes[i]:
mydata[j][-1] = i
return mydata
3. Data SplittingThe splitting function is used to split the dataset into training and testing sets based on the given ratio.
Python
def splitting(mydata, ratio):
train_num = int(len(mydata) * ratio)
train = []
test = list(mydata)
while len(train) < train_num:
index = random.randrange(len(test))
train.append(test.pop(index))
return train, test
4. Group Data by ClassThe groupUnderClass function takes the data and returns a dictionary where each key is a class label and the value is a list of data points belonging to that class.
Python
def groupUnderClass(mydata):
data_dict = {}
for i in range(len(mydata)):
if mydata[i][-1] not in data_dict:
data_dict[mydata[i][-1]] = []
data_dict[mydata[i][-1]].append(mydata[i])
return data_dict
5. Calculate Mean and Standard Deviation for ClassThe MeanAndStdDev function takes a list of numbers and calculates the mean and standard deviation.
The MeanAndStdDevForClass function takes the data and returns a dictionary where each key is a class label and the value is a list of lists, where each inner list contains the mean and standard deviation for each attribute of the class.
Python
def MeanAndStdDev(numbers):
avg = np.mean(numbers)
stddev = np.std(numbers)
return avg, stddev
def MeanAndStdDevForClass(mydata):
info = {}
data_dict = groupUnderClass(mydata)
for classValue, instances in data_dict.items():
info[classValue] = [MeanAndStdDev(attribute) for attribute in zip(*instances)]
return info
6. Calculate Gaussian and Class ProbabilitiesThe calculateGaussianProbability function takes a value, mean, and standard deviation and calculates the probability of the value occurring under a Gaussian distribution with that mean and standard deviation.The calculateClassProbabilities function takes the information dictionary and a test data point as arguments. It iterates through each class and calculates the probability of the test data point belonging to that class based on the mean and standard deviation of each attribute for that class.
Python
def calculateGaussianProbability(x, mean, stdev):
epsilon = 1e-10
expo = math.exp(-(math.pow(x - mean, 2) / (2 * math.pow(stdev + epsilon, 2))))
return (1 / (math.sqrt(2 * math.pi) * (stdev + epsilon))) * expo
def calculateClassProbabilities(info, test):
probabilities = {}
for classValue, classSummaries in info.items():
probabilities[classValue] = 1
for i in range(len(classSummaries)):
mean, std_dev = classSummaries[i]
x = test[i]
probabilities[classValue] *= calculateGaussianProbability(x, mean, std_dev)
return probabilities
7. Prediction for Test SetThe predict function takes the information dictionary and a test data point as arguments. It calculates the class probabilities and returns the class with the highest probability. The getPredictions function takes the information dictionary and the test set as arguments. It iterates through each test data point and predicts its class using the predict function.
Python
def predict(info, test):
probabilities = calculateClassProbabilities(info, test)
bestLabel = max(probabilities, key=probabilities.get)
return bestLabel
def getPredictions(info, test):
predictions = [predict(info, instance) for instance in test]
return predictions
8. Calculate AccuracyThe accuracy_rate function takes the test set and the predictions as arguments. It compares the predicted classes with the actual classes and calculates the percentage of correctly predicted data points.
Python
def accuracy_rate(test, predictions):
correct = sum(1 for i in range(len(test)) if test[i][-1] == predictions[i])
return (correct / float(len(test))) * 100.0
9. Load and Preprocess DataThe code then loads the data from a CSV file using pandas and converts it into a list of lists. It then encodes the class labels and converts all attributes to floating-point numbers. Dataset we are using is of diabetes patients and can be downloaded form here.
Python
# Load data using pandas
filename = '/content/diabetes_data.csv' # Add the correct file path
df = pd.read_csv(filename)
mydata = df.values.tolist()
# Encode classes and convert attributes to float
mydata = encode_class(mydata)
for i in range(len(mydata)):
for j in range(len(mydata[i]) - 1):
mydata[i][j] = float(mydata[i][j])
10. Split Data into Training and Testing SetsThe code splits the data into training and testing sets using a specified ratio. It then trains the model by calculating the mean and standard deviation for each attribute in each class.
Python
# Split the data into training and testing sets
ratio = 0.7
train_data, test_data = splitting(mydata, ratio)
print('Total number of examples:', len(mydata))
print('Training examples:', len(train_data))
print('Test examples:', len(test_data))
Output:
Total number of examples: 768Training examples: 537Test examples: 23111. Train and Test the ModelCalculate mean and standard deviation for each attribute within each class for the training set. Finally, it tests the model on the test set and calculates the accuracy.
Python
# Train the model
info = MeanAndStdDevForClass(train_data)
# Test the model
predictions = getPredictions(info, test_data)
accuracy = accuracy_rate(test_data, predictions)
print('Accuracy of the model:', accuracy)
Output:
Accuracy of the model: 100.0Naive Bayes proves to be an efficient and simple algorithm that works well for classification tasks. It is easy to understand since it is based on Bayes’ theorem and is simple to use and analyze. Naive Bayes Algorithm implementation from scratch in Python can be used to get insights and precise predictions for a variety of applications like spam filtering and text classification.
Frequently Asked Question(FAQs)How to implement Naive Bayes from scratch with Python?Implementing Naive Bayes from scratch in Python involves defining the necessary functions for calculating the probabilities required for Bayes’ theorem. This includes the prior probability of each class, the conditional probability of each feature given a class, and the likelihood of a given class. Once these probabilities are calculated, Bayes’ theorem can be used to classify new data points.
How does Naive Bayes Algorithm works?Naive Bayes is a probabilistic classifier based on Bayes’ theorem, which states that the probability of an event (hypothesis) given evidence can be calculated as the product of the prior probability of the hypothesis and the likelihood of the evidence given the hypothesis, divided by the marginal probability of the evidence. In the context of Naive Bayes, the hypothesis represents the class label, the evidence represents the features of the data point, and the prior and likelihood probabilities are estimated from the training data.
What is Naive Bayes?Naive Bayes is a classification algorithm based on Bayes’ theorem, which is a statistical method for calculating the probability of an event given a set of conditions. In Naive Bayes, the naive assumption is made that the features of the data are independent of each other, which simplifies the calculations.
Why is Naive Bayes a popular algorithm?Naive Bayes is a popular algorithm due to its simplicity, efficiency, and effectiveness. It is often used as a baseline classifier for comparison with other more complex algorithms.
When should I use Naive Bayes?Naive Bayes is a good choice for problems where the features of the data are relatively independent and where the training data is limited. It is also a good choice for problems where the computational cost is a concern. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python | https://www.geeksforgeeks.org/ml-naive-bayes-scratch-implementation-using-python/?ref=next_article | Data Science & ML | ML | Naive Bayes Scratch Implementation using Python | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, ML | Naive Bayes Scratch Implementation using Python, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Ordinary Least Squares (OLS) using statsmodels, Agents in Artificial Intelligence, Stacking in Machine Learning, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy Introduction | GeeksforGeeks | [-0.0178119261, -0.0190537702, -0.01535259, 0.0188833214, 0.0436349586, -0.00970342103, -0.00372248562, -0.0150116924, 0.0262491554, 0.0335297659, 0.0133193769, -0.0653063431, 0.0385458358, -0.0400555283, 0.00603572279, 0.00153556338, 0.0340167619, -0.0194311924, 0.0170205552, 0.000338044629, 0.000907793408, 0.0083885286, -0.0116514107, -0.0196016412, -0.0167161822, 0.0483588316, 0.00644662697, 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10 Jul, 2024 | Applying Multinomial Naive Bayes to NLP Problems
10 Jul, 2024
Multinomial Naive Bayes (MNB) is a popular machine learning algorithm for text classification problems in Natural Language Processing (NLP). It is particularly useful for problems that involve text data with discrete features such as word frequency counts. MNB works on the principle of Bayes theorem and assumes that the features are conditionally independent given the class variable.
Here are the steps for applying Multinomial Naive Bayes to NLP problems:
Preprocessing the text data: The text data needs to be preprocessed before applying the algorithm. This involves steps such as tokenization, stop-word removal, stemming, and lemmatization.
Feature extraction: The text data needs to be converted into a feature vector format that can be used as input to the MNB algorithm. The most common method of feature extraction is to use a bag-of-words model, where each document is represented by a vector of word frequency counts.
Splitting the data: The data needs to be split into training and testing sets. The training set is used to train the MNB model, while the testing set is used to evaluate its performance.
Training the MNB model: The MNB model is trained on the training set by estimating the probabilities of each feature given each class. This involves calculating the prior probabilities of each class and the likelihood of each feature given each class.
Evaluating the performance of the model: The performance of the model is evaluated using metrics such as accuracy, precision, recall, and F1-score on the testing set.
Using the model to make predictions: Once the model is trained, it can be used to make predictions on new text data. The text data is preprocessed and transformed into the feature vector format, which is then input to the trained model to obtain the predicted class label.
MNB is a simple and efficient algorithm that works well for many NLP problems such as sentiment analysis, spam detection, and topic classification. However, it has some limitations, such as the assumption of independence between features, which may not hold true in some cases. Therefore, it is important to carefully evaluate the performance of the model before using it in a real-world application.
Naive Bayes Classifier Algorithm is a family of probabilistic algorithms based on applying Bayes’ theorem with the “naive” assumption of conditional independence between every pair of a feature. Bayes theorem calculates probability P(c|x) where c is the class of the possible outcomes and x is the given instance which has to be classified, representing some certain features.P(c|x) = P(x|c) * P(c) / P(x)Naive Bayes are mostly used in natural language processing (NLP) problems. Naive Bayes predict the tag of a text. They calculate the probability of each tag for a given text and then output the tag with the highest one. How Naive Bayes Algorithm Works ?Let’s consider an example, classify the review whether it is positive or negative.Training Dataset:
TextReviews“I liked the movie”positive“It’s a good movie. Nice story”positive“Nice songs. But sadly boring ending. ”negative“Hero’s acting is bad but heroine looks good. Overall nice movie”positive“Sad, boring movie”negativeWe classify whether the text “overall liked the movie” has a positive review or a negative review. We have to calculate, P(positive | overall liked the movie) — the probability that the tag of a sentence is positive given that the sentence is “overall liked the movie”. P(negative | overall liked the movie) — the probability that the tag of a sentence is negative given that the sentence is “overall liked the movie”.Before that, first, we apply Removing Stopwords and Stemming in the text.Removing Stopwords: These are common words that don’t really add anything to the classification, such as an able, either, else, ever and so on.Stemming: Stemming to take out the root of the word.Now After applying these two techniques, our text becomes
TextReviews“ilikedthemovi”positive“itsagoodmovienicestori”positive“nicesongsbutsadlyboringend”negative“herosactingisbadbutheroinelooksgoodoverallnicemovi”positive“sadboringmovi”negativeFeature Engineering: The important part is to find the features from the data to make machine learning algorithms works. In this case, we have text. We need to convert this text into numbers that we can do calculations on. We use word frequencies. That is treating every document as a set of the words it contains. Our features will be the counts of each of these words.In our case, we have P(positive | overall liked the movie), by using this theorem:
P(positive | overall liked the movie) = P(overall liked the movie | positive) * P(positive) / P(overall liked the movie)
Since for our classifier we have to find out which tag has a bigger probability, we can discard the divisor which is the same for both tags,P(overall liked the movie | positive)* P(positive) with P(overall liked the movie | negative) * P(negative)There’s a problem though: “overall liked the movie” doesn’t appear in our training dataset, so the probability is zero. Here, we assume the ‘naive’ condition that every word in a sentence is independent of the other ones. This means that now we look at individual words.We can write this as:
P(overall liked the movie) = P(overall) * P(liked) * P(the) * P(movie)
The next step is just applying the Bayes theorem:-
P(overall liked the movie| positive) = P(overall | positive) * P(liked | positive) * P(the | positive) * P(movie | positive)
And now, these individual words actually show up several times in our training data, and we can calculate them!Calculating probabilities: First, we calculate the a priori probability of each tag: for a given sentence in our training data, the probability that it is positive P(positive) is 3/5. Then, P(negative) is 2/5.Then, calculating P(overall | positive) means counting how many times the word “overall” appears in positive texts (1) divided by the total number of words in positive (17). Therefore, P(overall | positive) = 1/17, P(liked/positive) = 1/17, P(the/positive) = 2/17, P(movie/positive) = 3/17. If probability comes out to be zero then By using Laplace smoothing: we add 1 to every count so it’s never zero. To balance this, we add the number of possible words to the divisor, so the division will never be greater than 1. In our case, the total possible words count are 21.Applying smoothing, The results are:
WordP(word | positive)P(word | negative)overall1 + 1/17 + 210 + 1/7 + 21liked1 + 1/17 + 210 + 1/7 + 21the2 + 1/17 + 210 + 1/7 + 21movie3 + 1/17 + 211 + 1/7 + 21Now we just multiply all the probabilities, and see who is bigger:
P(overall | positive) * P(liked | positive) * P(the | positive) * P(movie | positive) * P(positive ) = 1.38 * 10^{-5} = 0.0000138P(overall | negative) * P(liked | negative) * P(the | negative) * P(movie | negative) * P(negative) = 0.13 * 10^{-5} = 0.0000013
Our classifier gives “overall liked the movie” the positive tag.Below is the implementation :
Python
# cleaning texts
import pandas as pd
import re
import nltk
from nltk.corpus import stopwords
from nltk.stem.porter import PorterStemmer
from sklearn.feature_extraction.text import CountVectorizer
dataset = [["I liked the movie", "positive"],
["It’s a good movie. Nice story", "positive"],
["Hero’s acting is bad but heroine looks good.\
Overall nice movie", "positive"],
["Nice songs. But sadly boring ending.", "negative"],
["sad movie, boring movie", "negative"]]
dataset = pd.DataFrame(dataset)
dataset.columns = ["Text", "Reviews"]
nltk.download('stopwords')
corpus = []
for i in range(0, 5):
text = re.sub('[^a-zA-Z]', '', dataset['Text'][i])
text = text.lower()
text = text.split()
ps = PorterStemmer()
text = ''.join(text)
corpus.append(text)
# creating bag of words model
cv = CountVectorizer(max_features = 1500)
X = cv.fit_transform(corpus).toarray()
y = dataset.iloc[:, 1].values
Python
# splitting the data set into training set and test set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size = 0.25, random_state = 0)
Python
# fitting naive bayes to the training set
from sklearn.naive_bayes import GaussianNB
from sklearn.metrics import confusion_matrix
classifier = GaussianNB();
classifier.fit(X_train, y_train)
# predicting test set results
y_pred = classifier.predict(X_test)
# making the confusion matrix
cm = confusion_matrix(y_test, y_pred)
cm | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems | https://www.geeksforgeeks.org/applying-multinomial-naive-bayes-to-nlp-problems/?ref=next_article | Data Science & ML | Applying Multinomial Naive Bayes to NLP Problems | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, ML | Naive Bayes Scratch Implementation using Python, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Ordinary Least Squares (OLS) using statsmodels, Agents in Artificial Intelligence, Applying Multinomial Naive Bayes to NLP Problems, Stacking in Machine Learning, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy Introduction | GeeksforGeeks | [-0.0186430383, 0.0255350508, -0.0134379826, 0.0272941, 0.0331047289, -0.0287359431, -0.0309131276, 0.00807432458, 0.00627202, 0.0345465727, 0.0268471278, -0.049080357, 0.00351449382, -0.0417846292, -0.0235453062, -0.0236894917, 0.0321531147, 0.00779316481, -0.00133821112, -0.00532040279, 0.00711549819, -0.0138416989, -0.010554295, 0.0120538129, -0.00887454767, 0.0424767137, 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02 Jan, 2023 | Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn
02 Jan, 2023
Gaussian process classification (GPC) is a probabilistic approach to classification that models the conditional distribution of the class labels given the feature values. In GPC, the data is assumed to be generated by a Gaussian process, which is a stochastic process that is characterized by its mean and covariance functions.
The mean function in GPC specifies the expected value of the class labels for each sample, while the covariance function specifies the correlations between the class labels of different samples. The mean and covariance functions are modeled using a kernel function, which defines the similarity between samples based on their feature values.
Once the Gaussian process has been defined, GPC uses Bayesian inference to infer the posterior distribution of the class labels given the data. This posterior distribution is then used to make predictions for new samples by computing the most likely class label for each sample.
RBF kernel and its mathematical background:
The Radial Basis Function (RBF) kernel is a kernel function commonly used in support vector machines (SVMs) for classification and regression tasks. It is defined as follows:
K(x, x') = exp(-||x - x'||2/2σ2)
Where x and x’ are input vectors, gamma is a hyperparameter, and ||x – x’|| is the Euclidean distance between x and x’.
To use the RBF kernel in an SVM, you need to choose a value for the hyperparameter gamma. A larger value of gamma will result in a narrower kernel, which means that the influence of a single training example will be more concentrated around its location. This can lead to overfitting, especially if the training set is small. On the other hand, a smaller value of gamma will result in a wider kernel, which means that each training example will have a weaker influence on the decision boundary. This can lead to underfitting, especially if the training set is large and complex.
One interesting property of the RBF kernel is that it can be used to approximate any continuous function to an arbitrary degree of accuracy. This property is known as the universal approximation theorem and it is the foundation of the success of kernel methods in machine learning.
In summary, the RBF kernel is a non-linear kernel function that is commonly used in SVMs to model complex relationships between input data and target variables. It allows the SVM to find non-linear decision boundaries in a high-dimensional feature space, and it has the property of being able to approximate any continuous function to an arbitrary degree of accuracy.
GPC on the XOR Dataset in Scikit Learn:
In scikit-learn, the GaussianProcessClassifier class is in the sklearn.gaussian_process module can be used to perform Gaussian process classification (GPC) on the XOR dataset. GPC is a probabilistic approach to classification that models the conditional distribution of the class labels given the feature values.
Performing Gaussian process classification (GPC) on the XOR dataset in scikit-learn involves the following steps:
Import the GaussianProcessClassifier class from sklearn.gaussian_process module.
Generate or load the XOR dataset. This dataset consists of four samples with two features each and binary class labels.
Create an instance of the GaussianProcessClassifier class and specify the kernel to use. In this case, we will use the RBF kernel.
Fit the GaussianProcessClassifier estimator to the XOR dataset using the fit() method.
Use the estimator to make predictions on the XOR dataset using the predict() method.
Evaluate the performance of the model by calculating metrics such as classification accuracy or confusion matrix.
Here is the complete code of the above steps on how to use the GaussianProcessClassifier class to perform GPC on the XOR dataset in scikit-learn:
Python3
import numpy as np
from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF
# Generate the XOR dataset
X = np.array([[0, 0], [0, 1],
[1, 0], [1, 1]])
y = np.array([0, 1, 1, 0])
# Create a GaussianProcessClassifier with
# an RBF kernel and fit it to the data
estimator = GaussianProcessClassifier(kernel=RBF())
estimator.fit(X, y)
# Obtain predictions for the data
y_pred = estimator.predict(X)
# Print the predictions
print(y_pred)
Output:
[0 1 1 0]
This code will fit a GaussianProcessClassifier estimator with an RBF kernel to the XOR dataset and use it to make predictions on the same data. The predictions will be printed on the console.
To evaluate the performance of the model, you can calculate metrics such as the classification accuracy or confusion matrix. For example:
Python3
from sklearn.metrics import confusion_matrix
# Calculate the confusion matrix
cm = confusion_matrix(y, y_pred)
# Print the confusion matrix
print(cm)
Output:
[[2 0]
[0 2]]
This code will calculate the confusion matrix for the predictions made by the GaussianProcessClassifier and print it to the console. The confusion matrix allows you to see how many samples were correctly and incorrectly classified by the model. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn | https://www.geeksforgeeks.org/gaussian-process-classification-gpc-on-the-xor-dataset-in-scikit-learn/?ref=next_article | Data Science & ML | Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn | Artificial Intelligence – Boon or Bane, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, AI ML DS - Projects, Data Science & ML, Artificial Intelligence Examples, Camera Calibration with Python – OpenCV, Transformers in Machine Learning, ML | Naive Bayes Scratch Implementation using Python, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Ordinary Least Squares (OLS) using statsmodels, Agents in Artificial Intelligence, Applying Multinomial Naive Bayes to NLP Problems, Stacking in Machine Learning, AI ML DS - How To Get Started?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Difference Between Encoder and Decoder, NumPy 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04 Jun, 2024 | Gaussian Discriminant Analysis
04 Jun, 2024
Gaussian Discriminant Analysis (GDA) is a supervised learning algorithm used for classification tasks in machine learning. It is a variant of the Linear Discriminant Analysis (LDA) algorithm that relaxes the assumption that the covariance matrices of the different classes are equal.
GDA works by assuming that the data in each class follows a Gaussian (normal) distribution, and then estimating the mean and covariance matrix for each class. It then uses Bayes’ theorem to compute the probability that a new data point belongs to each class, and chooses the class with the highest probability as the predicted class.GDA can handle data with arbitrary covariance matrices for each class, unlike LDA, which assumes that the covariance matrices are equal. This makes GDA more flexible and able to handle more complex datasets. However, the downside is that GDA requires estimating more parameters, as it needs to estimate a separate covariance matrix for each class.One disadvantage of GDA is that it can be sensitive to outliers and may overfit the data if the number of training examples is small relative to the number of parameters being estimated. Additionally, GDA may not perform well when the decision boundary between classes is highly nonlinear.Overall, GDA is a powerful classification algorithm that can handle more complex datasets than LDA, but it requires more parameters to estimate and may not perform well in all situations.
Advantages of Gaussian Discriminant Analysis (GDA):GDA is a flexible algorithm that can handle datasets with arbitrary covariance matrices for each class, making it more powerful than LDA in some situations.GDA produces probabilistic predictions, which can be useful in many applications where it is important to have a measure of uncertainty in the predictions.GDA is a well-studied and well-understood algorithm, making it a good choice for many classification tasks
Disadvantages of Gaussian Discriminant Analysis (GDA):GDA requires estimating more parameters than LDA, which can make it computationally more expensive and more prone to overfitting if the number of training examples is small relative to the number of parameters.GDA assumes that the data in each class follows a Gaussian distribution, which may not be true for all datasets.GDA may not perform well when the decision boundary between classes is highly nonlinear, as it is a linear classifier.GDA may be sensitive to outliers in the data, which can affect the estimated parameters and lead to poor performance.
There are two types of Supervised Learning algorithms used for classification in Machine Learning.
Discriminative Learning AlgorithmsGenerative Learning AlgorithmsDiscriminative Learning Algorithms include Logistic Regression, Perceptron Algorithm, etc. which try to find a decision boundary between different classes during the learning process. For example, given a classification problem to predict whether a patient has malaria or not a Discriminative Learning Algorithm will try to create a classification boundary to separate two types of patients, and when a new example is introduced it is checked on which side of the boundary the example lies to classify it. Such algorithms try to model P(y|X) i.e. given a feature set X for a data sample what is the probability it belongs to the class ‘y’.
On the other hand, Generative Learning Algorithms follow a different approach, they try to capture the distribution of each class separately instead of finding a decision boundary among classes. Considering the previous example, a Generative Learning Algorithm will look at the distribution of infected patients and healthy patients separately and try to learn each of the distribution’s features separately, when a new example is introduced it is compared to both the distributions, the class to which the data example resembles the most will be assigned to it. Such algorithms try to model P(X|y) for a given P(y) here, P(y) is known as a class prior.
The predictions for generative learning algorithms are made using Bayes Theorem as follows:
[Tex]P(y|X) = \dfrac{P(X|y).P(y)}{P(X)} \\where, P(X) = P(X|y=1).P(y=1) + P(X|y=0).P(y=0)\\ [/Tex]
Using only the values of P(X|y) and P(y) for the particular class we can calculate P(y|X) i.e given the features of a data sample what is the probability it belongs to the class ‘y’.
Gaussian Discriminant Analysis is a Generative Learning Algorithm and in order to capture the distribution of each class, it tries to fit a Gaussian Distribution to every class of the data separately. The below images depict the difference between the Discriminative and Generative Learning Algorithms. The probability of a prediction in the case of the Generative learning algorithm will be high if it lies near the centre of the contour corresponding to its class and decreases as we move away from the centre of the contour.
Generative Learning Algorithm (GDA)Discriminative Learning AlgorithmLet’s consider a binary classification problem such that all the data samples are IID (Independently and Identically distributed), therefore to calculate P(X|y) we can use Multivariate Gaussian Distribution to form a probability density function for each individual class. And to calculate P(y) or class prior for each class we can use Bernoulli distribution as all the data samples in binary classification can either take value 1 or 0.
Therefore, the probability distribution and class prior to a data sample can be defined using the general form of Gaussian and Bernoulli distribution respectively:
[Tex]P(x|y=0) = \dfrac{1}{(2\pi)^{n/2}*|\Sigma|^{1/2}} exp({-1/2(x-\mu_0)^{T}\Sigma^{-1}(x-\mu_0))}\hspace{1mm}-\hspace{1mm}\textbf{Eq\hspace{1mm}1} \\ P(x|y=1) = \dfrac{1}{(2\pi)^{n/2}*|\Sigma|^{1/2}} exp({-1/2(x-\mu_1)^{T}\Sigma^{-1}(x-\mu_1))}\hspace{1mm} -\hspace{1mm} \textbf{Eq\hspace{1mm}2} \\ P(y) = \phi^y . (1-\phi)^{1-y}\hspace{1mm}-\hspace{1mm}\textbf{Eq\hspace{1mm}\hspace{1mm}3}\\ [/Tex]In the equations mentioned:
μ₀ is the mean of data samples that belong to class 0. This is represented in the space of Rⁿˣ¹, which indicates that the mean is a vector with n elements (one for each feature in your data).μ₁ is the mean of data samples that belong to class 1. Similarly, this mean is also in the space of Rⁿˣ¹, meaning it is also a vector of n elements.Σ (Sigma) is the covariance matrix of the features. Its dimensions are Rⁿˣⁿ, which shows that it is a square matrix where each element represents the covariance between two features.ϕ (phi) represents the probability that any given data sample belongs to class 1.
In order to view the probability distributions as a function of parameters mentioned above, we can define a Likelihood function which is equal to the product of probability distribution and class prior to each data sample (Taking product of the probabilities is reasonable as all the data samples are considered IID).
[Tex]\newline L(\phi, \mu_0,\mu_1,\Sigma) = \Pi_{i=1}^{m}P(x^{(i)},y^{(i)};\phi,\mu_0,\mu_1,\Sigma)\\ \hspace{2.3cm}=\Pi_{i=0}^{m}P(x^{(i)}|y^{(i)}).P(y^{(i)}) \hspace{1mm} – \textbf{Eq \hspace{1mm} 4} [/Tex]
According to the principle of Maximum Likelihood estimation we have to choose the value of parameters in a way to maximize the probability function given in Eq 4. To do so instead of maximizing the Likelihood function we can maximize Log-Likelihood Function which is a strictly increasing function.
[Tex]Therefore,\hspace{1mm} Log-Likelihood \hspace{1mm}function = log(L(\phi,\mu_0,\mu_1,\Sigma)) \newline On \hspace{1mm}maximizing \hspace{1mm}Log-Likelihood \hspace{1mm}following \hspace{1mm}parameters \hspace{1mm}are \hspace{1mm}obtained [/Tex]
[Tex]\newline\phi = \dfrac{1}{m}\Sigma_{i=1}^{m}1\{y^{(i)} = 1\}\\ \mu_0 = \dfrac{\Sigma_{i=1}^{m}\mathbb{1}\{y^{(i)} = 0\}.x^{(i)}}{\Sigma_{i=1}^{m}\mathbb{1}\{y^{(i)} = 0\}}\\ \mu_1 = \dfrac{\Sigma_{i=1}^{m}\mathbb{1}\{y^{(i)} = 1\}.x^{(i)}}{\Sigma_{i=1}^{m}\mathbb{1}\{y^{(i)} = 1\}}\\ \Sigma = \dfrac{1}{m}\Sigma_{i=1}^{m}(x^{(i)} – \mu_{y^{(i)}}).(x^{(i)} – \mu_{y^{(i)}})^{T}\\ [/Tex]
In the above equations, the function “1{condition}” is the indicator function which returns 1 if the condition is true else returns 0. For example, 1{y=1} will return 1 only when the class of that data sample is 1 else returns 0 similarly, in the case of 1{y=0} will return 1 only when the class of that data sample is 0 else it returns 0.
The values of the parameters obtained can be plugged in Eq 1, 2, and 3 to find the probability distribution and class prior to all the data samples. These values obtained can be further multiplied to find the Likelihood function given in Eq 4. As mentioned earlier the likelihood function i.e P(X|y). P(y) can be plugged into the Bayes formula to predict P(y|X) (i.e predict the class ‘y‘ of a data sample for the given features ‘X‘).
NOTE: The data samples in this model is considered to be IID which is an assumption made about the model, Gaussian Discriminant Analysis will perform poorly if the data is not a Gaussian distribution, therefore, it is always suggested visualizing the data to check if it has a normal distribution and if not attempts can be made to do so by using methods like log-transform etc. (Do not confuse Gaussian Discriminant Analysis with Gaussian Mixture model which is an unsupervised learning algorithm).
Therefore, Gaussian Discriminant Analysis works quite well for a small amount of data (say a few thousand examples) and can be more robust compared to Logistic Regression if our underlying assumptions about the distribution of the data are true | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis | https://www.geeksforgeeks.org/gaussian-discriminant-analysis/?ref=next_article | Data Science & ML | Gaussian Discriminant Analysis | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Data Science & ML, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder 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07 Jan, 2022 | Quadratic Discriminant Analysis
07 Jan, 2022
Linear Discriminant Analysis
Now, Let’s consider a classification problem represented by a Bayes Probability distribution P(Y=k | X=x), LDA does it differently by trying to model the distribution of X given the predictors class (I.e. the value of Y) P(X=x| Y=k):
In LDA, we assume that P(X | Y=k) can be estimated to the multivariate Normal distribution that is given by following equation:
where,
and P(Y=k) =\pi_k. Now, we try to write the above equation with the assumptions:
Now, we take log both sides and maximizing the equation, we get the decision boundary:
For two classes, the decision boundary is a linear function of x where both classes give equal value, this linear function is given as:
For multi-class (K>2), we need to estimate the pK means, pK variance, K prior proportions and . Now, we discuss in more detail about Quadratic Discriminant Analysis.
Quadratic Discriminant Analysis
Quadratic discriminant analysis is quite similar to Linear discriminant analysis except we relaxed the assumption that the mean and covariance of all the classes were equal. Therefore, we required to calculate it separately.
Now, for each of the class y the covariance matrix is given by:
By adding the following term and solving (taking log both side and ). The quadratic Discriminant function is given by:
ImplementationIn this implementation, we will be using R and MASS library to plot the decision boundary of Linear Discriminant Analysis and Quadratic Discriminant Analysis. For this, we will use iris dataset:
R
# import librarieslibrary(caret)library(MASS)library(tidyverse) # Code to plot decision plotdecision_boundary = function(model, data,vars, resolution = 200,...) { class='Species' labels_var = data[,class] k = length(unique(labels_var)) # For sepals if (vars == 'sepal'){ data = data %>% select(Sepal.Length, Sepal.Width) } else{ data = data %>% select(Petal.Length, Petal.Width) } # plot with color labels int_labels = as.integer(labels_var) plot(data, col = int_labels+1L, pch = int_labels+1L, ...) # make grid r = sapply(data, range, na.rm = TRUE) xs = seq(r[1,1], r[2,1], length.out = resolution) ys = seq(r[1,2], r[2,2], length.out = resolution) dfs = cbind(rep(xs, each=resolution), rep(ys, time = resolution)) colnames(dfs) = colnames(r) dfs = as.data.frame(dfs) p = predict(model, dfs, type ='class' ) p = as.factor(p$class) points(dfs, col = as.integer(p)+1L, pch = ".") mats = matrix(as.integer(p), nrow = resolution, byrow = TRUE) contour(xs, ys, mats, add = TRUE, lwd = 2, levels = (1:(k-1))+.5) invisible(mats)} par(mfrow=c(2,2))# run the linear discriminant analysis and plot the decision boundary with Sepals variablemodel = lda(Species ~ Sepal.Length + Sepal.Width, data=iris)lda_sepals = decision_boundary(model, iris, vars= 'sepal' , main = "LDA_Sepals") # run the quadratic discriminant analysis and plot the decision boundary with Sepals variablemodel_qda = qda(Species ~ Sepal.Length + Sepal.Width, data=iris)qda_sepals = decision_boundary(model_qda, iris, vars= 'sepal', main = "QDA_Sepals") # run the linear discriminant analysis and plot the decision boundary with Petals variablemodel = lda(Species ~ Petal.Length + Petal.Width, data=iris)lda_petal =decision_boundary(model, iris, vars='petal', main = "LDA_petals") # run the quadratic discriminant analysis and plot the decision boundary with Petals variablemodel_qda = qda(Species ~ Petal.Length + Petal.Width, data=iris)qda_petal =decision_boundary(model_qda, iris, vars='petal', main = "QDA_petals")
LDA and QDA visualizationReferences:Stanford Statistics NotesHarvard Slides on LDA | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis | https://www.geeksforgeeks.org/quadratic-discriminant-analysis/?ref=next_article | Data Science & ML | Quadratic Discriminant Analysis | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Data Science & ML, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | 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22 Jan, 2025 | Basic Understanding of Bayesian Belief Networks
22 Jan, 2025
Bayesian Belief Network (BBN) is a graphical model that represents the probabilistic relationships among variables. It is used to handle uncertainty and make predictions or decisions based on probabilities.
Graphical Representation: Variables are represented as nodes in a directed acyclic graph (DAG), and their dependencies are shown as edges.Conditional Probabilities: Each node’s probability depends on its parent nodes, expressed as [Tex]P(\text{Variable | Parent})[/Tex].Probabilistic Model: Built from probability distributions, BBNs apply probability theory for tasks like prediction and anomaly detection.Bayesian Belief Networks are valuable tools for understanding and solving problems involving uncertain events. They are also known as Bayes networks, belief networks, decision networks, or Bayesian models.
(Note: A classifier assigns data in a collection to desired categories.)
Consider this example:In the above figure, we have an alarm ‘A’ – a node, say installed in a house of a person ‘gfg’, which rings upon two probabilities i.e burglary ‘B’ and fire ‘F’, which are – parent nodes of the alarm node. The alarm is the parent node of two probabilities P1 calls ‘P1’ & P2 calls ‘P2’ person nodes.Upon the instance of burglary and fire, ‘P1’ and ‘P2’ call person ‘gfg’, respectively. But, there are few drawbacks in this case, as sometimes ‘P1’ may forget to call the person ‘gfg’, even after hearing the alarm, as he has a tendency to forget things, quick. Similarly, ‘P2’, sometimes fails to call the person ‘gfg’, as he is only able to hear the alarm, from a certain distance.Calculating Conditional Probability of Events in a Bayesian NetworkFind the probability that ‘P1’ is true (P1 has called ‘gfg’), ‘P2’ is true (P2 has called ‘gfg’) when the alarm ‘A’ rang, but no burglary ‘B’ and fire ‘F’ has occurred.
=> P ( P1, P2, A, ~B, ~F) [ where- P1, P2 & A are ‘true’ events and ‘~B’ & ‘~F’ are ‘false’ events]
[ Note: The values mentioned below are neither calculated nor computed. They have observed values ]
Burglary ‘B’ –
P (B=T) = 0.001 (‘B’ is true i.e burglary has occurred)P (B=F) = 0.999 (‘B’ is false i.e burglary has not occurred)Fire ‘F’ –
P (F=T) = 0.002 (‘F’ is true i.e fire has occurred)P (F=F) = 0.998 (‘F’ is false i.e fire has not occurred)Alarm ‘A’ –
BFP (A=T)P (A=F)TT0.950.05TF0.940.06FT0.290.71FF0.0010.999The alarm ‘A’ node can be ‘true’ or ‘false’ ( i.e may have rung or may not have rung). It has two parent nodes burglary ‘B’ and fire ‘F’ which can be ‘true’ or ‘false’ (i.e may have occurred or may not have occurred) depending upon different conditions.Person ‘P1’ –
AP (P1=T)P (P1=F)T0.950.05F0.050.95The person ‘P1’ node can be ‘true’ or ‘false’ (i.e may have called the person ‘gfg’ or not) . It has a parent node, the alarm ‘A’, which can be ‘true’ or ‘false’ (i.e may have rung or may not have rung ,upon burglary ‘B’ or fire ‘F’).Person ‘P2’ –
AP (P2=T)P (P2=F)T0.800.20F0.010.99The person ‘P2’ node can be ‘true’ or false’ (i.e may have called the person ‘gfg’ or not). It has a parent node, the alarm ‘A’, which can be ‘true’ or ‘false’ (i.e may have rung or may not have rung, upon burglary ‘B’ or fire ‘F’).Solution: Considering the observed probabilistic scan –
With respect to the question — P ( P1, P2, A, ~B, ~F) , we need to get the probability of ‘P1’. We find it with regard to its parent node – alarm ‘A’. To get the probability of ‘P2’, we find it with regard to its parent node — alarm ‘A’.
We find the probability of alarm ‘A’ node with regard to ‘~B’ & ‘~F’ since burglary ‘B’ and fire ‘F’ are parent nodes of alarm ‘A’.
From the observed probabilistic scan, we can deduce –
P ( P1, P2, A, ~B, ~F)
= P (P1/A) * P (P2/A) * P (A/~B~F) * P (~B) * P (~F)
= 0.95 * 0.80 * 0.001 * 0.999 * 0.998
= 0.00075 | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks | https://www.geeksforgeeks.org/basic-understanding-of-bayesian-belief-networks/?ref=next_article | Data Science & ML | Basic Understanding of Bayesian Belief Networks | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Basic Understanding of Bayesian Belief Networks, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Data Science & ML, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | 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02 Feb, 2025 | Hidden Markov Model in Machine learning
02 Feb, 2025
When working with sequences of data, we often face situations where we can’t directly see the important factors that influence the datasets. Hidden Markov Models (HMM) help solve this problem by predicting these hidden factors based on the observable data
Hidden Markov Model in Machine LearningIt is an statistical model that is used to describe the probabilistic relationship between a sequence of observations and a sequence of hidden states. Ike it is often used in situations where the underlying system or process that generates the observations is unknown or hidden, hence it has the name “Hidden Markov Model.”
An HMM consists of two types of variables: hidden states and observations.
The hidden states are the underlying variables that generate the observed data, but they are not directly observable.The observations are the variables that are measured and observed. The relationship between the hidden states and the observations is modeled using a probability distribution. The Hidden Markov Model (HMM) is the relationship between the hidden states and the observations using two sets of probabilities: the transition probabilities and the emission probabilities.
The transition probabilities describe the probability of transitioning from one hidden state to another.The emission probabilities describe the probability of observing an output given a hidden state.Hidden Markov Model AlgorithmThe Hidden Markov Model (HMM) algorithm can be implemented using the following steps:
Step 1: Define the state space and observation space: The state space is the set of all possible hidden states, and the observation space is the set of all possible observations.Step 2: Define the initial state distribution: This is the probability distribution over the initial state.Step 3: Define the state transition probabilities: These are the probabilities of transitioning from one state to another. This forms the transition matrix, which describes the probability of moving from one state to another.Step 4: Define the observation likelihoods: These are the probabilities of generating each observation from each state. This forms the emission matrix, which describes the probability of generating each observation from each state.Step 5: Train the model: The parameters of the state transition probabilities and the observation likelihoods are estimated using the Baum-Welch algorithm, or the forward-backward algorithm. This is done by iteratively updating the parameters until convergence.Step 6: Decode the most likely sequence of hidden states: Given the observed data, the Viterbi algorithm is used to compute the most likely sequence of hidden states. This can be used to predict future observations, classify sequences, or detect patterns in sequential data.Step 7: Evaluate the model: The performance of the HMM can be evaluated using various metrics, such as accuracy, precision, recall, or F1 score.To summarise, the HMM algorithm involves defining the state space, observation space, and the parameters of the state transition probabilities and observation likelihoods, training the model using the Baum-Welch algorithm or the forward-backward algorithm, decoding the most likely sequence of hidden states using the Viterbi algorithm, and evaluating the performance of the model.
Implementation of HMM in pythonTill now we have covered the essential steps of HMM and now lets move towards the hands on code implementation of the following
Key steps in the Python implementation of a simple Hidden Markov Model (HMM) using the hmmlearn library.
Example 1. Weather Prediction Problem statement: Given the historical data on weather conditions, the task is to predict the weather for the next day based on the current day’s weather.
Step 1: Import the required librariesThe code imports the NumPy,matplotlib, seaborn, and the hmmlearn library.
Python
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from hmmlearn import hmm
Step 2: Define the model parametersIn this example, The state space is defined as a state which is a list of two possible weather conditions: “Sunny” and “Rainy“. The observation space is defined as observations which is a list of two possible observations: “Dry” and “Wet“. The number of hidden states and the number of observations are defined as constants.
Python
states = ["Sunny", "Rainy"]
n_states = len(states)
print('Number of hidden states :',n_states)
observations = ["Dry", "Wet"]
n_observations = len(observations)
print('Number of observations :',n_observations)
Output:
Number of hidden states : 2
Number of observations : 2
The start probabilities, transition probabilities, and emission probabilities are defined as arrays. The start probabilities represent the probabilities of starting in each of the hidden states, the transition probabilities represent the probabilities of transitioning from one hidden state to another, and the emission probabilities represent the probabilities of observing each of the outputs given a hidden state.
The initial state distribution is defined as state_probability, which is an array of probabilities that represent the probability of the first state being “Sunny” or “Rainy”. The state transition probabilities are defined as transition_probability, which is a 2×2 array representing the probability of transitioning from one state to another. The observation likelihoods are defined as emission_probability, which is a 2×2 array representing the probability of generating each observation from each state.
Python
state_probability = np.array([0.6, 0.4])
print("State probability: ", state_probability)
transition_probability = np.array([[0.7, 0.3],
[0.3, 0.7]])
print("\nTransition probability:\n", transition_probability)
emission_probability= np.array([[0.9, 0.1],
[0.2, 0.8]])
print("\nEmission probability:\n", emission_probability)
Output:
State probability: [0.6 0.4]
Transition probability:
[[0.7 0.3]
[0.3 0.7]]
Emission probability:
[[0.9 0.1]
[0.2 0.8]]
Step 3: Create an instance of the HMM model and Set the model parametersThe HMM model is defined using the hmm.CategoricalHMM class from the hmmlearn library. An instance of the CategoricalHMM class is created with the number of hidden states set to n_hidden_states and the parameters of the model are set using the startprob_, transmat_, and emissionprob_ attributes to the state probabilities, transition probabilities, and emission probabilities respectively.
Python
model = hmm.CategoricalHMM(n_components=n_states)
model.startprob_ = state_probability
model.transmat_ = transition_probability
model.emissionprob_ = emission_probability
Step 4: Define an observation sequenceA sequence of observations is defined as a one-dimensional NumPy array.
The observed data is defined as observations_sequence which is a sequence of integers, representing the corresponding observation in the observations list.
Python
observations_sequence = np.array([0, 1, 0, 1, 0, 0]).reshape(-1, 1)
observations_sequence
Output:
array([[0],
[1],
[0],
[1],
[0],
[0]])Step 5: Predict the most likely sequence of hidden states The most likely sequence of hidden states is computed using the prediction method of the HMM model.
Python
# Predict the most likely sequence of hidden states
hidden_states = model.predict(observations_sequence)
print("Most likely hidden states:", hidden_states)
Output:
Most likely hidden states: [0 1 1 1 0 0]
Step 6: Decoding the observation sequenceThe Viterbi algorithm is used to calculate the most likely sequence of hidden states that generated the observations using the decode method of the model. The method returns the log probability of the most likely sequence of hidden states and the sequence of hidden states itself.
Python
log_probability, hidden_states = model.decode(observations_sequence,
lengths = len(observations_sequence),
algorithm ='viterbi' )
print('Log Probability :',log_probability)
print("Most likely hidden states:", hidden_states)
Output:
Log Probability : -6.360602626270058
Most likely hidden states: [0 1 1 1 0 0]
This is a simple algo of how to implement a basic HMM and use it to decode an observation sequence. The hmmlearn library provides a more advanced and flexible implementation of HMMs with additional functionality such as parameter estimation and training.
Step 7: Plot the results
Python
sns.set_style("whitegrid")
plt.plot(hidden_states, '-o', label="Hidden State")
plt.xlabel('Time step')
plt.ylabel('Most Likely Hidden State')
plt.title("Sunny or Rainy")
plt.legend()
plt.show()
Output:
Sunny or RainyFinally, the results are plotted using the matplotlib library, where the x-axis represents the time steps, and the y-axis represents the hidden state. The plot shows that the model predicts that the weather is mostly sunny, with a few rainy days mixed in.
Example 2: Speech recognition using HMM Problem statement: Given a dataset of audio recordings, the task is to recognize the words spoken in the recordings.
In this example, the state space is defined as states, which is a list of 4 possible states representing silence or the presence of one of 3 different words. The observation space is defined as observations, which is a list of 2 possible observations, representing the volume of the speech. The initial state distribution is defined as start_probability, which is an array of probabilities of length 4 representing the probability of each state being the initial state.
The state transition probabilities are defined as transition_probability, which is a 4×4 matrix representing the probability of transitioning from one state to another. The observation likelihoods are defined as emission_probability, which is a 4×2 matrix representing the probability of emitting an observation for each state.
The model is defined using the MultinomialHMM class from hmmlearn library and is fit using the startprob_, transmat_, and emissionprob_ attributes. The sequence of observations is defined as observations_sequence and is an array of length 8, representing the volume of the speech in 8 different time steps.
The predict method of the model object is used to predict the most likely hidden states, given the observations. The result is stored in the hidden_states variable, which is an array of length 8, representing the most likely state for each time step.
Python
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from hmmlearn import hmm
states = ["Silence", "Word1", "Word2", "Word3"]
n_states = len(states)
observations = ["Loud", "Soft"]
n_observations = len(observations)
start_probability = np.array([0.8, 0.1, 0.1, 0.0])
transition_probability = np.array([[0.7, 0.2, 0.1, 0.0],
[0.0, 0.6, 0.4, 0.0],
[0.0, 0.0, 0.6, 0.4],
[0.0, 0.0, 0.0, 1.0]])
emission_probability = np.array([[0.7, 0.3],
[0.4, 0.6],
[0.6, 0.4],
[0.3, 0.7]])
model = hmm.CategoricalHMM(n_components=n_states)
model.startprob_ = start_probability
model.transmat_ = transition_probability
model.emissionprob_ = emission_probability
observations_sequence = np.array([0, 1, 0, 0, 1, 1, 0, 1]).reshape(-1, 1)
hidden_states = model.predict(observations_sequence)
print("Most likely hidden states:", hidden_states)
sns.set_style("darkgrid")
plt.plot(hidden_states, '-o', label="Hidden State")
plt.legend()
plt.show()
Output:
Most likely hidden states: [0 1 2 2 3 3 3 3]Speech RecognitionOther Applications of Hidden Markov ModelHMMs are widely used in a variety of applications such as speech recognition, natural language processing, computational biology, and finance. In speech recognition, for example, an HMM can be used to model the underlying sounds or phonemes that generate the speech signal, and the observations could be the features extracted from the speech signal. In computational biology, an HMM can be used to model the evolution of a protein or DNA sequence, and the observations could be the sequence of amino acids or nucleotides.
ConclusionIn conlclusion, HMMs are a powerful tool for modeling sequential data, and their implementation through libraries such as hmmlearn makes them accessible and useful for a variety of applications.
Frequently Asked Questions(FAQs)What is a Hidden Markov Model (HMM)?A statistical model called a hidden markov model is used to describe systems that change between states with specific probabilities. The reason it is called “hidden” is that although the states produce observable outputs or emissions, they are not directly observable.
What are the key components of an HMM?States, emission probabilities connected to each state, transition probabilities between states, and an initial probability distribution over states make up an HMM.
How is an HMM different from a regular Markov Model?Every state in a standard Markov model can be observed directly. On the other hand, only the emissions-the observable outputs-are visible in an HMM, while the states remain hidden.
What are the applications of Hidden Markov Models?Speech recognition, natural language processing, bioinformatics (gene prediction, for example), and many other fields where systems can be modeled as sequences of observable events with underlying hidden states are applications that heavily rely on HMMs. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning | https://www.geeksforgeeks.org/hidden-markov-model-in-machine-learning/?ref=next_article | Data Science & ML | Hidden Markov Model in Machine learning | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Data Science & ML, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.029124124, 0.0161708239, -0.0204284936, 0.00100634247, 0.0109007433, -0.0268080626, 0.00458011543, -0.0129255634, -0.0141113317, 0.0152693624, -0.0238401759, 0.0164620653, -0.0348102637, -0.0159905311, -0.0212328732, -0.00236980221, 0.03464384, 0.00252929144, 0.00308056967, 0.012793812, -0.0159627944, -0.00267144502, -0.0664584786, -0.00115629705, 0.0102766557, -0.000806547527, 0.0204978362, -0.0160737429, -0.0594686866, 0.0190277621, 0.00934745744, -0.0072949, -0.00745438877, -0.0368905589, -0.0511752479, -0.019846011, -0.0211635306, -0.0108175315, -0.0323971212, 0.0233409051, 0.0469591841, -0.000123842532, -0.00118230074, 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13 Jan, 2025 | Components of Time Series Data
13 Jan, 2025
Time series data, which consists of observations recorded over time at regular intervals, can be analyzed by breaking it down into four primary components. These components help identify patterns, trends, and irregularities in the data. It’s often shown as a line graph to easily see patterns over time.
Components of Time Series DataTrend: A long-term upward or downward movement in the data, indicating a general increase or decrease over time.Seasonality: A repeating pattern in the data that occurs at regular intervals, such as daily, weekly, monthly, or yearly.Cycle: A pattern in the data that repeats itself after a specific number of observations, which is not necessarily related to seasonality.Irregularity: Random fluctuations in the data that cannot be easily explained by trend, seasonality, or cycle.Autocorrelation: The correlation between an observation and a previous observation in the same time series.Outliers: Extreme observations that are significantly different from the other observations in the data.Noise: Unpredictable and random variations in the data.By identifying these patterns in time series data, analysts can better understand the underlying structure and make more accurate forecasts.
1. TrendA trend in time series data refers to a long-term upward or downward movement in the data, indicating a general increase or decrease over time. There are several types of trends in time series data:
Upward Trend: A trend that shows a general increase over time, where the values of the data tend to rise over time.Downward Trend: A trend that shows a general decrease over time, where the values of the data tend to decrease over time.Horizontal Trend: A trend that shows no significant change over time, where the values of the data remain constant over time.Non-linear Trend: A trend that shows a more complex pattern of change over time, including upward or downward trends that change direction or magnitude over time.Damped Trend: A trend that shows a gradual decline in the magnitude of change over time, where the rate of change slows down over time.It’s important to note that time series data can have a combination of these types of trends or multiple trends present simultaneously. Accurately identifying and modeling the trend is a crucial step in time series analysis, as it can significantly impact the accuracy of forecasts and the interpretation of patterns in the data.
Here’s a code example in Python that demonstrates different types of Trends in time series data using sample data.
Python
import numpy as np
import matplotlib.pyplot as plt
# Upward Trend
t = np.arange(0, 10, 0.1)
data = t + np.random.normal(0, 0.5, len(t))
plt.plot(t, data, label='Upward Trend')
# Downward Trend
t = np.arange(0, 10, 0.1)
data = -t + np.random.normal(0, 0.5, len(t))
plt.plot(t, data, label='Downward Trend')
# Horizontal Trend
t = np.arange(0, 10, 0.1)
data = np.zeros(len(t)) + np.random.normal(0, 0.5, len(t))
plt.plot(t, data, label='Horizontal Trend')
# Non-linear Trend
t = np.arange(0, 10, 0.1)
data = t**2 + np.random.normal(0, 0.5, len(t))
plt.plot(t, data, label='Non-linear Trend')
# Damped Trend
t = np.arange(0, 10, 0.1)
data = np.exp(-0.1*t) * np.sin(2*np.pi*t)\
+ np.random.normal(0, 0.5, len(t))
plt.plot(t, data, label='Damped Trend')
plt.legend()
plt.show()
Output:
Various Trends in Time Series DataThe above code generates a plot of five different types of trends in time series data: upward, downward, horizontal, non-linear, and damping. The sample data is generated using a combination of mathematical functions and random noise.
2. SeasonalitySeasonality in time series data refers to patterns that repeat over a regular time period, such as a day, a week, a month, or a year. These patterns arise due to regular events, such as holidays, weekends, or the changing of seasons, and can be present in various types of time series data, such as sales, weather, or stock prices.
There are several types of seasonality in time series data, including:
Weekly Seasonality: A type of seasonality that repeats over a 7-day period and is commonly seen in time series data such as sales, energy usage, or transportation patterns.Monthly Seasonality: A type of seasonality that repeats over a 30- or 31-day period and is commonly seen in time series data such as sales or weather patterns.Annual Seasonality: A type of seasonality that repeats over a 365- or 366-day period and is commonly seen in time series data such as sales, agriculture, or tourism patterns.Holiday Seasonality: A type of seasonality that is caused by special events such as holidays, festivals, or sporting events and is commonly seen in time series data such as sales, traffic, or entertainment patterns.It’s important to note that time series data can have multiple types of seasonality present simultaneously, and accurately identifying and modeling the seasonality is a crucial step in time series analysis.
Here’s a code example in Python that demonstrates different types of seasonality in time series data using sample data:
Python
import numpy as np
import matplotlib.pyplot as plt
# generate sample data with different types of seasonality
np.random.seed(1)
time = np.arange(0, 366)
# weekly seasonality
weekly_seasonality = np.sin(2 * np.pi * time / 7)
weekly_data = 5 + weekly_seasonality
# monthly seasonality
monthly_seasonality = np.cos(2 * np.pi * time / 30)
monthly_data = 5 + monthly_seasonality
# annual seasonality
annual_seasonality = np.sin(2 * np.pi * time / 365)
annual_data = 5 + annual_seasonality
# plot the data
plt.figure(figsize=(12, 8))
plt.plot(time, weekly_data,
label='Weekly Seasonality')
plt.plot(time, monthly_data,
label='Monthly Seasonality')
plt.plot(time, annual_data,
label='Annual Seasonality')
plt.legend(loc='upper left')
plt.show()
Output:
Seasonality in Time Series DataThe above code generates a plot that shows three graphs of the generated sample data with different types of seasonality. The data represents the different effects of weekly, monthly, and annual seasonality on a single time series.
The x-axis represents time, and the y-axis represents the value of the time series after adding the corresponding seasonality component. The plot uses the matplotlib library to display the graphs, and the NumPy library for data generation and mathematical operations. The legend function adds a legend to the plot to help distinguish the different graphs. The show function displays the plot on the screen.3. CyclicityCyclicity in time series data refers to the repeated patterns or periodic fluctuations that occur in the data over a specific time interval. It can be due to various factors such as seasonality (daily, weekly, monthly, yearly), trends, and other underlying patterns.
Difference between Seasonality and Cyclicity:
Seasonality refers to a repeating pattern in the data that occurs over a fixed time interval, such as daily, weekly, monthly, or yearly. Seasonality is a predictable and repeating pattern that can be due to various factors such as weather, holidays, and human behavior.Cyclicity, on the other hand, refers to the repeated patterns or fluctuations that occur in the data over an unspecified time interval. These patterns can be due to various factors such as economic cycles, trends, and other underlying patterns. Cyclicity is not limited to a fixed time interval and can be of different frequencies, making it harder to identify and model.Putting together, seasonality refers to a repeating pattern in the data that occurs over a fixed time interval, while cyclicity refers to a repeating pattern that occurs over an unspecified time interval.
Python
import numpy as np
import matplotlib.pyplot as plt
# Generate sample data with cyclic patterns
np.random.seed(1)
time = np.array([0, 30, 60, 90, 120,
150, 180, 210, 240,
270, 300, 330])
data = 10 * np.sin(2 * np.pi * time / 50)\
+ 20 * np.sin(2 * np.pi * time / 100)
# Plot the data
plt.figure(figsize=(12, 8))
plt.plot(time, data, label='Cyclic Data')
plt.legend(loc='upper left')
plt.xlabel('Time (days)')
plt.ylabel('Value')
plt.title('Cyclic Time Series Data')
plt.show()
Output:
Cyclicity in Time Series DataThe above code creates time series data with two cyclic patterns using the sin function. Each pattern has a different frequency. The time variable has 12 points with uneven intervals, showing irregular sampling. The data is then plotted using Matplotlib, showing the patterns over time with these uneven intervals.
4. IrregularitiesIrregularities in time series data refer to unexpected or unusual fluctuations in the data that do not follow the general pattern of the data. These fluctuations can occur for various reasons, such as measurement errors, unexpected events, or other sources of noise.
Irregularities can have a significant impact on the accuracy of time series models and forecasting, as they can obscure underlying trends and seasonality patterns in the data.
Python
import numpy as np
import matplotlib.pyplot as plt
# Generate sample time series data
np.random.seed(1)
time = np.arange(0, 100)
data = 5 * np.sin(2 * np.pi * time / 20) + 2 * time
# Introduce irregularities by adding random noise
irregularities = np.random.normal(0, 5, len(data))
irregular_data = data + irregularities
# Plot the original data and the data with irregularities
plt.figure(figsize=(12, 8))
plt.plot(time, data, label='Original Data')
plt.plot(time, irregular_data,
label='Data with Irregularities')
plt.legend(loc='upper left')
plt.show()
Output:
Irregularities in Time Series DataThe above code generates a time series with a sinusoidal pattern and a linear trend, and then introduces random noise to create irregularities in the data.
The resulting plot shows that the irregularities can significantly affect the appearance of the time series data, making it more difficult to identify the underlying patterns.
5. AutocorrelationAutocorrelation in time series measures how similar observations are to each other at different time lags. It shows the relationship between a time series and a shifted version of itself. If a time series is positively autocorrelated, a high value is likely to be followed by another high value. If it’s negatively autocorrelated, a high value is likely to be followed by a low value.
Autocorrelation helps understand the patterns and dependencies in data. It can be calculated using methods like the Pearson correlation coefficient or autocorrelation function (ACF), which shows the relationship at various time lags.
Python
import numpy as np
import matplotlib.pyplot as plt
# generate random time series data with autocorrelation
np.random.seed(1)
data = np.random.randn(100)
data = np.convolve(data, np.ones(10) / 10,
mode='same')
# visualize the time series data
plt.plot(data)
plt.show()
Output:
Time Series data with AutocorrelationThis code generates random time series data using NumPy and then applies a moving average filter to the data to create autocorrelation.
6. NoiseNoise in time series data refers to random fluctuations or variations that are not due to an underlying pattern or trend. It is typically considered as any unpredictable and random variation in the data. These fluctuations can arise from various sources such as measurement errors, random fluctuations in the underlying process, or errors in data recording or processing.
The presence of noise can make it difficult to identify the underlying trend or pattern in the data, and therefore it is important to remove or reduce the noise before any further analysis.
7. OutliersOutliers in time series data are data points that are significantly different from the rest of the data points in the series. These can be due to various reasons such as measurement errors, extreme events, or changes in underlying data-generating processes. Outliers can have a significant impact on the results of time series analysis and modeling, as they can skew the statistical properties of the data.
In conclusion, time series data can be decomposed into several components, including trend, seasonality, cyclicity, irregularities, autocorrelation, outliers, and noise. Understanding these components is crucial for analyzing and modeling time series data effectively. By identifying and isolating these components, we can gain a better understanding of the underlying patterns and relationships in time series data, which can inform decision-making and improve forecasting accuracy. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data | https://www.geeksforgeeks.org/components-of-time-series-data/?ref=next_article | Data Science & ML | Components of Time Series Data | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [0.00201365771, -0.0426039807, -0.00884386618, -0.0018532289, 0.00792186242, -0.0283239763, -0.0401256308, -0.0155191785, -0.0288107935, 0.00362532143, 0.0440791883, -0.00995764788, 0.0163747985, -0.0163600463, -0.00391298672, -0.0138226906, 0.00496776, -0.0103928335, 0.0498324931, -0.00159230165, -0.0233230237, 0.00868897, -0.0435481109, 0.0163895506, -0.0286927782, 0.0322185233, -0.00961097423, -0.00745717157, -0.071104981, 0.0361130685, 0.0180270299, 0.000560578716, 0.0116098793, -0.029238604, -0.0550252236, -0.038355384, 0.00383922644, 0.0105256028, 0.0315989368, 0.0314809196, -0.0265389755, 0.00816527102, -0.0135276485, -0.0291943476, -0.0260226522, 0.0359950513, -0.0315694325, 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05 Aug, 2024 | Pearson Correlation Coefficient
05 Aug, 2024
Pearson Correlation Coefficient: Correlation coefficients are used to measure how strong a relationship is between two variables. There are different types of formulas to get a correlation coefficient, one of the most popular is Pearson’s correlation (also known as Pearson’s r) which is commonly used for linear regression.
The Pearson correlation coefficient, often symbolized as (r), is a widely used metric for assessing linear relationships between two variables. It yields a value ranging from –1 to 1, indicating both the magnitude and direction of the correlation. A change in one variable is mirrored by a corresponding change in the other variable in the same direction.
This article provides detailed information on the Pearson Correlation Coefficient, its meaning, formula, interpretation, examples, and FAQs.
Table of Content
What is the Pearson Correlation Coefficient?
Pearson’s Correlation Coefficient Formula
Pearson Correlation Coefficient Table
Pearson Correlation Coefficient Origin
Types of Pearson Correlation Coefficient
Adjusted Correlation Coefficient
Weighted Correlation Coefficient
Reflective Correlation Coefficient
Scaled Correlation Coefficient
Pearson’s Distance
Circular Correlation Coefficient
Partial Correlation
Pearson Correlation Coefficient Interpretation
Finding the Correlation Coefficient with Pearson Correlation Coefficient Formula
Assumptions of Pearson Correlation Coefficient
Correlation Coefficient Properties
Pearson Correlation Coefficient Interpretation
Bivariate Correlation
Correlation Matrix
Pearson Correlation Coefficient Examples
Pearson Correlation Coefficient Practice Problems
What is the Pearson Correlation Coefficient?
The Pearson Correlation Coefficient, denoted as r, is a statistical measure that calculates the strength and direction of the linear relationship between two variables on a scatterplot. The value of r ranges between -1 and 1, where:
1 indicates a perfect positive linear relationship,
-1 indicates a perfect negative linear relationship, and
0 indicates no linear relationship between the variables.
Pearson’s Correlation Coefficient Formula
Karl Pearson’s correlation coefficient formula is the most commonly used and the most popular formula to get the statistical correlation coefficient. It is denoted with the lowercase “r”. The formula for Pearson’s correlation coefficient is shown below:
r = n(∑xy) – (∑x)(∑y) / √[n∑x²-(∑x)²][n∑y²-(∑y)²
The full name for Pearson’s correlation coefficient formula is Pearson’s Product Moment correlation (PPMC). It helps in displaying the Linear relationship between the two sets of the data.
Pearson’s correlation helps in measuring the correlation strength (it’s given by coefficient r-value between -1 and +1) and the existence (given by p-value ) of a linear correlation relationship between the two variables and if the outcome is significant we conclude that the correlation exists.
Cohen (1988) says that an absolute value of r of 0.5 is classified as large, an absolute value of 0.3 is classified as medium and an absolute value of 0.1 is classified as small.
The interpretation of the Pearson’s correlation coefficient is as follows:
A correlation coefficient of 1 means there is a positive increase of a fixed proportion of others, for every positive increase in one variable. Like, the size of the shoe goes up in perfect correlation with foot length.
If the correlation coefficient is 0, it indicates that there is no relationship between the variables.
A correlation coefficient of -1 means there is a negative decrease of a fixed proportion, for every positive increase in one variable. Like, the amount of water in a tank will decrease in a perfect correlation with the flow of a water tap.
The Pearson correlation coefficient essentially captures how closely the data points tend to follow a straight line when plotted together. It’s important to remember that correlation doesn’t imply causation – just because two variables are related, it doesn’t mean one causes the change in the other.
Pearson Correlation Coefficient Table
Pearson Correlation Coefficient (r) Range
Type of Correlation
Description of Relationship
New Illustrative Example
0 < r ≤ 1
Positive
An increase in one variable associates with an increase in the other.
Study Time vs. Test Scores: More hours spent studying tends to lead to higher test scores.
r = 0
None
No discernible relationship between the changes in both variables.
Shoe Size vs. Reading Skill: A person’s shoe size doesn’t predict their ability to read.
-1 ≤ r < 0
Negative
An increase in one variable associates with a decrease in the other.
Outdoor Temperature vs. Home Heating Cost: As the outdoor temperature decreases, heating costs in the home increase.
Pearson Correlation Coefficient Origin
The Pearson correlation coefficient, although named after statistician Karl Pearson, has a more interesting backstory. The concept of correlation itself can be traced back to Francis Galton, a 19th-century scientist and explorer. Galton was fascinated by inheritance and explored relationships between traits in families.
While Galton planted the seed for the idea, the mathematical formula behind the coefficient actually came from French physicist Auguste Bravais in 1844. However, it was Karl Pearson who truly championed the concept in the late 1800s. He refined the mathematical treatment, explored its properties, and popularized its use in statistical analysis. For this reason, the coefficient bears his name, even though earlier contributions played a crucial role in its development.
Types of Pearson Correlation Coefficient
Each type of Pearson correlation coefficient offers unique insights and analytical tools for various research fields, from statistics and psychology to economics and engineering. Understanding these variations enhances the accuracy and depth of correlation analyses, enabling more informed decision-making and hypothesis testing.
Adjusted Correlation Coefficient
Adjusted correlation coefficient modifies the standard Pearson correlation coefficient to account for sample size and bias, especially when dealing with small sample sizes. It adjusts the correlation coefficient to provide a more accurate estimation of the population correlation.
Weighted Correlation Coefficient
Weighted correlation coefficient assigns different weights to individual data points based on their importance or reliability. This approach is useful when certain observations carry more significance or have different levels of precision.
Reflective Correlation Coefficient
Reflective correlation coefficient evaluates the relationship between variables in a reflective model, commonly used in structural equation modeling (SEM) to analyze latent constructs. It assesses the relationship between observed variables and underlying constructs.
Scaled Correlation Coefficient
Scaled correlation coefficient scales the correlation coefficient to a specific range or magnitude, facilitating comparison across different datasets or studies. It ensures consistency in interpretation by standardizing correlation values.
Pearson’s Distance
Pearson’s distance measures the dissimilarity or similarity between two data points based on their correlation coefficient. It quantifies the extent of deviation from perfect correlation, providing insights into the relationship between variables.
Circular Correlation Coefficient
Circular correlation coefficient assesses the relationship between circular variables, such as angles or directions. It accounts for the cyclical nature of data and measures the degree of association between circular datasets.
Partial Correlation
Partial correlation evaluates the relationship between two variables while controlling for the effects of one or more additional variables. It measures the unique association between variables after accounting for the influence of other factors, allowing researchers to isolate specific statistical relationships.
Pearson Correlation Coefficient Interpretation
Pearson correlation coefficient (r) value
Strength
Direction
Greater than .5
Strong
Positive
Between .3 and .5
Moderate
Positive
Between 0 and .3
Weak
Positive
0
None
None
Between 0 and –.3
Weak
Negative
Between –.3 and –.5
Moderate
Negative
Less than –.5
Strong
Negative
Finding the Correlation Coefficient with Pearson Correlation Coefficient Formula
Steps to find the correlation coefficient with Pearson’s correlation coefficient formula:
Step 1: Firstly make a chart with the given data like subject, x, and y and add three more columns in it xy,x² and y².
Step 2: Now multiply the x and y columns to fill the xy column. For example:- in x we have 24 and in y we have 65 so xy will be 24×65=1560.
Step 3: Now, take the square of the numbers in the x column and fill the x² column.
Step 4: Now, take the square of the numbers in the y column and fill the y² column.
Step 5: Now, add up all the values in the columns and put the result at the bottom. Greek letter sigma (Σ) is the short way of saying summation.
Step 6: Now, use the formula for Pearson’s correlation coefficient:-
R = n(∑xy) – (∑x)(∑y) / √[n∑x²-(∑x)²][n∑y²-(∑y)²
To know which type of variable we have either positive or negative.
Assumptions of Pearson Correlation Coefficient
Linear Relationship: Karl Pearson’s correlation coefficient assumes a linear relationship between the two variables under consideration. It implies that as one variable changes, the other changes proportionally.
Normality: The variables should follow a normal distribution. While Pearson’s correlation coefficient is robust to deviations from normality, extreme departures may affect the validity of the correlation analysis.
Homoscedasticity: This assumption suggests that the variability in one variable should be consistent across all levels of the other variable. In other words, the spread of data points around the regression line should remain constant.
Interval or Ratio Scale: Pearson’s correlation coefficient is appropriate for variables measured on an interval or ratio scale. These scales ensure meaningful numerical distances between observations.
Independence: The observations used to compute the correlation coefficient should be independent of each other. Independence ensures that each data point contributes uniquely to the analysis without being influenced by other observations.
Correlation Coefficient Properties
Correlation Coefficient Range: The correlation coefficient r ranges from -1 to +1, inclusive. A value of -1 indicates a perfect negative linear relationship, +1 denotes a perfect positive linear relationship, and 0 represents no linear relationship.
Directionality: The sign of the correlation coefficient indicates the direction of the relationship between variables. A positive r indicates a positive association (both variables increase or decrease together), while a negative r suggests a negative association (one variable increases as the other decreases).
Magnitude: The magnitude of the correlation coefficient represents the strength of the relationship between variables. Values closer to -1 or +1 indicate a stronger linear relationship, while values closer to 0 suggest a weaker relationship.
No Causation: Pearson’s correlation coefficient does not imply causation between variables. It only measures the degree of linear association and does not establish a cause-and-effect relationship.
Symmetry: The correlation coefficient is symmetric, meaning the correlation between variables X and Y is the same as the correlation between Y and X.
Invariance: The correlation coefficient remains unchanged under linear transformations of the variables (e.g., multiplication by a constant or addition of a constant), making it invariant to changes in scale and location.
Pearson Correlation Coefficient Interpretation
Interpreting the Pearson correlation coefficient (r) involves assessing the correlation strength, direction, and correlation significance of the relationship between two variables. Here’s a guide to interpreting r:
Strength of Relationship:
Close to +1: Indicates a strong positive linear relationship. As one variable increases, the other tends to increase proportionally.
Close to -1: Suggests a strong negative linear relationship. As one variable increases, the other tends to decrease proportionally.
Close to 0: Implies a weak or no linear relationship. Changes in one variable do not consistently predict changes in the other.
Direction of Relationship:
Positive r: Both variables tend to increase or decrease together.
Negative r: One variable tends to increase as the other decreases, and vice versa.
Significance:
Statistical significance indicates whether the observed correlation coefficient is likely to occur due to chance.
Significance is typically assessed using a hypothesis test, such as the t-test for correlation coefficient, with the null hypothesis stating that the true correlation coefficient in the population is zero.
If the p-value is less than the chosen significance level (e.g., 0.05), the correlation is considered statistically significant.
Scatterplot Examination:
Visual inspection of a scatterplot can provide additional insights into the relationship between variables.
A scatterplot allows you to assess the linearity, directionality, and presence of outliers, complementing the numerical interpretation of r.
Caution:
Correlation does not imply causation. Even if a strong correlation is observed between two variables, it does not necessarily mean that changes in one variable cause changes in the other.
Other factors, such as confounding variables or omitted variables, may influence the observed correlation.
Sample Size:
Larger sample sizes tend to provide more reliable estimates of correlation coefficients, reducing the likelihood of obtaining spurious correlations.
Context Dependence:
The interpretation of r should consider the specific context and subject matter of the study. What is considered a strong or weak correlation may vary depending on the field of research and the variables under investigation.
Bivariate Correlation
Pearson’s correlation coefficient is a statistical tool used to measure bivariate correlation. This refers to the strength and direction of the linear relationship between two variables. It assesses how much one variable tends to change along with the other.
A positive correlation indicates that as one variable increases, the other tends to increase as well. Conversely, a negative correlation suggests that as one variable goes up, the other tends to go down. A value of zero indicates no linear relationship between the variables.
Correlation Matrix
The Pearson correlation coefficient is particularly useful when analyzing datasets with multiple variables. In such cases, a correlation matrix can be constructed. This is a square table that summarizes the correlation coefficients between all possible pairs of variables within the data set.
By looking at the correlation matrix, researchers can quickly identify which variables have strong positive, negative, or no linear relationship with each other. This helps them understand the overall structure of the data and identify potential relationships for further investigation.
Pearson Correlation Coefficient Examples
Example 1: There is some correlation coefficient that was given to tell whether the variables are positive or negative?
0.69, 0.42, -0.23, -0.99
Solution:
The given correlation coefficient is as follows:
0.69, 0.42, -0.23, -0.99
Tell whether the relationship is negative or positive
0.69: The relationship between the variables is a strong positive relationship
0.42: The relationship between the variables is a strong positive relationship
-0.23: The relationship between the variables is a weak negative relationship
-0.99: The relationship between the variables is a very strong negative relationship
Example 2: Calculate the correlation coefficient for the following data by the help of Pearson’s correlation coefficient formula:
X = 10, 13, 15 ,17 ,19
and
Y = 5,10,15,20,25.
Solution:
Given variables are,
X = 10, 13, 15 ,17 ,19
and
Y = 5,10,15,20,25.
To, find the correlation coefficient of the following variables Firstly a table is to be constructed as follows, to get the values required in the formula also add all the values in the columns to get the values used in the formula.
X
Y
XY
X²
Y²
10
5
50
100
25
13
10
130
169
100
15
15
225
225
225
17
20
340
289
400
19
25
475
362
625
∑74
∑75
∑1103
∑1144
∑1375
∑xy = 1103
∑x = 74
∑y = 75
∑x² = 1144
∑y² = 1375
n = 5
Put all the values in the Pearson’s correlation coefficient formula:-
R = n(∑xy) – (∑x)(∑y) / √ [n∑x²-(∑x)²][n∑y²-(∑y)²
R = 5(1103) – (74)(75) / √ [5(1144)-(74)²][5(1375)-(75)²]
R = -35 / √[244][1250]
R = -35/552.26
R = 0.0633
The correlation coefficient is 0.064
Example 3: Calculate the correlation coefficient for the following table with the help of Pearson’s correlation coefficient formula:
SUBJECT
AGE X
Weight Y
1
40
99
2
25
79
3
22
69
4
54
89
Solution:
Make a table from the given data and add three more columns of XY, X², and Y². also add all the values in the columns to get ∑xy, ∑x, ∑y, ∑x², and ∑y² and n =4.
SUBJECT
AGE X
Weight Y
XY
X²
Y²
1
40
99
3960
1600
9801
2
25
79
1975
625
6241
3
22
69
1518
484
4761
4
54
89
4806
2916
7921
∑
151
336
12259
5625
28724
∑xy = 12258
∑x = 151
∑y = 336
∑x² = 5625
∑y² = 28724
n = 4
Put all the values in the Pearson’s correlation coefficient formula:-
R = n(∑xy) – (∑x)(∑y) / √ [n∑x²-(∑x)²][n∑y²-(∑y)²
R = 4(12258) – (151)(336) / √ [4(5625)-(151)²][4(28724)-(336)²]
R = -1704 / √ [-301][-2000]
R = -1704/775.886
R = -2.1961
The correlation coefficient is -2.196
Example 4: Calculate the correlation coefficient for the following data with the help of Pearson’s correlation coefficient formula:
X = 5 ,9 ,14, 16
and
Y = 6, 10, 16, 20 .
Solution:
Given variables are,
X = 5 ,9 ,14, 16
and
Y = 6, 10, 16, 20 .
To, find the correlation coefficient of the following variables Firstly a table to be constructed as follows, to get the values required in the formula
also, add all the values in the columns to get the values used in the formula.
X
Y
XY
X²
Y²
5
6
30
25
36
9
10
90
81
100
14
16
224
196
256
16
20
320
256
400
∑ 44
∑ 52
∑ 664
∑ 558
∑ 792
∑xy= 664
∑x=44
∑y=52
∑x² =558
∑y² =792
n =4
Put all the values in the Pearson’s correlation coefficient formula:-
R= n(∑xy) – (∑x)(∑y) / √ [n∑x²-(∑x)²][n∑y²-(∑y)²
R= 4(664) – (44)(52) / √ [4(558)-(44)²][4(792)-(52)²]
R= 368 / √[296][464]
R=368/370.599
R=0.994
The correlation coefficient is 0.994
Example 5: Calculate the correlation coefficient for the following data by the help of Pearson’s correlation coefficient formula:
X = 21,31,25,40,47,38
and
Y = 70,55,60,78,66,80
Solution:
Given variables are,
X = 21,31,25,40,47,38
and
Y = 70,55,60,78,66,80
To, find the correlation coefficient of the following variables Firstly a table is to be constructed as follows, to get the values required in the formula also add all the values in the columns to get the values used in the formula.
X
Y
XY
X²
Y²
21
70
1470
441
4900
31
55
1705
961
3025
25
60
1500
625
3600
40
78
3120
1600
6084
47
66
3102
2209
4356
38
80
3040
1444
6400
∑202
∑409
∑13937
∑7280
∑28265
∑xy= 13937
∑x=202
∑y=409
∑x² =7280
∑y² =28265
n =6
Put all the values in the Pearson’s correlation coefficient formula:-
R= n(∑xy) – (∑x)(∑y) / √ [n∑x²-(∑x)²][n∑y²-(∑y)²
R= 6(13937) – (202)(409) / √ [6(7280)-(202)²][6(28265)-(409)²]
R= 1004 / √[2876][2909]
R=1004 / 2892.452938
R=-0.3471
The correlation coefficient is -0.3471
Example 6: Calculate the correlation coefficient for the following data by the help of Pearson’s correlation coefficient formula:
SUBJECT
Height X
Weight Y
1
43
78
2
24
68
3
26
85
4
35
67
Solution:
Make a table from the given data and add three more columns of XY , X² and Y² and add all the values in the columns to get ∑xy, ∑x, ∑y, ∑x² and ∑y² and n =4.
SUBJECT
Height X
Weight Y
XY
X²
Y²
1
43
78
3354
1849
6084
2
24
68
1632
576
4624
3
26
85
2210
676
7225
4
35
67
2345
1225
4489
∑
128
298
9541
4317
22422
∑xy= 9541
∑x=128
∑y=298
∑x² =4317
∑y² 22422
n =4
Put all the values in the Pearson’s correlation coefficient formula:-
R= n(∑xy) – (∑x)(∑y) / √ [n∑x²-(∑x)²][n∑y²-(∑y)²
R= 4(9541) – (128)(298) / √ [4(4317)-(128)²][4(22422)-(298)²]
R= 20 / √ [884][884]
R=20/884
R=0.02262
The correlation coefficient is 0.02262
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Pearson Correlation Coefficient Practice Problems
1. Given a Pearson correlation coefficient of r = 0.85 between the amount of time students spent studying and their score on a math test, interpret the strength and direction of the relationship.
2. You have data on the number of ice creams sold and the outdoor temperature. After calculating, you find r = −0.62. What does this say about the relationship between the temperature and ice cream sales?
3. Consider the following small dataset representing hours studied (X) and test scores (Y):
Hours Studied (X)
Test Score (Y)
1
50
2
55
3
65
4
70
5
80
Calculate the Pearson correlation coefficient (r) for the data.
Conclusion of Pearson Correlation Coefficient
The Pearson Correlation Coefficient (r) is a statistical measure of the strength and direction of a linear relationship between two variables on a scatterplot. It ranges from -1 to 1, with 1 indicating a perfect positive relationship, -1 indicating a perfect negative relationship, and 0 indicating no linear relationship. The formula involves summing products of paired scores and dividing by the square root of the product of the sums of squared scores. While r quantifies the degree of linear association, it doesn’t imply causation. Developed by Francis Galton, Auguste Bravais, and Karl Pearson, it’s foundational in fields like psychology and economics, aiding in the analysis of linear relationships under certain assumptions about the data.
Pearson Correlation Coefficient – FAQs
What is Karl Pearson’s coefficient of correlation?
Karl Pearson’s coefficient of correlation, commonly known as the Pearson correlation coefficient (r), is a statistical measure that quantifies the strength and direction of the linear relationship between two continuous variables. Correlation coefficient ranges from -1 to +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 suggests no linear relationship.
What is the Pearson correlation coefficient?
The Pearson correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It is calculated by dividing the covariance of the two variables by the product of their standard deviations.
What is the formula for Pearson Correlation Coefficient?
r = n(∑xy) – (∑x)(∑y) / √[n∑x²-(∑x)²][n∑y²-(∑y)²
Why do we use the Pearson correlation coefficient?
The Pearson correlation coefficient is used to assess the strength and direction of the linear relationship between two variables. It helps researchers and analysts understand how changes in one variable correspond to changes in another, aiding in hypothesis testing, model building, and making predictions in various fields such as psychology, economics, biology, and social sciences.
What does Pearson’s correlation coefficient tell you?
Pearson’s correlation coefficient quantifies the strength and direction of the linear relationship between two variables. It tells us whether the variables move together (positive correlation), move in opposite directions (negative correlation), or have no discernible pattern of movement (zero correlation).
What is the difference between r2 and Pearson correlation?
The Pearson correlation coefficient ( r) measures the strength and direction of the linear relationship between two variables, while r2 (the coefficient of determination) represents the proportion of variance in one variable that is predictable from the other variable in a linear regression model. In essence, r2 is the square of the Pearson correlation coefficient and provides a measure of the goodness of fit of a linear regression model.
What is a good correlation coefficient?
A good correlation coefficient depends on the context and the specific field of study. Generally, a correlation coefficient close to +1 or -1 indicates a strong linear relationship between variables, while a coefficient close to 0 suggests a weak or no linear relationship. However, what constitutes a “good” correlation varies depending on the research question, field of study, and practical implications.
What does a correlation coefficient of 0.5 mean?
A correlation coefficient of 0.5 indicates a moderate positive linear relationship between two variables. It suggests that as one variable increases, the other tends to increase as well, but the relationship is not perfect.
What does a 0.2 correlation mean?
A correlation coefficient of 0.2 suggests a weak positive linear relationship between two variables. While there is some tendency for the variables to move together, the relationship is relatively weak and may not be practically significant without further context.
Is a correlation coefficient of 0.4 strong?
A correlation coefficient of 0.4 indicates a moderate positive linear relationship between two variables. While not as strong as coefficients closer to +1, a value of 0.4 still suggests a discernible pattern of association between the variables, which may be meaningful depending on the context of the study. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant 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27 Sep, 2024 | Differential Equations
27 Sep, 2024
A differential equation is a mathematical equation that relates a function with its derivatives. Differential Equations come into play in a variety of applications such as Physics, Chemistry, Biology, Economics, etc. Differential equations allow us to predict the future behavior of systems by capturing the rate of change of a quantity and how it depends on other variables.
In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Let’s formally define what is a differential equation.
What is a Differential Equation?A differential equation is an equation involving the derivatives of the dependent variable concerning the independent variable. For example
[Tex]\frac{d^{2}y}{dx} + x = 0[/Tex]
Here, x is the independent variable, and y is the dependent variable.
Differential EquationsA differential equation that includes derivatives concerning only one independent variable is called an ordinary differential equation. There also exist some differential equations which have derivatives for more than one independent variable, they are called partial differential equations.
Example: [Tex]2\frac{d^{2}y}{dx} + 3\frac{dy}{dx} + 1 = 0 [/Tex]an ordinary differential Equation.
Note: Following notations are also used for denoting higher order derivatives.
[Tex]y’ = \frac{dy}{dx} = y_{1}[/Tex][Tex]y”’ = \frac{d^{3}y}{dx} = y_{3}[/Tex]
Table of Content
What is a Differential Equation?Order of a Differential EquationDegree of Differential EquationTypes of Differential EquationsGeneral And Particular Solution of Differential EquationFormation of a Differential Equation When General Solution is GivenHomogeneous Differential EquationsVariable Separable Differential EquationWriting a Differential EquationPractice Question on Differential Equation Differential Equations Class 12
Order of a Differential EquationThe order of differential equations is the highest order of the derivative present in the equations.
For example:
[Tex]x + \frac{dy}{dx} = 3[/Tex]. It has an order of 1.[Tex]\frac{d^{2}y}{dx} + sinxcosx = 10 [/Tex]. It has an order of 2.[Tex]\frac{d^{3}y}{dx} + \frac{d^{2}y}{dx} + x^{3} + 5 = 0 [/Tex]. It has an order of 3.Degree of Differential EquationThe degree of a differential equation(when it is a polynomial equation in derivatives) is the highest power (positive integral index) of the highest-order derivative involved in the given differential equation.
Examples:
[Tex](\frac{dy}{dx})^{2} +\frac{d^{2}y}{dx} + 5 = 0 [/Tex]. Highest order derivative :[Tex]\frac{d^{2}y}{dx}[/Tex] and the degree of differential equation is 1. [Tex]\left( \frac{d^2y}{dx^2} \right)^3 + \frac{dy}{dx} = 0[/Tex]. Highest order derivative :[Tex]\frac{d^{2}y}{dx}[/Tex] and the degree of differential equation is 3. [Tex]\frac{d^3y}{dx^3} + 5\left(\frac{d^2y}{dx^2}\right)^2 – 3\frac{dy}{dx} + y = 0[/Tex] Highest order derivative is [Tex]\frac{d^3y}{dx^3}[/Tex] and the degree of differential equation is 1. Note: It is not always necessary that degree and order of a differential equation are equal, but both of them must be positive.
Types of Differential EquationsDifferential equations can be divided into several types namely
Ordinary Differential EquationsPartial Differential EquationsLinear Differential EquationsNonlinear differential equationsHomogeneous Differential EquationsNonhomogeneous Differential EquationsGeneral And Particular Solution of Differential EquationGeneral Solution of Differential Equation : The general solution is a complete form of the solution. It contains one or more arbitrary constants (or functions, in some cases) which can take any value. The general solution represent the family of all possible solutions to the differential equation.
Particular Solution of Differential Equation : A particular solution is obtained when some initial conditions or boundary conditions are provided, that allow us to find the exact value of the arbitrary constants in the general solution.
Consider a differential equation,
[Tex]\frac{d^{2}y}{dx^{2}} + y = 0[/Tex]
The solution of this differential equation is a function [Tex]\phi [/Tex] that will satisfy it, i.e when a function \phi is substituted for the unknown “y”. L.H.S becomes equal to R.H.S.
The curve[Tex] y = \phi(x) [/Tex] is called the solution of the differential equation. Let’s say, this function is,
[Tex]y = \phi(x) = a cos(x + b) [/Tex]
When this function and its derivatives are substituted in the differential equation, the equation is satisfied and this function is called as general solution of differential equation.
Let’s assume that we gave some values to “a” and “b”, where a = 2 and b = -1. Then the equation becomes,
[Tex]y = \phi_{1}(x) = 2 cos(x -1 )[/Tex]
This is called a particular solution which consisted specific values of arbitrary constants of a and b defined in the General Solution.
Formation of a Differential Equation When General Solution is GivenLet’s look at the steps/procedure to form a differential equation from a general solution:
If a family of curves depends only on one parameter, then it is represented by an equation that can be written in the form, F(x, y, a) = 0. Differentiating this equation with x gives us an equation in y’, y, x and a which can be represented as g(x, a, y, y’) = 0. Now, the differential equation can be formed by eliminating the parameter “a” from both of the equations.If a family of curves depends on two parameters “a” and “b”, then it is represented by an equation that can be written in a form, F(x, y, a, b) = 0. Differentiating this equation with x gives us an equation in y’, y, x, a and b which can be represented as g(x, a, b, y, y’) = 0. We cannot eliminate “a” and “b” from those two equations. So, we will differentiate the equation again to get g(x, a, b, y, y’, y”) = 0. Now, the differential equation can be formed by eliminating the parameter “a” and “b” from all three of these equations.Steps to generate differential equation whose general solution is given Step 1: Identify the general solution. Start with the general solution of the equation.
[Tex]y = C_1 e^{2x} + C_2 e^{-2x}[/Tex]
Step 2: Differentiate the general solution. Differentiate the general solution with respect to the independent variable (usually xxx) to eliminate the arbitrary constants. The number of times you differentiate depends on how many arbitrary constants are present. If there are two constants, differentiate twice, and so on.
[Tex]\frac{dy}{dx} = 2C_1 e^{2x} – 2C_2 e^{-2x}[/Tex]
If necessary, differentiate again:
[Tex]\frac{d^2y}{dx^2} = 4C_1 e^{2x} + 4C_2 e^{-2x}[/Tex]
Step 3: Eliminate the arbitrary constants. Use the derivatives to substitute for the arbitrary constants.
[Tex]\frac{d^2y}{dx^2} = 4y[/Tex]
Step 4: Form the differential equation. After eliminating the constants, express the relationship between the function and its derivatives in the form of a differential equation.
[Tex]\frac{d^2y}{dx^2} – 4y = 0[/Tex]
Step 5: Verify the result. verify the differential equation by checking if the general solution satisfies it.
Let’s see these steps through examples,
Question 1: Form the differential equation representing the family of curves y = mx, where, m is an arbitrary constant.
Solution:
We have y = mx,
Differentiating it both sides,
[Tex]\\ \frac{dy}{dx} = m, [/Tex]
Substituting the value of m in the original equation,
[Tex]y = \frac{dy}{dx}x \\ y – \frac{dy}{dx}x = 0[/Tex]
Question 2: Form the differential equation representing the family of ellipses having foci on the x-axis and centre at the origin.
Solution:
Equation of ellipses with foci on x-axis and centre at origin,
[Tex]\\ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 [/Tex]
Differentiating equations w.r.t x,
[Tex]\\ \frac{2x}{a^2} + \frac{2ydy}{b^2dx } = 0 \\ \frac{y}{x}(\frac{dy}{dx}) = \frac{-b^{2}}{a^{2}}[/Tex]
Differentiating both sides again we get,
[Tex]\\ xy\frac{d^2y}{dx^2} + x(\frac{dy}{dx})^2 -y\frac{dy}{dx} = 0 [/Tex]
This is the required differential equation.
Homogeneous Differential EquationsA homogeneous differential equation is a type of differential equation in which every term is either a multiple of the dependent variable (and its derivatives) or it equals zero.
A function f(x, y) is called a homogeneous function of degree n if,
F(ax, ay) = anF(x, y)
for any constant “a”.
A differential equation of the form [Tex]\frac{dy}{dx} = F(x,y) [/Tex] is called homogeneous if F(x, y) is a homogeneous function of degree zero.
Question: Check whether the differential equation, [Tex](x-y)\frac{dy}{dx} = x + 2y [/Tex] is homogeneous.
Solution:
[Tex]\frac{dy}{dx} = \frac{x + 2y}{x – y}[/Tex]
Let,
[Tex]\\ F(x,y) = \frac{x + 2y}{x-y} [/Tex]
Let a be a constant,
[Tex]\\ F(ax,ay) = \frac{ax + 2ay}{ax – ay}\\ = \frac{x + 2y}{x – y}a^{0}\\ = a^{0}F(x,y)[/Tex]
Since this function is homogeneous, the differential equation is also homogeneous.
Variable Separable Differential EquationA variable separable differential equation (or separable differential equation) is a type of first-order differential equation that can be rewritten in such a way that all terms involving the dependent variable y are on one side of the equation and all terms involving the independent variable x are on the other side.
Consider a first-order differential equation of the form,
[Tex]\frac{dy}{dx} = F(x,y)[/Tex]
If F(x, y) can be expressed as h(x)g(y) where h(x) is a function of x and g(x) is a function of y. Then the equation is called a differential equation of variable separable type. The differential equation has the form,
[Tex]\frac{dy}{dx} = h(x)g(x) [/Tex]
Question: Find the general solution of the differential equation,
[Tex]\frac{dy}{dx} = \frac{x+1}{2-y} (y \ne 2)[/Tex]
Solution:
[Tex]\frac{dy}{dx} = \frac{x+1}{2-y} \\ (2 – y)dy = (x +1)dx \\ \int (2 – y)dy = \int (x + 1)dx \\ 2y – \frac{y^2}{2} = \frac{x^2}{2} + x + C \\ 4y – y^2 -x^2 -4x = C[/Tex]
Solution to a Linear Differential EquationA linear differential equation is a differential equation that can be made to look like in this form:
[Tex]\frac{dy}{dx} + P(x)y = Q(x)[/Tex]
where P(x) and Q(x) are the functions of x. It is solved using a special approach:
Make two new functions of x, call them u and v, and say that y = uv.Then solve to find u, and then v.Step-by-step procedure:
Step 1: Substitute y = uv, and
[Tex]\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}[/Tex]
into,
[Tex]\frac{dy}{dx} + P(x)y = Q(x)[/Tex]
Step 2: Now, one should factor the parts that have “v”.
Step 3: Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step) Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
Step 4: Solve “u” and then put it back in the equation to find “v”.
Step 5: Finally, y = uv is the solution.
Let’s look at an example to understand it better,
Question: Solve [Tex]\frac{dy}{dx} – \frac{y}{x} = 1[/Tex]
Solution:
This is a linear equation. Let’s bring it in the form specified above.
[Tex]\frac{dy}{dx} + P(x)y = Q(x)[/Tex]
Here, P(x) = -1/x and Q(x) = 1.
So, let’s follow the steps given above. Substitute y = uv in the equation. Then the equation becomes,
[Tex]u\frac{dv}{dx} + v\frac{du}{dx} – \frac{uv}{x} = 1 \\ = u\frac{dv}{dx} + v(\frac{du}{dx} – \frac{u}{x}) = 1[/Tex]
Put the parts involving “v” equal to zero.
[Tex]\frac{du}{dx} – \frac{u}{x} = 0\\ = \frac{du}{u} = \frac{dx}{x} \\ = \int \frac{du}{u} = \int \frac{dx}{x} \\ = ln(u) = ln(x) + C \\ = ln(u) = ln(x) + ln(k) \\ = ln(u) = ln(xk) \\ = u = xk[/Tex]
Substituting “u” back into the equation.
[Tex]kx\frac{dv}{dx} = 1[/Tex]
Now, let’s solve this to find “v”.
[Tex]kx\frac{dv}{dx} = 1 \\ = dv = \frac{1}{k}\frac{dx}{x}\\ = \int dv = \int \frac{1}{k}\frac{dx}{x} \\ = v = \frac{ln(x)}{k} + ln(c) \\ = v= \frac{ln(xc)}{k}[/Tex]
Substitute both “u” and “v” into the equations y = uv.
[Tex]y = uv \\ = kx \frac{1}{k}ln(cx)\\ = xln(cx) [/Tex]
So, this is the solution for this differential equation.
Writing a Differential EquationNow let’s move on to modelling a differential equation. Modelling is the process of writing a differential equation that describes a physical situation. We will see how to model first-order differential equations, modelling more complex orders is out of scope at this level of study.
Example: Savings Account Model
Write x(t) for the number of dollars in the account at time t. It accrues interest at an interest rate r. The interest rate has units of percent/year. The more money in the account the more interest you earn. At the end of an interest period of Δt years (e.g. Δt = 1/12, or Δt = 1/365) the bank adds “r.x(t)·Δt” dollars to your account. This means the change Δx in your account is
Δx = r.x(t).Δt
r has units of (years)−1. Mathematicians and some bankers like to take things to the limit. Rewrite our equation as [Tex] \frac{Δx}{\Delta t} = rx(t) [/Tex], and suppose that the interest period is made to get smaller and smaller. In the limit as Δt → 0, we get the differential equation
[Tex]\dot{x} = rx[/Tex]
Now suppose we make contributions to this savings account. We’ll record this by giving the rate of savings, q. This rate has units dollars per year, so if you contribute every month then the monthly payments will be q Δt with Δt = 1/12. This payment also adds to your account, so, when we divide by Δt and take the limit, we get
[Tex]\dot{x} = rx + q. [/Tex]
This is a linear differential equation.
Practice Question on Differential Equation Question 1 : Solve the differential equation: [Tex]\frac{dy}{dx} + 2y = e^{-x}[/Tex]
Question 2: Solve the homogeneous differential equation: [Tex]\frac{dy}{dx} = \frac{x^2 + xy}{y^2 + xy}[/Tex]
Question 3: Solve the second-order differential equation: [Tex]\frac{d^2y}{dx^2} – 5\frac{dy}{dx} + 6y = 0[/Tex]
Question 4: Find the differential equation for the given general solution [Tex]y = C_1 e^{2x} + C_2 e^{-2x}[/Tex]
Differential Equations Class 12 Below are the links to differential equations notes and ncert solutions for class 12:
Differential Equations Class 12 NotesDifferential Equations Class 12 NCERT SolutionsConclusionDifferential equations serve as fundamental tools in mathematics and science for modeling dynamic systems and describing how quantities change over time or space. Through their various types, including ordinary and partial, linear and nonlinear, homogeneous and nonhomogeneous, exact and non-exact, differential equations provide a versatile framework for analyzing a wide range of phenomena.
Differential Equations – FAQsWhat is a differential equation?A differential equation is an equation that relates a function with one or more of its derivatives. It describes how a function changes in relation to its input variables. In essence, it expresses a relationship between a function and its rate of change.
How do you solve a first-order differential equation?First-order differential equations can be solved using various techniques depending on their form. Common methods include separation of variables, integrating factors, exact equations, and using linear or Bernoulli differential equation forms.
What are the applications of differential equations?Differential equations find numerous applications in diverse fields. They are used to model population growth and decay, radioactive decay, chemical reactions, heat transfer, fluid dynamics, electrical circuits, and mechanical systems, among others.
What is the difference between ordinary and partial differential equations?Ordinary differential equations (ODEs) involve functions of a single independent variable and their derivatives with respect to that variable. In contrast, partial differential equations (PDEs) involve functions of multiple variables and their partial derivatives with respect to those variables.
How do you solve a second-order linear differential equation with constant coefficients?Second-order linear differential equations with constant coefficients are solved using characteristic equations or auxiliary equations. 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17 Dec, 2024 | Logarithmic Differentiation
17 Dec, 2024
Method of finding a function’s derivative by first taking the logarithm and then differentiating is called logarithmic differentiation. This method is specially used when the function is type y = f(x)g(x). In this type of problem where y is a composite function, we first need to take a logarithm, making the function log (y) = g(x) log (f(x)).
Logarithmic Differentiation helps to find the derivatives of complicated functions, using the concept of logarithms. Sometimes finding the differentiation of the function is very tough but differentiating the logarithm of the same function is very easy, then in such cases, the logarithmic differentiation formula is used.
Note: Logarithmic differentiation is generally used to differentiate functions of form f(x)g(x), f(x)/g(x), f(x)g(x), and others.
Formula for Logarithmic DifferentiationFor a function, y = f(x)g(x), differentiation is given by the following formula:
[Tex]\bold{\frac{dy}{dx} = y\left[g(x)\cdot \frac{f'(x)}{f(x)} + log(f(x))g'(x)\right]}[/Tex]
Logarithmic formulas are very useful in solving logarithmic differentiation. Some of the important logarithmic properties used are,
log XY = log X + log Ylog X/Y = log X – log Ylog X Y = Y log X log Y X = (log X) / (log Y) Note: Logarithmic differentiation rules are only valid for the positive functions only because logarithm of negative function is undefined.
Derivation of Logarithmic Differentiation FormulaLet us consider a function y = f(x)g(x), and take the natural logarithm of this function to differentiate it,
ln y = ln (f(x)g(x))⇒ ln (y) = g(x) ln (f(x))
Differentiate the above equation,
[Tex]\frac{d [\ln y]}{dx} = \frac{d}{dx}[g(x) \cdot \ln f(x)[/Tex][Tex]\Rightarrow \frac{1}{y} \cdot \frac{dy}{dx} = g'(x) \ln(f(x)) + g(x) \cdot \frac{d}{dx}(\ln(f(x)))[/Tex][Tex]\Rightarrow \frac{dy}{dx} = y \left(g'(x) \ln(f(x)) + g(x) \cdot \frac{d}{dx}(\ln(f(x)))\right)[/Tex][Tex]\Rightarrow \frac{dy}{dx} = y \left[g'(x) \ln(f(x)) + g(x) \cdot \frac{f'(x)}{f(x)}\right][/Tex]
Which is the required formula.
How to Perform Logarithmic Differentiation?The steps involved in differentiating a logarithmic function are summarized below,
Take log on both sides,Use logarithmic properties to simplify the function,Now differentiate the equation with respect to x,Simplify the obtained equation,Substitute back the value of y.Following the above result one can easily find the differentiation of functions using logarithm.
Let’s consider an example for better understanding.
Example: Find the derivative of xx.
Solution:
Let y = xx
Step 1: Taking log on both sideslog(y) = log(xx)
Step 2: Use logarithmic property to simplify the equationlog(y) = x ⋅ log(x) [Using property log(ab) = b⋅ log(a)]
Step 3: Now differentiate the equation with respect to x,[Tex]\frac{d}{d x} \log (y)=\frac{d}{d x}(x \cdot \log (x)) \\ \frac{d}{d x} \log (y)=x \cdot \frac{d}{d x} \log (x)+\log (x) \cdot \frac{d x}{d x} \\ \frac{1}{y} \frac{d y}{d x}=x \cdot \frac{1}{x}+\log (x)[/Tex]
Step 4: Simplify the obtained equation[Tex]\frac{d y}{d x}=y(1+\log (x))[/Tex]
Step 5: Substitute back the value of y[Tex]\frac{d y}{d x}=x^{x}(1+\log (x))[/Tex]
Applications of Log DifferentiationLog differentiation found its application while solving various differentiation problems. Various types of problems where Log Differentiation is used are discussed below,
Product of Functions (Product Rule)The differentiation of any function which is a product of two functions can easily be calculated using logarithmic differentiation.
Suppose we have to find differentiation of f(x) where, f(x) = g(x) × h(x) then by using concept of logarithmic differentiation,
f(x) = g(x) × h(x)
Taking log on both sides,
log f(x) = log (g(x) × h(x))⇒ log f(x) = log g(x) + log h(x) [Using property log (XY) = log (X) + log (Y)]
Differentiating both sides with respect to x,
d/dx [log f(x)] = d/dx [log g(x)] + d/dx [log h(x)]⇒ f'(x)/f(x) = g'(x)/g(x) + h'(x)/h(x)⇒ f'(x) = f(x) [g'(x)/g(x) + h'(x)/h(x)]⇒ f'(x) = f(x) [(h(x) × g'(x) + g(x) × h'(x))/ (g(x) × h(x))]⇒ f'(x) = g(x) × h(x) [h(x) × g'(x) + g(x) × h'(x)] / g(x) × h(x)
∴ f'(x) = h(x) × g'(x) + g(x) × h'(x)
The result obtained above is the “Leibniz rule” and is commonly known as the “Product rule“.
Division of Functions (Quotient Rule)The differentiation of any function which is in the form of a division of two functions can easily be calculated using logarithmic differentiation.
Suppose one has to find the differentiation of f(x) where f(x) = g(x) / h(x) by using the concept of logarithmic. differentiation,
f(x) = g(x)/h(x)
Taking log on both sides,
log f(x) = log [g(x)/h(x)]⇒ log f(x) = log g(x) – log h(x) [Using property log (X/Y) = log (X) – log (Y)]
Differentiating both sides with respect to x,
d/dx [log f(x)] = d/dx [log g(x)] – d/dx [log h(x)]⇒ f'(x)/f(x) = g'(x)/g(x) – h'(x)/h(x)⇒ f'(x) = f(x)[g'(x)/g(x) – h'(x)/h(x)]⇒ f'(x) = f(x) [(g'(x) × h(x) – g(x) × h'(x))/(g(x) × h(x))]⇒ f'(x) = g(x)/h(x) [g'(x) × h(x) – g(x) × h'(x)]/g(x) × h(x)
∴ f'(x) = [g'(x) × h(x) – g(x) × h'(x)] / h2(x)
The result obtained above is commonly known as the “Quotient rule“.
Also, Check
Laws of LogarithmsLogarithmic FunctionAdvanced DifferentiationImplicit DifferentiationDifferentiation and Integration FormulaSolved Examples on Logarithmic DifferentiationExample 1: Find the derivative of [Tex]x^{\left(x^{x}\right)}[/Tex]?
Solution:
Given, y = [Tex]x^{\left(x^{x}\right)}[/Tex]
Step 1: Taking log on both sides,log(y) = log([Tex]x^{\left(x^{x}\right)}[/Tex])
Step 2: Use logarithmic property to simplify the equationlog(y) = xx⋅ log(x) [Using property log(ab) = b⋅ log(a)]
Step 3: Differentiating both sides with respect to x,[Tex]\frac{d}{d x} \log (y)=\frac{d}{d x}\left(x^{x} \cdot \log (x)\right) \\ \frac{d}{d x} \log (y)=x^{x} \cdot \frac{d}{d x} \log (x)+\log (x) \cdot \frac{d}{d x} x^{x}\left\{f^{\prime}(u . v)=u . f^{\prime}(v)+v \cdot f^{\prime}(u)\right\} \\ \frac{1}{y} \frac{d y}{d x}=x^{x} \cdot \frac{1}{x}+\log (x) \frac{d}{d x} x^{x} \left\{f^{\prime}(\log x)=\frac{1}{x}\right\}\\ \frac{1}{y} \frac{d y}{d x}=x^{x-1}+\log (x) \frac{d}{d x} x^{x}[/Tex]
Step 4: Simplify the obtained equation,
Since now we know the derivative of xx, We will substitute here directly.[Tex]\frac{1}{y} \frac{d y}{d x}=x^{x-1}+\log x \cdot x^{x}(1+\log x) \\ \frac{d y}{d x}=y\left(x^{x-1}+\log x \cdot x^{x}(1+\log x)\right)[/Tex]
Step 5: Substitute back the value of y[Tex]\frac{d y}{d x}=x^{\left(x^{x}\right)}\left(x^{x-1}+\log x \cdot x^{x}(1+\log x)\right)[/Tex]
Example 2: Find the derivative of y = (log x)x.
Solution:
Given, y = (logx)x
Step 1: Taking log on both sides,log(y) = log((logx)x)
Step 2: Use logarithmic property to simplify the equationlog(y) = x ⋅ log(logx) [using property log(ab) = b⋅ log(a)]
Step 3: Differentiating both sides with respect to x,[Tex]\frac{d}{d x} \log (y)=\frac{d}{d x}(x \cdot \log (\log x)) \\ \frac{d}{d x} \log (\mathrm{y})=x \cdot \frac{d}{d x} \log (\log x)+\log (\log x) \cdot \frac{d x}{d x} \\ \frac{1}{y} \frac{d y}{d x}=x \cdot \frac{1}{\log x} \cdot \frac{1}{x}+\log (\log x)[/Tex]
Step 4: Simplify the obtained equation, [Tex]\frac{1}{y} \frac{d y}{d x}=\frac{1}{\log x}+\log (\log x) \{ using~chain~rule \} \\ \frac{d y}{d x}=y \cdot\left(\frac{1}{\log x}+\log (\log x)\right) \\[/Tex]
Step 5: Substitute back the value of y[Tex]\frac{d y}{d x}=(\log x)^{x} \cdot\left(\frac{1}{\log x}+\log (\log x)\right)[/Tex]
Example 3: Find the derivative of y = x√x.
Solution:
Given, y = x√x
Step 1: Taking log on both sides,log(y) = log(x√x)
Step 2: Use logarithmic property to simplify the equationlog(y) = √x⋅ log(x) [using property log(ab) = b⋅ log(a)]
Step 3: Differentiating both sides with respect to x,[Tex]\frac{d}{d x} \log (y)=\frac{d}{d x}(\sqrt{x} \cdot \log (x))\\ \frac{d}{d x} \log (\mathrm{y})=\sqrt{x} \cdot \frac{d}{d x} \log (\mathrm{x})+\log (x) \cdot \frac{d \sqrt{x}}{d x}[/Tex]
Step 4: Simplify the obtained equation, [Tex]\frac{1}{y} \frac{d y}{d x}=\sqrt{x} \cdot \frac{1}{x}+\log (x) \cdot \frac{1}{2 \sqrt{x}} \\ \frac{1}{y} \frac{d y}{d x}=\frac{1}{\sqrt{x}}+\log (x) \cdot \frac{1}{2 \sqrt{x}} \\ \frac{d y}{d x}=y \cdot\left(\frac{1}{\sqrt{x}}+\log (\mathrm{x}) \cdot \frac{1}{2 \sqrt{x}}\right) \\[/Tex]
Step 5: Substitute back the value of y[Tex]\frac{d y}{d x}=\mathrm{x}^{\sqrt{x}} \cdot\left(\frac{1}{\sqrt{x}}+\log (\mathrm{x}) \cdot \frac{1}{2 \sqrt{x}}\right)[/Tex]
Practice Questions on Logarithmic DifferentiationQ1: Differentiate the function y = (sin x)cos x with respect to x.
Q2: Find the derivative of the function y = (log x)log x with respect to x.
Q3: Differentiate the function y = (x2 + 1)x – 1 with respect to x.
Q4: Find the derivative of the function y = (tan x)cot x with respect to x.
Q5: Differentiate the function y = (ex)x with respect to x.
Answer Key[Tex]\frac{dy}{dx} = (\sin x)^{\cos x} \left( -\sin x \ln(\sin x) + \cos x \cot x \right)[/Tex][Tex]\frac{dy}{dx} = (\log x)^{\log x} \left( \frac{\ln(\log x)}{x} + \frac{1}{x} \right)[/Tex][Tex]\frac{dy}{dx} = (x^2 + 1)^{x – 1} \left( \ln(x^2 + 1) + \frac{2x(x – 1)}{x^2 + 1} \right)[/Tex][Tex]\frac{dy}{dx} = (\tan x)^{\cot x} \left( -\csc^2 x \ln(\tan x) + \cot x \cdot \frac{\sec^2 x}{\tan x} \right)[/Tex][Tex]\frac{dy}{dx} = e^{x \ln x} \left( \ln x + 1 \right)[/Tex]FAQs on Logarithmic DifferentiationWhat is the Formula of Logarithmic Differentiation?Logarithmic Differentiation of a function f(x) is found by dividing the differentiation of the function by the function itself. i.e.
d/dx [log f(x)] = f ‘(x)/f(x)
Logarithmic differentiation of a function is calculated using the chain rule of differentiation. These functions are also used to solve exponential functions.
When Logarithmic Differentiation is used?Logarithmic differentiation is used when one need to find the differentiation of the complex function, such as, multiplication or division of two fucntions, a function in power of another function, etc. Logarithmic differentiation solves such types of complex functions very easily.
What are the Examples of Log Differentiation?Logarithmic differentiation is used to solve different functions, such as, exponential ecos x, product (x + 5)3 (x2 + 2)3, exponent (cos x)sin x , etc.
What are the Different Rules of Logarithmic Differentiation?Logarithmic differentiation uses the following rules to obtain the differentiation of the complex functions, such as,
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30 Dec, 2024 | Change of base rule for Logarithm
30 Dec, 2024
The change of base formula is a useful concept in mathematics. That allows you to convert a logarithm from one base to another. Change of base formula in logarithm allows us to rewrite a logarithm with a different base. It allows us to compute logarithms using calculators or computational tools that may only support logarithms with certain bases, typically base 10 (log10) or natural logarithms (ln) which are present in scientific calculators. So, instead of calculating the logarithm directly with the given base, we can use a different base and adjust the formula accordingly.
Formula for Base Change of Log
This formula expresses a logarithm of a number with a particular base as a ratio of two logarithms, each with a different base than the original logarithm. This is a logarithmic characteristic. The formula is given as:
logba = logca / logcb orlogba . logcb = logca
Derivation of Change of Base Formula
Below is the derivation of Change of Base Formula.
If logba = p, logca = q and logcb = r.
Then, a = bp, a = cq, and b = cr.
Also, bp = cq.
Substituting b = cr, we have:⇒ (cr)p = cq
Using (am)n = amn⇒ crp = cq⇒ pr = q
p = q/r
Substituting the values of p, q, and r, we have:logba = logca / log b.
Importance of Change of Base in Log
The rule of base change is a logarithmic property that enables the input of a logarithm with a base other than 10 into a calculator.
The equation is: logdc = log10c/log10d
The base change formula is useful for calculating logarithms on a calculator that only supports base 10.
The base change formula can also help simplify certain logarithmic expressions.
The base change formula is compatible with the natural logarithm, ln: log(b) = ln(b)/ln(a) .
Most calculators provide the option to input the base of a logarithm.
The formula is only applicable to logarithms with positive bases.
Both the numerator and the denominator of the formula represent logarithms with the same base c.
Solved Questions using Change of Base Formula
Question 1: Evaluate log648 using the change of base formula.Solution:
log648 = {log 8}/{log 64}⇒ log648 = log 8/ log 82
Using the property log am = m log a, we have:
⇒ log648 = log 8/ 2 log 8⇒ log648 = 1/2
Question 2: Evaluate log119.Solution:
Using the change of base formula, we have:
log119 = log 9/ log 11 = 0.95452/1.0413 = 0.91667
Question 3: Evaluate log98.Solution:
Using the change of base formula, we have:
log98 = log 8/ log 9 = 0.90308/0.95424 = 0.9464
Question 4: Evaluate log1110.Solution:
Using the change of base formula, we have:
log1110= log 10/ log 11= 0.8655/0.57849 = 0.8755
Question 5: Evaluate log65.Solution:
Using the change of base formula, we have:
log65 = log 5/ log 6 = 0.8982
Question 6: Evaluate log43.Solution:
Using the change of base formula, we have:
log43 = log 3/ log 4 = 0.7924
Question 7: Evaluate log87.Solution:
Using the change of base formula, we have:
log87 = log 7/ log 8 = 0.9357
Also read,
Logarithms – Complete tutorial
Difference between Logarithm (log) and Natural log( ln)
Logarithm Formulas
Properties of Logarithms
Change of Base Formula – FAQs
How to use change of base formula?
Identify the logarithm and its base.
Choose a new base (commonly 10 or e).
Apply the formula: loga(b) = (logc(b)) / (logc(a)).
Calculate the new base logarithms and simplify if needed.
When to use change of base formula?
To evaluate logarithms with bases not supported by calculators or software.
When solving equations with different bases.
For comparing logarithmic functions with various bases.
To simplify expressions or reveal patterns.
How do you change log base 2 to base e?
Use the formula: loga(b) = (logc(b)) / (logc(a)).
Set a = 2 and c = e to change from base 2 to base e.
Equation becomes: log2(x) = (loge(x)) / (loge(2)).
How do you change log base e to log base 10?
Use the formula: loga(b) = (logc(b)) / (logc(a)).
Set a = e and c = 10 to change from base e to base 10.
Equation becomes: loge(x) = (log10(x)) / (log10(e)).
Since log10(e) is a constant, you can simplify further if needed. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm | https://www.geeksforgeeks.org/change-of-base-formula/?ref=lbp | Data Science & ML | Change of base rule for Logarithm | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0233155154, -0.027713025, -0.0200718064, -0.0012129891, -0.037944857, 0.0203112755, -0.0180907492, 0.0323064663, 0.0128115602, 0.0141177513, 0.00252530328, -0.000697315671, -0.0274082478, -0.00223141024, 0.0248176344, -0.0276694857, -0.0250353329, 0.0191248171, -0.0105366101, 0.0786762536, -0.0185043775, -0.0426253751, -0.0144007588, 0.0201806556, -0.00210215175, -0.00881134905, 0.00308315572, -0.0216610059, 0.0222379062, -0.00764121907, 0.0593881644, 0.00370087544, -0.053118445, -0.0282790419, -0.0476759821, -0.0428866148, 0.0320016854, 0.017688008, -0.00784803275, 0.000527578813, 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11 Nov, 2024 | Properties of Logarithms
11 Nov, 2024
Logarithms serve as essential mathematical tools that help simplify complex calculations, particularly those involving exponential relationships. Understanding the properties of logarithms enables us to solve equations, manipulate algebraic expressions, and better grasp functions in calculus. Here, we’ll explore the fundamental and advanced properties of logarithms, illustrating their applications across various fields.What is a Logarithm?A logarithm answers the question: "To what power must we raise a base number to obtain a specific value?" It serves as the inverse operation of exponentiation. For any base aaa and number x, the logarithm is defined as follows:\log_a(x) = y \iff a^y = xIn this equation, a represents the base, x is the argument, and y is the exponent. Common logarithm bases include 10 (common logarithm) and e (natural logarithm), denoted by ln.Fundamental Properties of LogarithmsLogarithmic properties make calculations more manageable, especially when working with products, quotients, and powers. Let’s delve into these essential properties of logarithms in detail.1. Product PropertyThe product property of logarithms states that the logarithm of a product equals the sum of the logarithms of the factors. This property is particularly useful in breaking down complex multiplications into simpler additions:\log_a(m \cdot n) = \log_a(m) + \log_a(n)
Example:\log_{10}(100) = \log_{10}(10 \times 10) = \log_{10}(10)+\log_{10}(10)=22. Quotient PropertyAccording to the quotient property, the logarithm of a quotient equals the difference between the logarithms of the numerator and the denominator:\log_a\left(\frac{m}{n}\right) = \log_a(m) - \log_a(n)
Example:\log_{2}\left(\frac{8}{2}\right) = \log_{2}(8) - \log_{2}(2) =3-1=23. Power PropertyThe power property asserts that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base number. This property is particularly useful in exponential equations and growth-decay models:\log_a(m^n) = n \cdot \log_a(m)
Example: \log_{3}(27) = \log_{3}(3^3) = 3 \cdot \log_{3}(3) = 3 \cdot 1 = 34. Change of Base FormulaThe change of base formula allows us to convert logarithms from one base to another, which is handy when working with calculators or tables that only support specific bases, like 10 or eee:\log_a(m) = \frac{\log_b(m)}{\log_b(a)}
Example: \log_{2}(8) = \frac{\log_{10}(8)}{\log_{10}(2)} \approx \frac{0.9031}{0.3010} \approx 35. Reciprocal PropertyThe reciprocal property of logarithms states that the logarithm of the reciprocal of a number is the negative of the logarithm of the number itself:\log_a\left(\frac{1}{m}\right) = -\log_a(m)Example: \log_{10}\left(\frac{1}{100}\right) = -\log_{10}(100) = -2Additional Properties and Identities of LogarithmsLogarithm of 1For any base a (where a>0a > 0a>0 and a≠1a \neq 1a=1), the logarithm of 1 is always 0. This property holds because any number raised to the power 0 equals 1:\log_a(1) = 0Example: Since 10^0 = 1, it follows that \log_{10}(1) = 0.Logarithm of the BaseThe logarithm of a base with itself is always 1, as raising a number to the power of 1 produces the number itself:\log_a(a) = 1
Example: For base 2, l\log_{2}(2) = 1 because 2^1 = 2.Advanced Applications of Logarithmic PropertiesLogarithmic properties aren’t just theoretical; they play a significant role in practical applications across various fields.Mathematics: Simplify complex expressions, solve exponential equations, and perform polynomial division.Physics and Chemistry: Logarithmic properties help in measuring the intensity of sound in decibels, pH levels in chemistry, and radioactive decay calculations.Engineering and Computer Science: Used in algorithms, signal processing, and complexity analysis, especially when dealing with exponential time complexities and optimizations.Using Logarithmic Properties in Problem SolvingMastering the properties of logarithms is essential for tackling a wide array of mathematical problems. Here’s how to apply each property:Product Property helps combine multiple terms into one.Quotient Property allows for simplification when dividing terms.Power Property enables solving for variables in exponents.Change of Base Formula provides flexibility when calculators only support certain bases.Each property offers a unique advantage, and combined, they simplify exponential and logarithmic equations, providing efficient solutions.Also Read:Logarithm Rules | List of all the Log Rules with ExamplesLaws of LogarithmsConclusionMastering the properties of logarithms is crucial for anyone dealing with exponential functions. These properties offer tools to simplify, manipulate, and solve equations across mathematics, science, and engineering, fostering a deeper understanding of exponential relationships and enhancing problem-solving skills. By understanding and applying the product, quotient, power, and change of base properties, we unlock a world of mathematical potential, enabling more efficient and accurate computations. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms | https://www.geeksforgeeks.org/properties-of-logarithms/ | Data Science & ML | Properties of Logarithms | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, NumPy Introduction, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.00733511755, -0.00637318753, -0.0104364567, 0.00894369557, -0.00769543881, -0.00997318607, -0.00658873701, 0.0058713113, 0.0343592353, 0.0370616466, 0.0245018657, 0.0201007947, -0.0122380648, -0.00887935236, 0.0167935584, 0.00674959505, -0.0341276, 0.0305758584, -0.0315024, 0.0341533348, 0.00432385877, -0.0373190194, -0.0419517234, 0.0320943557, -0.0196632631, -0.00030402132, 0.018170502, 0.0128364554, -0.00719356257, 0.00133592437, 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10 Sep, 2024 | Division Property of Equality
10 Sep, 2024
Division Property of Equality is a fundamental concept in mathematics used to maintain balance in an equation. It states that if two numbers or expressions are equal, dividing both sides of the equation by the same non-zero number will keep them equal. This property is important when solving equations because it allows us to simplify and isolate variables. For example, if a = b, then a/c = b/c, as long as c ≠ 0. In this article, we will discuss Division Property of Equality in detail.Table of ContentWhat is Equality?Properties of EqualityWhat is the Division Property of Equality?Division Property of Equality FormulaDivision Property of Equality: Practice Questions with SolutionsPractice Problems: Division Property of EqualityFAQsWhat is Equality?Equality refers to the condition of two values, expressions, or quantities being identical or equivalent in value, magnitude, or status. In mathematics, equality is represented by the symbol "=", indicating that the expressions on either side of the equals sign have the same value.For example, in the equation: 5+3=85 + 3 = 85+3=8 This means that the sum of 5 and 3 is equal to 8.Properties of EqualitySome of the common properties of equalities are:Reflexive Property of EqualitySymmetric Property of EqualityTransitive Property of EqualitySubstitution Property of EqualityAddition Property of EqualitySubtraction Property of EqualityMultiplication Property of EqualityDivision Property of EqualityDistributive Property of EqualityIn this article, we will discuss Division Property of Equality in detail.What is the Division Property of Equality?Division Property of Equality states that if two values or expressions are equal, then dividing both sides of the equation by the same non-zero number will not change the equality. In other words, if a = b, then dividing both a and b by the same non-zero number c will result in a/c = b/c, as long as c ≠ 0. This property is often used to solve equations where a variable needs to be isolated by eliminating a coefficient through division.Division Property of Equality FormulaIf a = b and c ≠ 0, then:a/c = b/cThis property ensures that the equation remains balanced after division, just as it does with addition, subtraction, and multiplication.Division Property of Equality: Practice Questions with SolutionsQuestion 1: Solve the equation 4x = 20.Solution:To isolate x, divide both sides by 4:x = 20/4 = 5So, x = 5.Question 2: Solve the equation x/3 = 7.Solution:To solve for x, multiply both sides by 3:x = 7⋅3 = 21So, x = 21Question 3: Solve the proportion 5/x = 15/9Solution:Cross-multiply to solve for x:5 ⋅ 9 = 15 ⋅ x ⟹ 45 = 15xDivide both sides by 15:x = 45/15 = 3So, x = 3Question 4: Solve the equation (2y − 4)/5 = 6.Solution:First, multiply both sides by 5:2y − 4 = 30Then, add 4 to both sides:2y = 34Finally, divide both sides by 2:y = 34/2 = 17So, y = 17.Question 5: If a/b = c/d and b = 4, d = 8, and c = 12, find a.Solution:Use the proportion formula:a/4 = 12/8.Cross-multiply to solve for a:8a = 4 ⋅ 12⟹ 8a = 48.Divide both sides by 8:a = 48/8 = 6So, a = 6Question 6: Solve the inequality 3x/4 > 6.Solution:First, multiply both sides by 4:3x > 24Then, divide both sides by 3:x > 24/3 = 8So, x > 8.Practice Problems: Division Property of EqualityProblem 1: Solve 5x = 10 for x.Problem 2: If a/6 = 4/5, find a.Problem 3: Solve for z: 12z = −144Problem 4: Solve for m: 6m = −42Problem 5: Solve for n: 7n = 0Problem 6: Solve for p: p/4 = 3Problem 7: Solve for q: q/−5 = 7Problem 8: Solve for r: r/9 = −11Problem 9: Solve for s: 3s = 24Problem 10: Solve for t: −4t = −28Answer Keyx = 2a = 4.8z = −12m = −7n = 0p = 12q = −35r = −99s = 8t = 7Read More,Properties of Equality InequalitiesMultiplication Property of EqualitySubtraction Property of EqualityTransitive PropertyFAQs: Division Property of EqualityWhy must the divisor be a non-zero number?Division by zero is undefined in mathematics. Therefore, the Division Property of Equality only applies when dividing by a non-zero number.Can the Division Property of Equality be used with inequalities?Yes, but with a crucial difference. When dividing both sides of an inequality by a positive number, the inequality sign remains the same. However, when dividing by a negative number, the inequality sign must be reversed.What happens if you divide both sides of an equation by zero?Division by zero is not allowed because it is undefined. If an equation involves division by zero, the equation has no valid solution. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality | https://www.geeksforgeeks.org/division-property-of-equality/?ref=ml_lbp | Data Science & ML | Division Property of Equality | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, NumPy Introduction, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.00742842, -0.00873465, -0.010272827, 0.0322528929, 0.0077946526, 0.0191783849, 0.0206799395, 5.1453786e-05, 0.0445827283, 0.0244399291, -0.0263443384, -0.00134437915, 0.0114386678, -0.0269058961, -0.00193950732, 0.0328876972, -0.00670816237, 0.0600621626, -0.0457302555, 0.0304461457, -0.0439235084, -0.00189830619, -0.00358908041, -0.00350973, -0.0392113142, 0.00569491833, 0.0117499661, -0.0227186345, -0.0160532, 0.00843555946, 0.0143319061, -0.0293230321, 0.000343533902, 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07 Nov, 2024 | Divisibility Rule of 23
07 Nov, 2024
Divisibility rules are simple shortcuts that help determine if one number is divisible by another without performing full division. The divisibility rule for 23 helps us quickly determine if a number is divisible by 23 without needing to perform long division.Divisibility Rule of 23:Take the number's last digit (unit digit) and multiply it by 7.Add this value to the rest of the digits in the number.Check the result: If the number is divisible by 23 (or is 0), then the original number is divisible by 23.Mathematical ProofA general number N can be written as:N = 10^n a_n + 10^{n-1} a_{n-1} + \cdots + 10 a_1 + a_0Here, a_n, a_{n-1}, \dots, a_1, a_0 are the digits of the number. We want to show that N is divisible by 23, i.e., N = 23k for some integer k.We can factor out 10 from all terms except the last one, giving:N = 10 \left( 10^{n-1} a_n + 10^{n-2} a_{n-1} + \cdots + 10 a_2 + a_1 \right) + a_0Now, to introduce the rule of subtracting twice the last digit, we add and subtract 70 a_0N = 10 \left( 10^{n-1} a_n + 10^{n-2} a_{n-1} + \cdots + 10 a_2 + a_1 \right) + 70 a_0 - 70 a_0 + a_0This simplifies to:N = 10 \left( 10^{n-1} a_n + 10^{n-2} a_{n-1} + \cdots + 10 a_2 + a_1 + 7 a_0 \right) - 69 a_0Now, notice that:69 \equiv 0 \mod 23 so the term 69 a_0 contributes nothing to the remainder modulo 7.We only need to check whether 10 \left( 10^{n-1} a_n + 10^{n-2} a_{n-1} + \cdots + 10 a_2 + a_1 + 7 a_0 \right) \equiv 0 \mod 2310 (\overline{a_na_{n-1}......a_2a_1} + 7a_0) \equiv 0 (mod 23)since 10 ≡ 10 (mod 23), for N to be divisible by 7, \overline{a_na_{n-1}......a_2a_1} + 7a_0) \equiv 0 (mod 7)This leads to a rule for checking if a three-digit number is divisible by 23:Remove the last digit c.Multiply c by 7.Subtract this result from the number formed by the remaining two digits.If the result is divisible by 23, then the original number N, is also divisible by 23.More Examples of Divisibility by 23 RuleHere are a few examples of numbers divisible by 23, applying the divisibility rule:For 2829:Take the last digit (9) and multiply it by 7 to get 63.Add it to the remaining number (282): 282 + 63 = 345.Since 345 is still large, apply the rule again:Take the last digit (5) of 345, and multiply it by 7 to get 35.Add it to the remaining number (34): 34 + 35 = 69.Divide 69 by 23: 69 ÷ 23 = 3.Since 69 is divisible by 23, 2829 is also divisible by 23.For 4761:Take the last digit (1) and multiply it by 7 to get 7.Add it to the remaining number (476): 476 + 7 = 483.Since 483 is still large, apply the rule againTake the last digit (3) of 483, and multiply it by 7 to get 21.Add it to the remaining number (48): 48 + 21 = 69.Divide 69 by 23: 69 ÷ 23 = 3.Since 69 is divisible by 23, 4761 is also divisible by 23.Divisibility Rule of 23 Solved QuestionsQuestion 1: Check if the given number is divisible by 23 or not: 28395041Solution: Check 28395041 is divisible by 23 28395041 ⇒ 2839504 + 1 × 7 = 28395112839511 ⇒ 283951 + 1 × 7 = 283958283958 ⇒ 28395 + 8 × 7 = 2845128451 ⇒ 2845 + 1 × 7 = 28522852 ⇒ 285 + 2 × 7 = 299299 ⇒ 29 + 9 × 7 = 92Since 92 is divisible by 23 (92 ÷ 23 = 4)28395041 is also divisible by 23.Question 2: Check if the given number is divisible by 23 or not: 142857Solution: Check 142857 is divisible by 23142857 ⇒ 14285 + 7 × 7 = 1433414334 ⇒ 1433 + 4 × 7 = 14611461 ⇒ 146 + 1 × 7 = 153153 ⇒ 15 + 3 × 7 = 3636 ⇒ 3 + 6 × 7 = 45Since 45 is not divisible by 23 (45 ÷ 23 ≈ 1.956),142857 is not divisible by 23.Read More:Divisibility Rule by 3Divisibility Rule by 5Divisibility Rule of 4Divisibility Rule by 8Divisibility Rule by 13Quiz about Number DivisibilityFAQs on Divisibility Rule on 23What is the divisibility rule for 23?The divisibility rule for 23 involves adding 7 times the last digit of the number to the rest of the number. Repeat this process until you get a number that is easy to check for divisibility by 23.How do I apply the divisibility rule for 23?To check if a number is divisible by 23:Take the last digit of the number and multiply it by 7.Add the result to the remaining part of the number.Repeat the process with the new number until you can easily check if it's divisible by 23.Can I use this rule for numbers with more than 3 digits?Yes, the divisibility rule for 23 works for numbers with any number of digits. You may need to apply the rule multiple times. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23 | https://www.geeksforgeeks.org/divisibility-rule-of-23/?ref=ml_lbp | Data Science & ML | Divisibility Rule of 23 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, NumPy Introduction, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0227655228, -0.0194469672, -0.0129570933, 0.0413403772, 0.00564324437, 0.00929309055, 0.0260727536, 0.0192430951, 0.0409326367, 0.0549996905, -0.0144294901, 0.00341482833, -0.027295975, -0.0123568084, 0.0232638717, 0.00961022172, 0.00409722794, 0.0124134393, -0.0271147564, 0.0218141284, 0.0158565827, 0.0215762779, -0.00496367691, 0.0130250501, -0.00990470126, -0.00437471783, 0.0364701413, -0.0203643832, -0.0155167989, 0.0185635276, 0.0224823691, -0.000920956, 0.0157546476, 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21 Oct, 2024 | Divisibility Rule of 17
21 Oct, 2024
The divisibility rule for 17 states that a number is divisible by 17 if the following condition holds:Divisibility by 17: To check divisibility by 17,Step 1: Multiply the last digit by 5.Step 2: Subtract this product from the remaining digits of the number.Step 3: Check if the result is divisible by 17.If the result is 0 or a number that can be divided evenly by 17, then the original number is divisible by 17.Alternate Divisibility Rule of 17Other then this there are some more rules which can also be used to check divisibility by 17. Some of these are:Alternate Rule 1Take the number formed by the last two digits of the given number. Multiply the rest of the number by 2. Subtract this product from the number formed by the last two digits. If the result is 0 or divisible by 17, the original number is divisible by 17.Example: Check if 442 is divisible by 17.Take the last two digits: 42.Multiply the remaining part (4) by 2: 4 × 2 = 8.Subtract the product from the last two digits: 42 - 8 = 34.Check if 34 is divisible by 17: 34 ÷ 17 = 2 (a whole number).So, 442 is divisible by 17.Alternate Rule 2Find the sum of 9 times the last digit and 5 times the rest of the number. If the sum is 0 or divisible by 17, the original number is divisible by 17.Example: Check if 289 is divisible by 17.Last digit: 9.Rest of the number: 28.Calculate: 9 × 9 = 81 and 5 × 28 = 140.Sum: 81 + 140 = 221.Check if 221 is divisible by 17: 221 ÷ 17 = 13 (a whole number).Since the result is divisible by 17, 289 is divisible by 17.Other Divisibility Rules:Divisibility Rule for 3Divisibility Rule for 4Divisibility Rule for 7Divisibility Rules of 11Divisibility Rules of 13Divisibility Rule of 17: Worksheet You can download free worksheet on Divisibility Rule of 17 from below:Download Free Worksheet on Divisibility Rule of 17Also Check: Practice Questions on Divisibility Rules.FAQs on Divisibility Rule of 17 What is the divisibility rule of 17?A number is divisible by 17 if the 5 times the last digit, when subtracted from the remaining digits, produces a number that is divisible by 17. Can a number be divisible by 17 if it is not divisible by 17 using the rule?No, if the rule does not show divisibility, then the number is not divisible by 17.Is 1234123412341234 divisible by 17?Yes, it is divisible by 17. Any 16-digit number composed of a 4-digit sequence repeated four times will be evenly divisible by 17.Are there any exceptions to the divisibility rule of 17?No, there are no exceptions; this rule applies universally to all the whole numbers. If the process yields a number divisible by 17, the original number is also divisible by 17. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17 | https://www.geeksforgeeks.org/divisibility-rule-of-17/?ref=ml_lbp | Data Science & ML | Divisibility Rule of 17 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, NumPy Introduction, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0319161117, -0.00210125907, -0.0139661767, 0.0364525281, 0.00103983539, -0.0140582873, 0.0190552529, 0.0082783848, 0.00326414779, 0.0360840894, 0.00850866, -0.0138625531, -0.0058230781, 0.0150139276, -0.0169136971, 0.0206326377, -0.00271292706, 0.00902677886, -0.0372584909, -0.000383551756, -0.000152377266, 0.0313864797, 0.00694854744, 0.00513801025, -0.0250078626, 0.0236952938, 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15 Jul, 2024 | Practice Questions on Divisibility Rules
15 Jul, 2024
Divisibility rules are the rules that help us calculate difficult problems more simply they help to determine if a number is divisible by another number. And solving Practice Questions on Divisibility Rules are the best way to understand and master the concept of divisibility rules.In this article, we will learn about the Divisibility rules and solve some Practice Questions on Divisibility Rules to better understand their application and uses. What are Divisibility Rules?A divisibility rule is a set of rules that enables us to know whether a particular number is divisible by a divisor by simply looking at its digits instead of going through the complete division operation.Divisibility RulesBy using divisibility rules, we can determine whether an integer is divisible by another integer or not.Important FormulasVarious formulas for Divisibility Rules are:Divisibility RulesFormulaExampleDivisibility for 2For divisible by 2, the number's unit digit is 0,2,4,6 or 8.For example, 100, 222, 344, and 1658 are divisible by 2.Divisibility for 3A number is divisible by 3 if the sum of its digits is completely divisible by 3.For example, 27648 is divisible by 3 check it. Sum of digits = 2 + 7 + 6 + 4 + 8 = 27; 27 ÷ 3 = 9. Hence 27648 is divisible by 3.Divisibility by 4A number is divisible by 4 if the last two digits of that number are divisible by 4.For example, Check if 1124 is divisible by 4. The last 2 digits are 24 which is divisible by 4. So 1124 is divisible by 4.Divisibility for 5The number must contains it's unit digit is 0 or 5.For example, 10000, 2255, 65, 80, 925 are divisible by 5.Divisibility for 6The number is divisible by both 2 and 3, then it is divisible by 6.For example 12, 18, etc.Divisibility for 8For the divisibility of 8 the number's last three digits is totally divisible by 8.For example, 24, 80, 96, etc are divisible by 8.Divisibility for 9A number is divisible by 9 if sum of all its digits is completely divisible by 9.For example, Check if 16911 is divisible by 9 or not? Sum of digits = 1 + 6 + 9 + 1 + 1 = 18. It is exactly divisible by 9.Divisibility for 10Divisibility of 10 is that if its unit digit is 0.For example, 8000, 9010, 11020, 98670 are divisible by 10.Divisibility by 11A number is divisible by 11 if difference between sum of digits at odd places and sum of digits at even places is either 0 or is divisible by 11.For example, 121, 1331, 77, etc are divisible by 10.Practice Questions on Divisibility Rules with SolutionThese Practice Questions on Divisibility Rules will help you understand their application and usage in various mathematical problems.Problem 1: Use divisibility rules to check whether 448 is divisible by 4 or not?We know that,Divisibility rule of 4 is when the last two digits are completely divisible by 4 then the number is divisible by 4.The last two digits we have is 48 and we know that 48 is divisible by 4 in 12 times.So, Yes 448 is completely divisible by 4.Problem 2: Use divisibility rules to check whether 1024 is divisible by 2 or not?We know that, Divisibilty rule of 2 is if its unit digit is 0,2,4,6 or 8.In 1024 the last digit is 4 so it is divisible by 2.Yes, 1024 is divisible by 2.Problem 3: Use divisibility rules to check whether 1331 is divisible by 11 or not?We know that, Divisibilty of 11 is if difference between sum of digits at odd places and sum of digits at even places is either 0 or is divisible by 11.In 1331, the sum of digits at odd place is 1 + 3 = 4 and the sum of digits at even place is 1 + 3= 4.So, difference between digits at odd place and digits at even place is 4 - 4 = 0.Yes 1331 is divisible by 11.Problem 4: Use divisibility rules to check whether 1238913 is divisible by 3 or not?We know that, Disibility of 3 is the sum of all digits must be a multiple of 3.In 1238913 the sum of every digit is 1 + 2 +3+ 8+ 9+ 1+ 3 = 27 and 27 is multiple of 3.So Yes, 1238913 is divisible by 3.Problem 5: Determine if 524 is divisible by 2.We know that,A number is divisible by 2 if its last digit is even. Last Digit of 524: 4 (which is even)524 is divisible by 2.Practice Questions on Divisibility Rules : WorksheetSolve these worksheet containing Practice Questions on Divisibility Rules to test your understanding on the concept of Divisibility Rules.Q1: Use divisibility rules to check whether 14356 is divisible by 3 or not?Q2: Use divisibility rules to check whether 3476580 is divisible by 2 or not?Q3: Use divisibility rules to check whether 34543110 is divisible by 5 or not?Q4: Use divisibility rules to check whether 572 is divisible by 4 or not?Q5: Use divisibility rules to check whether 222582 is divisible by 3 or not?Q6: Use divisibility rules to check whether 1088 is divisible by 8 or not?Q7: Use divisibility rules to check whether 8565 is divisible by 3 or not?Q8: Use divisibility rules to check whether 9721 is divisible by 3 or not?Practice Questions on Divisibility Rules - FAQsWhat are Divisibility Rules?Divisibility rules are the rules that help us calculate difficult problems in a simpler way.What is a Quotient?A quotient is the result obtained by dividing one number by another. For example, in 20 ÷ 4, the quotient is 5.Check if 1234 is divisible by 4?Last two digits: 34 .Since 34 is not divisible by 4, 1234 is not divisible by 4.What is Divisibility Rule for 99?A number is divisible by 99 if the sum of its digits is divisible by 9 and the number formed by the last two digits is 00, 11, 22, 33, 44, 55, 66, 77, or 88.What is Divisibility Rule for 25?A number is divisible by 25 if its last two digits are 00, 25, 50, or 75.Can Divisibility Rules be Applied to Negative Numbers?Yes, divisibility rules apply to both positive and negative numbers. For example, -36 is divisible by 3 because the sum of its digits (-3 and -6) is -9, which is divisible by 3. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules | https://www.geeksforgeeks.org/practice-questions-on-divisibility-rules/ | Data Science & ML | Practice Questions on Divisibility Rules | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, NumPy Introduction, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0356784686, 0.000189891551, -0.0197389629, 0.0655796751, 0.00929045398, -0.000826251868, 0.0370056741, 0.00218924228, 0.0196739025, 0.0625609308, -0.00490546413, 0.0095116552, 0.00668808585, -0.011743186, -0.0190493353, 0.00677266298, -0.0110860886, 0.0221331399, 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02 Dec, 2024 | GCD Practice Questions Medium Level
02 Dec, 2024
The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), of two or more numbers is the largest number that divides all of them exactly, without leaving a remainder.
Key Points:It is the greatest number that is a factor of each of the numbers.For two numbers a and b, the GCD is the largest number d such that both a ÷ d and b ÷ d are integers.Read More:
Interesting Facts about GCDSolved Questions on Greatest Common Divisor (Medium)Example 1: A school has 42 boys and 70 girls who need to be grouped to make teams. Find the maximum number of groups so that boys and girls are equally distributed among each group also find the number of boys and girls in a group.
Answer:
To find the maximum possible number of group, we need to find the HCF of 42 and 70.
Prime factors of 42: [Tex]2 \times 3 \times 7[/Tex]Prime factors of 70: [Tex]2 \times 5 \times 7[/Tex]
Common factors: 2 \times 7 = 14
The HCF is 14, so a maximum of 14 groups can be formed.
Number of students in each groups:
Boys: 42 ÷ 14 = 3.
Girls: 70 ÷ 14 = 5.
Maximum 14 groups can be formed with each group 3 boys and 5 girls.
Example 2: If the HCF of two numbers is 1, what can you conclude about those numbers?
Answer:
When the HCF of two numbers is 1, it indicates that these two numbers are coprime . As Coprime numbers are integers that share no common factors other than 1. In other words, their HCF is the smallest possible, which is 1. This implies that the numbers have no common factors except for unity, making them mutually prime to each other. For example, 5 and 8 are coprime because their only common factor is 1.
Example 3: Can the HCF of two prime numbers be a prime number other than 1? Explain.
Answer:
The HCF (Highest Common Factor) of two prime numbers cannot be a prime number other than 1.
Consider the scenario where the HCF of two numbers is a prime number other than 1. Let’s say the HCF is ‘p’, where ‘p’ is a prime number greater than 1.
If ‘p’ is the HCF, it means ‘p’ is a common factor of the two numbers.However, since ‘p’ is a prime number greater than 1, it cannot be divided by any other number except 1 and itself.This implies that the two numbers can only be divided by ‘p’ and nothing else.But this contradicts the definition of HCF because the HCF is supposed to be the largest number that can exactly divide both of them. If ‘p’ is the HCF, it should be the largest, but it cannot be because it cannot be divided by any number other than 1 and itself.Therefore, the HCF of two numbers cannot be a prime number other than 1. It must always be 1 or a composite number (a number with more than two factors).
Example 4: Sarah has 12 apples and 16 oranges, and she wants to arrange them into equal-sized groups. She wants to ensure that no fruits are left over in each group. What is the largest number of apples and oranges she can put in each group?
Answer:
To find the largest number of groups of apples and oranges that Sarah can make without any fruits left over, we need to calculate the HCF of the number of apples and number of oranges she has, which is 12 and 16.
12 = 2 x 2 x 3 x 3 16 = 2 x 2 x 2 x 2
HCF ( 12, 16) = 2 x 2 = 4
The HCF of 12 and 16 is 4, so Sarah can make 4 groups with 3 apples and 4 oranges in each group, and no fruits will be left over.
Example 5. Sam is preparing dinner plates. She has 60 pieces of momos and 8 rolls. If she wants to make all the plates identical without any food left over, what is the greatest number of plates Sarah can prepare ?
Answer:
In order for all the plates to look identical with the highest no of plates, we need to find the HCF of 8 rolls and 60 pieces of momos
HCF (8,60) = 4
Hence, Sam can prepare a total of 4 plates with 15 momos and 2 rolls in each plate.
Example 6. A juice seller has three different types of fruit juices: apple juice, orange juice, and grape juice. He has 403 liters of apple juice, 434 liters of orange juice, and 465 liters of grape juice. What is the minimum number of identical containers he needs to store each type of juice separately without mixing them?
Answer:
For the minimum number of containers of equal size, the size of each container must be of the greatest volume.To get the greatest volume of each container, we need to find HCF of 403, 434 and 465.
H.C.F (403, 434, 465) = 31 litersEach container must be of the volume 31 liters.
Number of containers required are = (403/31) + (434/31) + (465/31) = 42Hence, the minimum number of containers required are 42.
Example 7. Emma has 48 math books and 64 science books. She wants to arrange them into stacks so that each stack has the same number of books, and each stack only contains one type of book. What is the maximum number of books in each stack?
Answer:
To arrange books in the largest possible equal stacks, we need to find the HCF of 48 and 64.
Prime factors of 48: 23 x 3Prime factors of 64: 26Common factors: 24 = 16
The HCF is 16, so each stack can have a maximum of 16 books.Math books: 48 ÷ 16 = 3 stacks.Science books: 64 ÷ 16 = 4 stacks.
The maximum number of books in each stack is 16, resulting in 7 stacks in total.
Also Read : Short Tricks to solve HCF
GCD Practice Problems (Medium)You can download the practice questions with answer key from below:
Free Download GCD Practice Questions (Medium)
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21 Aug, 2024 | Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts
21 Aug, 2024
To excel in the GRE Quantitative Exam, mastering math concepts is just the beginning. Our article, "Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts," offers you essential strategies to elevate your performance. We delve into effective GRE math tips, focusing on powerful math tricks and quantitative shortcuts designed to optimize your problem-solving efficiency. Discover quick calculation techniques and proven problem-solving methods that will streamline your approach and enhance your accuracy. By integrating these expert GRE quantitative strategies into your study plan, you'll significantly boost your speed and precision, leading to a higher test score. Whether you're targeting a perfect score or aiming to improve your current results, our comprehensive guide provides the tools you need to succeed in the GRE Quantitative section. Embrace these GRE quantitative exam tips to transform your preparation and achieve your desired score. GRE Verbal Quantitative Section - FormatThe GRE Quantitative Exam section is the third and last part of the whole GRE entrance examination. The section consists of 2 sections where you have to answer 27 questions. As the GRE is a computer-adaptive test, for that the difficulty of the second subpart of the GRE Verbal Reasoning section depends on your performance in the first subpart of the section. You will get 21 minutes to complete the first subsection and 27 minutes for the rest i.e. second subsection. Here we have provided the question types of this section as mentioned below. GRE PartNo. of sectionsTotal durationNo. of questionsQuantitative Reasoning247 minutesSection 1: 21 min.Section 2: 26 min.27Section 1: 12 ques.Section 2: 15 ques.As we all have learned the structure of the GRE Quantitative Section, we will go through the subsections and related tips with it. GRE Quantitative Reasoning Section In this part you need to solve math problems, interpret data, apply mathematical concepts, and manage your time effectively. There are 4 types of questions in this section as mentioned below. Quantitative Comparison QuestionsMultiple choice questions where you select one answer choiceMultiple choice questions where you select one or more answer choicesNumeric entry questionsThe goal in the GRE Quantitative Reasoning Section is to accurately solve mathematical problems and interpret data to demonstrate your quantitative skills.Tips for GRE Quantitative Exam PDFMastering the GRE Quantitative Exam involves more than just understanding math concepts—it's about applying strategic approaches to maximize your score. Here are essential tips to excel in the GRE Quantitative section:Tips for GRE Quantitative Exam PDF- Download!!!Tips for GRE Quantitative Exam MathsHere are some major tips to answer the questions of the Quantitative Reasoning Section as mentioned below. Slow Down on Word ProblemsMake sure you fully understand each question and do not rush through tricky ones. Translate words into math carefully. Check for keywords that can change the meaning and double-check your interpretation.Use the Calculator WiselyPractice without a calculator if possible. Use it only for complex calculations during the test. Avoid over-reliance; many problems can be solved with mental math or basic calculations.Spend 2 Minutes Per QuestionAim to solve each question in 1-2 minutes. If you are stuck for over 2 minutes, make an educated guess and move on. Prioritize questions based on your strengths to manage your time effectively.Note Key Info in Quant ComparisonWrite down important numbers and phrases from the questions. Approach these questions strategically. Often, you do not need to solve mathematically—just understand the relationships between quantities.Backsolve with Answer ChoicesPlug numbers from answer choices into the question to check if they work. Start with middle options. This method can quickly show you which answers are feasible without solving the entire problem.Pick Numbers When PossibleUse simple numbers in place of variables to make problems easier. Ensure the numbers you choose fit the problem’s conditions. This approach simplifies the math and helps you see patterns.Stick to Your MethodsBe consistent with your strategies and solve problems methodically, regardless of their difficulty. If you find a method that works, use it for similar problems. Adapt your approach based on the problem type.Memorize Answer ChoicesGet familiar with the wording of answer choices to save time during the test. This will help you quickly identify the correct answer or rule out incorrect ones. Practice recognizing patterns in answer choices.Analyze Tables/Graphs CarefullyRead all labels and understand the data trends before answering questions. Look for key details like scales and units. Make sure you grasp the overall picture before diving into the questions.Break Down Complex FiguresDivide tough shapes into smaller parts and label them to make geometry problems easier. Look for familiar shapes and properties within the figure. Redrawing and labeling can reveal hidden relationships.GRE Ideal ScoreYour target GRE score should match the average score of admitted students for the program you want.Score Over 160: Ideal for most programs.Score Over 150: Still good for many universities.Score Below 150: Might make it harder to get into top universities.Check the average GRE scores for universities you are interested in to see what score will make you competitive.University NameAverage GRE Verbal ScoreHarvard University164Stanford University162Massachusetts Institute of Technology (MIT)161University of California, Berkeley160University of Chicago163Yale University165Princeton University164Columbia University162University of Pennsylvania161University of Michigan159University of California, Los Angeles (UCLA)160Duke University162Northwestern University161University of Washington159University of California, San Diego (UCSD)158University of Texas at Austin157University of Wisconsin-Madison158New York University162University of Southern California (USC)160University of Florida156Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffTips For GRE Verbal Reasoning Test- FAQsHow to get 170 in gre quant?To achieve a 170 in the GRE Quantitative section, focus on mastering fundamental math concepts, practicing extensively with high-quality questions, and employing efficient problem-solving techniques. Utilize practice tests to simulate exam conditions and identify areas for improvement. Consistent review and strategic study, combined with a clear understanding of GRE question types, will help you reach a perfect score.Is a 149 verbal GRE score good?A score above the 75th percentile in either section will make you a competitive applicant. That means aiming for at least a 157 in Verbal Reasoning and at least a 163 in Quantitative Reasoning.Is a 159 verbal GRE score good?A good GRE score is considered to be 158+ on Verbal Reasoning, 159+ on Quantitative Reasoning, and 4.5+ on Analytical Writing.Is 292 a bad score in GRE?A GRE score average of 290 to 300 can take you to a quality university in the USA, which would surely help you take off your career ladder. Not just that, there are a variety of courses and MS programs that you can choose from. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts | https://www.geeksforgeeks.org/tips-for-gre-quantitative-exam/?ref=ml_lbp | Data Science & ML | Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Difference Between Encoder and Decoder | GeeksforGeeks | [0.00487085572, -0.013424146, 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11 Sep, 2024 | How to Send GRE Scores to Universities
11 Sep, 2024
When preparing for the GRE, understanding the GRE fee structure is crucial. The fee covers the cost of sending your scores to up to four colleges or scholarship programs. For those taking the computer-delivered GRE, you'll be able to designate your score recipients at the test center immediately after completing your exam. If you're opting for the paper-delivered GRE, you’ll need to specify your score recipients either on your admission ticket or during the registration process.Properly managing this aspect of your GRE fee ensures that your scores are sent to the right institutions, maximizing your application’s impact. For comprehensive information on GRE fees and score reporting, refer to official GRE resources and test preparation guides.How to Send GRE Scores to UniversitiesHow to Send GRE scores to UniversitiesETS allows you to send your most recent scores or the past 5-year scores to up to 4 universities for free. On the day of the test, you can select the score of the recent scores, all scores, or any score report of the GRE score to the university you want to send. You can send your GRE scores to the university from the past 5 years. In both situations, you need to state all your test scores. You can send your GRE scores to universities by following the below steps:Step 1: Log in to your ETS account.Step 2: Navigate to the "My GRE Scores" section on the homepage.Step 3: Choose "Send Additional Reports" from the options provided.Step 4: Review the test registration details displayed.Step 5: Proceed to send your additional reports.How to Send GRE Scores to Universities on Test DayOn the day of the test, you will receive your unofficial scores of verbal and quantitative aptitude on the day of the test itself. GRE analytical writing is checked by a human examiner, and hence GRE AWA scores are declared together with official GRE scores.Candidates can send their GRE scores to universities for free but up to 4 universities only.These candidates can choose any one of the below:Most recent: Sending scores from your current test.All: Sending scores from all your GRE test scores.Candidates who send their GRE scores to universities after the exam along with additional reports have to pay a certain amount of fee. These candidates can choose any one of the below:Most recent: Sending scores from your current test.All: Sending scores from all your GRE test scores.Any: Sending scores of any one or more than one test from the past 5-year tests.How to Send GRE Scores After TestLogin into your ETS account and upload the additional score report that you want to send to your selected college.You can apply in three ways: fax, online, and email.Select your GRE scores from past 5-year tests and send them to the university you have selected.Sending GRE Scores to Universities Before ApplyingYou can also send your past 5 years' test scores to universities before applying for the test. But in that case, you don't need to mention that you have already sent your GRE scores to universities. Think carefully about what you would like to do since you are sending scores before the exam. If you are not listed, contact ETS before taking the GRE test.How much time does it take to send GRE Scores to Universities?The four colleges you pre-selected will receive your official GRE scores automatically from ETS. If you request Additional Score Reports online for other colleges, it may take up to 5 days for them to be delivered. If you opt for mail or fax delivery, please allow approximately ten business days. If you've applied for score reinstatement, it will take two weeks for the process to be completed. Ensure you allow sufficient time to send your GRE scores before admission deadlines.Schedule for Sending Your GRE Scores to UniversitiesThe four colleges you have selected have already gotten your GRE scores. If you want to send additional score reports, it will take at most 5 working days. And if you are sending your GRE scores to universities by fax or mail. It may take at most 10 days. Many times candidates also apply for reinstatement. So for the scores to be reinstated it may take at most 2 weeks. Keep in mind that you have enough time to send your GRE scores to universities before their admission deadline.How Much Does it Cost to Send GRE Scores?People generally have queries about the fees of sending GRE scores to universities. Well, if you have sent your GRE scores to four colleges on the test day, the fee is null. That is, it is free. But if you want to send your GRE scores to more than four universities you need to pay a certain amount that is 2910 Rs. Also if you want to cancel sending your GRE scores to universities you need to pay 50$ for reinstatement.GRE Scores CancellationObviously, you can cancel your GRE scores if you are not satisfied. You can always choose to not accept your GRE scores. Your scores won't be available anywhere either on online review or sent to any GRE college. Cancellation of GRE scores should be done within 60 days after taking the test. They charge at most 50$ for the cancellation of your GRE scores.Bonus points: Send only those GRE scores to universities which reflects your best performance of all.GRE Scores ValidityGRE scores remain valid for a period of five years starting from the test date. For example, if a test is taken on September 10, 2022, the scores will remain valid until September 9, 2027. Each test taker has the option to request additional score reports, for which there is a fee of US$27 per recipient.How to Change Name on the GRE Score Report?Upon submission of valid documents, ETS can accommodate requests for name changes from candidates. Those wishing to send scores under a changed name should contact GRE assistance and provide supporting documentation. Following further review, the updated name will be reflected in their score reports and associated GRE records.During registration, ETS permits candidates to report their scores to four universities free of charge. After receiving their results, candidates can opt to send GRE scores to additional universities beyond the initial four. It is advisable to send official GRE scores to universities for enhanced preference and consideration.ConclusionIn conclusion, sending your GRE scores to universities is very important while applying for universities. Just make sure you are registered for the GRE test, choose the right University you want to be in and follow the steps for sending your GRE scores to universities. Keep in mind the university admission deadline to avoid any problems.GRE is known for being a hard exam, and somehow it is true. But there are many ways that can make it way easier like your willingness to score well and hard work. Through these, your chances of getting admitted into a University are higher. In the end, the process of score-sending should be done wisely to ensure a smooth and successful application journey.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffHow to Send GRE Scores to Universities- FAQsHow many days does it take to send GRE scores?It takes at most 5 working days.Can a candidate send unofficial scores to universities?Candidates are always suggested to send their official scores to universities.Is 330 a good GRE score?The GRE scores ranges from 260-340. So, getting 330 as score is good.Can you retake GRE exam if you score less?If anyone is not happy with their achieved results, they can apply for a score review. GRE score review fee in India is INR 5,900. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/How to Send GRE Scores to Universities | https://www.geeksforgeeks.org/how-to-send-gre-scores-to-universities/?ref=lbp | Data Science & ML | How to Send GRE Scores to Universities | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, How to Send GRE Scores to Universities, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.010945946, -0.00623534201, 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01 Oct, 2024 | GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities
01 Oct, 2024
When searching for the best GRE-accepting universities for admission in the USA, it's crucial to find a comprehensive list of universities accepting GRE scores to streamline your application process. This guide provides a detailed, list of universities accepting GRE scores for admission, based on extensive competitor analysis and addressing common queries from prospective students. Whether you're aiming for prestigious Ivy League institutions or renowned public universities, understanding the GRE score requirements and the acceptance criteria will help you target the right schools and increase your chances of admission success. Importance of GRE to Study in the USAThe SAT (or ACT) score has a significant influence on whether institutions will accept high school students applications while they are thinking about applying to universities. Nonetheless, the significance of a strong GRE score might not be as well known given that a considerably lower percentage of college graduates pursue graduate school applications. However, college students must be aware of the cause of the GRE in the event that they intend to apply to prestigious US schools for an MS with a GRE rating.Prospective students have to take the GRE examination so they can be taken into consideration for admission to master's applications at enormously appeared colleges inside the United States. inside the United States of America, technical grasp levels such as MS, MCA, MSC, MTech, and MBA require passing the GRE.First of all, it's vital to remember that graduate applications and all US universities that provide the GRE will compare candidates' results differently. That is a thing that a few STEM packages (technology, generation, engineering, and maths) will emphasize more than others, at the same time as some programs may not even take it into account in any respect.Taking the GRE situation assessments allows departments to assess a candidate's practice for graduate college by measuring their performance in a selected subject of observation. candidates have to for that reason be privy to the minimum GRE rating required for admission inside America.Most significantly, subscores from the GRE problem checks can be used to make manual placement decisions by way of revealing a man or woman's strengths and shortcomings.Top GRE Accepting Universities in the USAYou must submit your GRE results to US institutions that accept them after passing the exam. Thus, let's look at the list of US institutions with GRE scores provided below to find out the minimum GRE score needed for admission to US universities:University of PennsylvaniaUniversity of VirginiaDuke UniversityUniversity of North CarolinaGeorgia Institute of TechnologyStanford UniversityMassachusetts Institute of TechnologyUniversity of ColumbiaList of GRE Accepted Universities in USA 2024The following list of top US institutions that take the GRE includes information on their QS rankings for 2023, necessary GRE scores, tuition costs, and location:1. University of PennsylvaniaThe University of Pennsylvania was Founded in 1740, it is one of the oldest universities in the United States. The university offers a wide range of undergraduate, graduate, and professional programs across various disciplines.As a member of the private Ivy League universities, the institution has approximately 12,924 full-time graduate students and an additional 5,008 part-time students. The overall student body comprises nearly 30,000 currently enrolled students. QS World University Ranking 202313LocationPhiladelphia, USAGRE Required ScoresVerbal: 162Quantitative: 162Writing: 4.6Average Tuition Fee63,452 USD/ year (52,51,195.51 INR)2. University of VirginiaThe University of Virginia (UVA) is a public research university founded by Thomas Jefferson in 1819 in Charlottesville, Virginia. The university offers a wide range of undergraduate, graduate, and professional programs across various disciplines, including the Darden School of Business, the School of Law, and the School of Medicine. Regarding academics, the university provides 69 master's and 55 doctoral programs for international students. It maintains an acceptance rate of 23%, and approximately 10% of the total student population comes from international backgrounds.QS World University Ranking 2023253LocationCharlottesville, Virginia USAGRE Required ScoresVerbal: 159-164Quantitative: 160-166Writing: 4.0-5.0Average Tuition Fee56,837 USD/ year (47,03747.71 INR)3. Duke UniversityDuke University is super rich and known for creating international scholars. It has 10 schools, like Trinity College of Arts & Sciences and the new Sanford School of Public Policy. Duke offers lots of courses in teaching, management, humanities, and science. Getting in is tough – only 6% of applicants are accepted.QS World University Ranking 202350LocationDurham, USAGRE Required ScoresVerbal: 155-162Quantitative: 158-162Writing: 4.0-4.5Average Tuition Fee63,054 USD/ year (52,18667.46 INR)4. University of North CarolinaUNC is a leading U.S. university accepting GRE scores, recognized for excellent teaching and groundbreaking research. With 40.7% of classes having fewer than 20 students, it offers popular programs like Biological and Biomedical Sciences, Computer and Information Sciences, Management, Communication, Social Sciences, Journalism, Interdisciplinary Studies, Business, and Marketing. The student-faculty ratio is 16:1.QS World University Ranking 2023102LocationChapel Hill, USAGRE Required ScoresVerbal: 155-160Quantitative: 158-162Writing: 4.0-4.5Average Tuition Fee37,558 USD/ year (31,08489.75 INR)5. Georgia Institute of TechnologyGeorgia Institute of Technology is a great choice for international students. They offer a variety of tech-focused programs that help them rank high nationally. More than 60% of graduate students are from different countries. The university has six colleges and 28 schools covering areas like Computing, Engineering, Business, Design, Liberal Arts, and Sciences. According to U.S. News, it's the 44th best national university out of 443.QS World University Ranking 202388LocationAtlanta, USAGRE Required ScoresVerbal: 155-160Quantitative: 160-167Writing: 4.0-4.3Average Tuition Fee32,876 USD/ year (27,20983.78 INR)6. Stanford UniversityStanford University is in Silicon Valley, surrounded by big tech companies. It uses quarters for the academic year and is ranked 3rd among national universities in the US. Stanford has seven schools for things like Business, Education, and Medicine. Out of 17,000 students, more than 9,000 are in master's and PhD programs.QS World University Ranking 20233LocationStanford, USAGRE Required ScoresVerbal: 164Quantitative: 165Writing: 4.5Average Tuition Fee56,169 USD/ year (46,48830.09 INR)7. Massachusetts Institute of TechnologyMIT is a private and excellent university, welcoming both men and women. It's divided into five schools covering engineering, humanities, architecture and planning, social science management, and arts. With 50 departments, MIT provides a variety of graduate degree programs. Among the most sought-after courses are Mechanical Engineering, Mathematics, Computer Science, Physics, Aeronautical and Space Engineering, Bioengineering, Biomedical Engineering, and Econometrics and Quantitative Economics.QS World University Ranking 20231LocationCambridge, USAGRE Required ScoresVerbal: 155-162Quantitative: 158-162Writing: 4.5-5.3Average Tuition Fee57, 986 USD/ year (47,99214.19 INR)8. University of ColumbiaColumbia University is a top-notch Ivy League school, ranking 20th globally. Getting in is tough – only 7% of applicants make it. For the class of 2023, out of 42,500+ hopefuls, just 2,247 got in. People like studying Engineering, Computer Science, Business, Humanities, and Medicine. If you're into creative stuff, they also offer Dance, Film and Media Studies, Drama and Theatre Arts, Music, and Visual Arts.QS World University Ranking 202322LocationNew York, USAGRE Required ScoresVerbal: 161Quantitative: 167Writing: 4.0Average Tuition Fee65,524 USD/year (54,23,097.14 INR)GRE Score Requirements to Study in the USAThe GRE closing date for 2022 varies based totally on American institutions that provide the exam and the candidates' plans. in addition, the GRE exam consists of three sections:GRE Verbal (Score range: 130-170)GRE Quantitative Reasoning (Score range: 130–170)Analytical Writing on the GRE (0–5)To get admitted to the pleasant GRE colleges in the america for an MS or Ph.D. software, applicants need to have an average GRE score of 320 or extra and a four.5 GRE AWA. Similarly, the high-quality colleges in the usa have pretty excessive necessities for GRE scores. Typically, the least GRE score required for admission inside the america is ideal to be within the 75th percentile, but a score within the ninetieth percentile is ideal to be high-quality and can supply applicants admission to any university in their desire.GRE Cut-off for Specific Programs in the USAThe few US colleges that accept the GRE have program-specific requirements for GRE scores. The most popular fields of study for overseas students are:EngineeringEducationComputer ScienceChemistryPsychologyPhysicsMathematicsConclusionFor applicants hoping to enrol in grasp's applications at prestigious American universities, the Graduate file exam (GRE) is important. An excessive GRE score is essential to be taken into consideration for several technical master's applications, which include the MBA, MS, MCA, MSC, and MTech. It acts as a standardised tool to assess candidates' preparedness for the demands of postgraduate study.prospective college students interested in attending prestigious US schools need to be aware of the GRE rating criteria. This text shed light on the GRE prerequisites for prestigious universities consisting of Massachusetts Institute of Era, Stanford university, and college of Pennsylvania.Aspiring college students must try for an standard GRE score of 320 or above, with a four.5 GRE Analytical Writing evaluation (AWA) score for admission to extraordinary faculties.Also Read: GRE Exam Dates 2024: Check the Upcoming State-wise Dates ListGRE Exam Fee Waiver 2024: How to Get a GRE Fee Waiver?Score High on GRE: How to Get Good Score in GREGRE Accepting Universities in USA 2024-FAQsWhat is the minimum GRE score necessary for top institutions in the US?If you look at the GRE score range, folks often get between 260 and 340. This is the range that is thought to represent the score that a college or university would take into account before admitting the applicant.Therefore, a minimum score of 320 is required to be admitted to the best US universities. This is a respectable grade that will get you into a reputable university.Are there GRE sectional cutoffs or do institutions look at the whole score?It goes without saying that every university sets its own gre cutoff. The best GRE score to date is often 320 or above, and I advise you that top universities consider our entire profile when considering applicants rather than just our GRE score. So make every effort to enhance your profile. Don't rely just on your GRE score either.Which US colleges accept GRE results for master's degrees?Scores from the Graduate Record Examination (GRE) are accepted by many US colleges for entrance to master's degree programs. Numerous of these esteemed colleges provide a variety of programs in the humanities and sciences.The GRE is a standardised exam that assesses a student's critical thinking, argument analysis, and problem-solving skills. It is a crucial component in deciding whether to admit a student to a graduate school. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities | https://www.geeksforgeeks.org/gre-accepting-universities-in-usa/?ref=lbp | Data Science & ML | GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right 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09 Sep, 2024 | Score High on GRE: How to Get Good Score in GRE
09 Sep, 2024
Achieving a high score on the GRE (Graduate Record Examination) is essential for admission to top graduate programs. To excel, it’s crucial to implement effective strategies and use the best study resources. Our comprehensive guide explores proven methods to secure a top GRE exam score, including the use of GRE practice tests and mastering test-taking techniques. Learn how to effectively boost your GRE score total and track your progress with a GRE score calculator.Understanding your position within the GRE score range helps in setting realistic goals and improving your preparation. Whether you're aiming for competitive programs or seeking to enhance your scores for the GRE exam, our guide offers valuable insights to help you succeed.Score High on GRE: How to Get Good Score in GRETable of ContentGRE Scores RangeGRE Score PercentilesWhat's a Good GRE Score?How GRE Scoring Works?How Schools Use GRE Scores?How to Improve Your GRE Scores 10 Tips to Get Good Score in GRE What is a good GRE score for an MBA?What is a Good GRE score for a scholarship?GRE Scores RangeSECTIONSCORE RANGEVerbal Reasoning130–170, in 1 point incrementsQuantitative Reasoning130–170, in 1 point incrementsAnalytical Writing0–6, in half-point incrementsGRE Score PercentilesUnderstanding your GRE scores is essential for evaluating your performance and aiming for a top GRE exam score. Here’s a breakdown of key components:Scaled Scores vs. Percentile Ranks:Scaled Scores: These scores range from 130 to 170 for both the Verbal and Quantitative sections. For example, a score of 150 in Verbal represents a certain proficiency level but does not indicate how you compare to other test-takers.Percentile Ranks: This indicates how your scores stack up against others. A Verbal score of 150 might place you in the 47th percentile, meaning you performed better than 47% of test-takers. Percentile ranks provide context and are crucial for understanding your standing.Essay Scoring and Percentile Ranks:Analytical Writing: Essays are scored separately, with percentile ranks reflecting how your writing compares to others. Tracking recent percentile ranks can help assess and improve your essay skills.For a high GRE score, utilize a GRE exam score calculator to estimate your performance and explore effective study methods. Regular practice with GRE practice tests and understanding the GRE score range will help you achieve your desired GRE score and enhance your graduate school application.Analytical Writing Score PercentilesScorePercentile6.0995.5985.0914.5814.0563.5383.0172.572.021.511.0<1What's a Good GRE Score?Different colleges have different requirements when it comes to the score. The quantitative and the verbal are scores together. The average for that is around 260 to 340, whereas the analytical scoring is done separately. According to ETS, the scores are divided into the following ways provided below:Sections Objective Format Score Range Analytical Writing Critical Thinking and Analytical Writing Skills Subjective Type Questions 0-6, in half-point increments Verbal Reasoning Judge's Skills in analyzing and evaluating Multiple choice questions 130-170, in 1 point increments Quantitative Reasoning Quantitative reasoning and problem-solving skills; Arithmetic, algebra, geometry, and data analysis questions Multiple choice questions 130-170, in 1 Point increments When preparing for the GRE, knowing how your scores are evaluated can significantly impact your study strategy. The GRE provides an overall score and individual scores for each section of the exam. Here’s what you need to know about GRE scoring:Overall GRE Score: Ranges from 260 to 340.Section Scores:Verbal Reasoning: 130-170Quantitative Reasoning: 130-170Analytical Writing: 0-6 (in half-point increments)Recent data reveals that the average scores among test-takers are approximately 151 in Verbal, 155 in Quantitative, and 3.5 in Analytical Writing. To stand out, aim for scores higher than 158 in Verbal, 159 in Quantitative, and 4.5 in Writing. Achieving an overall score of 318+ can place you in the 75th percentile or higher, enhancing your chances for admission into competitive graduate programs.How GRE Scoring Works?Understanding how your GRE scores are calculated can help you tailor your preparation effectively. Here’s a breakdown of the GRE scoring system and what factors influence your final scores:Overall GRE Score: Your overall GRE score is calculated based on the scores you receive in the Verbal Reasoning and Quantitative Reasoning sections. This score ranges from 260 to 340. The Analytical Writing section (Essay) is scored separately and does not impact your overall score.Section Scores:Verbal Reasoning & Quantitative Reasoning: These scores range from 130 to 170. Your performance in these sections is influenced by the number of correct answers and the difficulty level of the questions.Analytical Writing: Scored from 0 to 6 in half-point increments, reflecting the quality of your essay response.Routing Modules: The GRE employs routing modules in both Verbal and Quantitative sections. Your performance in the initial routing module determines the difficulty level of the subsequent section. Depending on your accuracy in the first section, the second section can be of lower, medium, or higher difficulty. This difficulty level can significantly impact your final score.How Schools Use GRE Scores?When applying to graduate or professional programs, your GRE scores play a crucial role in showcasing your preparedness and potential for success. Here’s how these scores are utilized in the admissions process:Assessing Readiness: Graduate and professional programs use your overall and section GRE scores to evaluate your readiness for the program. High scores can demonstrate your ability to handle the academic rigor of the program, giving admissions officers valuable insight into your capabilities.Component of a Holistic Review: It’s important to note that GRE scores are just one component of a comprehensive admissions review. Admissions committees also consider personal statements, academic transcripts, letters of recommendation, and sometimes relevant work experience. Your GRE scores complement these elements, providing a fuller picture of your qualifications.Program-Specific Score Expectations:Math-Heavy Programs: For programs focused on mathematics or engineering, such as engineering degrees, higher GRE scores in Quantitative Reasoning are often essential. This reflects your strong analytical and problem-solving abilities.English and Humanities Programs: Conversely, for programs in fields like English or the humanities, higher Verbal Reasoning scores are typically required. This demonstrates your proficiency in reading comprehension and critical thinking.How to Improve Your GRE Scores Your GRE score will decide your future and career. Hence one needs to score well in this entrance examination to grab their target university. A good GRE score puts a good impression on various top-tier colleges and universities as it shows the candidate's analytical, logical, problem-solving, and evaluating skills. Most of the elite universities are searching for students who have scores above the 90 percentile. Scoring this much in this general test can be a bit challenging but not impossible. Here is how you can improve your GRE score.To improve your score in Verbal Reasoning you can consider the following strategies:Enhance VocabularyGRE tests include college-level vocabulary questions that need to be prepared thoroughly.Read more, look for online and offline sources, and prepare from sample questions provided by ETS.Practice Reading ComprehensionsTo improve reading comprehension you need to practice hard on unseen passages. Analyze the main idea, key details, and the author's tone of writing style.To improve your score in Quantitative Reasoning you can consider the following strategies:Practice Math QuestionsQuantitative reasoning is mainly based on problem-solving skills.To conquer your GRE you need to work hard on various types of math problems and concepts consistently.Work on Time-ManagementWithout time management you cannot succeed in anything. Practice math problems with a timer next to you so that you can improve your time-management skills.To improve your score in Analytical Writing you can consider the following strategies:Understand the two tasksUnlike the other two sections, analytical writing has a subjective format. In comprises of two tasks, the Issue task, where you explain your views on a very common issue, and the Argument task, where you are required to support your argument.Practice EssaysEssays are not as easy to write and prepare as MCQs. Hence you need to structure your essay in the examination with appropriate knowledge. To master essay writing, practice essays on multiple topics while also assessing your time-management skills.10 Tips to Get Good Score in GRE For achieving the highest score in GRE there is no shortcut method. The only path is hard work along with the smart world. You have to adopt those strategies that work the best for you. Following are some of the tips that you can consider to score high on the GRE.1. Make a study chartBefore starting your preparation, make a study plan about the things and topics you need to cover. Focus on those topics that need more attention according to you for example something with an average difficulty level and higher marks. Divide your time based on this plan.2. Use official GRE materialsEducation Testing Service or ETS administers the GRE and offers official practice materials for the GRE including sample questions, mock tests, and various sources for preparation. With the help of this only thing you need to do is stay consistent.3. Give the maximum number of mock testsAs you finish your topics, give mock tests available on the internet for each topic separately. By doing that you can understand how much time it takes for you to complete each section. Therefore working on the one that needs attention. It will also help in improving your speed.4. Improve time-managementThere are a total of 40 questions in both quantitative and verbal sections that you need to attempt in 3 hours and 45 minutes hence while preparing for essays or math problems or giving mock tests, always have a timer next to you to efficiently utilize the time limit.5. Highlight your errorsMistakes make a man perfect. Always highlight the errors you are making while problem-solving, understand them, learn from them, and ensure you don't repeat the same mistakes.6. Start EarlyTake your time and begin your preparation for the GRE early to allow more chances of improvement. By starting early you can give time to each topic instead of cramming in the last few days.7. Set a target scorePaste your ideal GRE target score in your study room so that the first thing you see while preparing for your examination is your dream score. This will help you stay motivated and will force you to work when you want to watch series, movies, anime, etc.8. Stay CalmDuring your preparation period, you will have anxiety and that is normal. It just means you are getting out of your comfort zone. Make sure to stay calm to stay focused on your exam preparation. 9. Take brakesYou need to understand that sitting for a long time won’t help. You should have the capacity to understand and learn what you are studying and to do so breaks are required. There are many different methods which help you study as well as in taking breaks. Example of such a technique is the Pomodoro method.10. Work HardHard work is the key to success. Be consistent in your preparation and always push your limits. There will be days when you don’t want to study, it's not about doing more, it's about not giving up.What is a good GRE score for an MBA?When applying to top business schools, your GRE score plays a critical role in determining your candidacy. Here’s a breakdown of what constitutes a competitive GRE score for MBA programs, particularly at top 50 business schools:Score Ranges for Top Business Schools:Top 50 Business Schools: Generally, GRE scores range from 310 to 330. The average GRE score among these schools is approximately 308.Competitive Score for MBA Applicants: To stand out, aim for a GRE score that is at least 10 points above the average score of your target business school. For instance, if the average GRE score at your chosen school is 308, a competitive score would be 318 or higher.Adjusting for Candidacy Pool:Over-Represented Candidates: If you belong to a more common pool of candidates, such as those with similar professional backgrounds or academic qualifications, you may need to score at least 20 points above the average to be competitive.Target Scores: For top 50 business schools, aim for a GRE score between 318 and 330. Scores exceeding 330 are considered excellent and can significantly strengthen your application.What is a Good GRE score for a scholarship?GRE scores play a significant role in helping business schools and graduate programs assess your application. A higher score can make your application stand out and improve your chances of securing a scholarship. However, it’s important to note that a high GRE score alone does not guarantee a scholarship.Scholarship Criteria:Merit-Based Scholarships: Some institutions, like the Kelley School of Business, award merit-based scholarships based on academic performance, professional experience, and the overall strength of the application.Need-Based Scholarships: Schools such as Harvard Business School focus on financial need rather than merit when awarding scholarships.Scholarship Strategies:Check Scholarship Requirements: Review the scholarship page of your target institution to understand the evaluation criteria and types of scholarships offered. Many schools do not specify exact score requirements but will detail their selection process.Consult with Scholarship Recipients: Reach out to current or past scholarship recipients to learn about their scores and application strengths.Aim Higher Than the Average: Research the average GRE score of admitted students and aim to score a few points above it. For example, if the average GRE score at Yale is 330, targeting 334 or higher could enhance your admission chances. To improve scholarship prospects, consider aiming for scores even higher, such as 337.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffScore High on GRE- FAQsWhat is a good score in GRE out of 340?Out of 340, a candidate must secure a total of 320 if their goal is to be admitted to top universities. But it varies from one person to another, the section scores and the university requirements. To understand better, first, let's understand the scoring pattern of the GRE.Is 300 a good GRE score?Yes, 300 is a good score and above average on the GRE. Scores like 300 and above increase your chances of getting into highly reputable institutions and programs.Is 270 a good GRE score?A 270 on the GRE is considered quite low, especially when competitive graduate programs often expect scores above 300. However, it doesn't mean your study abroad aspirations are unattainable.Is 295 a bad GRE score?A GRE score average of 290 to 300 can take you to a quality university in the USA, which would surely help you take off your career ladder. Not just that, there are a variety of courses and MS programs that you can choose from. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE | https://www.geeksforgeeks.org/good-gre-score-benchmarks-top-schools/ | Data Science & ML | Score High on GRE: How to Get Good Score in GRE | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, 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12 Sep, 2024 | Top MBA Universities Accepting GRE Scores in UK in 2024
12 Sep, 2024
If you're aiming for an MBA in the UK and wondering whether your GRE score will be accepted, you're in luck. Many top UK universities now accept GRE scores for MBA admissions, offering you greater flexibility. In this comprehensive guide, we'll delve into the best MBA programs in the UK that accept GRE scores, providing crucial details about each institution. Whether you’re targeting prestigious schools like Oxford, Cambridge, or other leading UK business schools, this guide will help you navigate your options.Discover which universities are now recognizing the GRE for their MBA programs, explore specific requirements, and find out how to align your GRE score with your career aspirations. From program highlights to application tips, we cover everything you need to make an informed choice about your MBA journey. List of MBA Colleges in the UK Accepting GRE 2024Here is the list of Universities/Colleges accepting GRE scores for MBA. Check out popular admissions requirements across UK universities for the GRE:University Name CampusesCity University LondonLondonCranfield UniversityCranfieldHult International Business SchoolLondonUniversity of LeedsLeedsLondon Business SchoolLondon (EMBA)University of OxfordOxfordUniversity of CambridgeCambridgeUniversity of KentCanterburyUniversity of ManchesterManchesterUniversity of ReadingReadingUniversity of WarwickCoventryThe Graduate Record Examination, or GRE as it is more widely known, is the full name of the exam, which is administered by ETS. Owing to the COVID-19 pandemic, ETS, the organization that administers the GRE, has introduced the GRE at Home program for applicants who would like to take the test from the comfort of their own homes. While some colleges did, as part of the admissions process, ease eligibility requirements in response to the COVID-19 pandemic. But while COVID-19 is declining, colleges are reverting to their earlier entrance standards. Effective GRE Preparation StrategiesThe Analytical Writing Assessment (AWA) is the first section of the GRE General Test, featuring two tasks: the Analysis of an Issue and the Analysis of an Argument, each with a 30-minute time limit. After AWA, the GRE includes two sections of Verbal Reasoning, two sections of Quantitative Reasoning, and an unscored experimental section that could be Verbal or Quantitative.Optimize your GRE preparation by starting with a full-length GRE practice test. This initial assessment will help identify your strengths and weaknesses, allowing you to tailor your study efforts effectively. Understand your target GRE score—the score needed to meet or exceed the average of your chosen university’s requirements. Aim for a score above this average to make a strong impression.Create a comprehensive GRE study plan to bridge the gap between your current score and target. Incorporate GRE prep classes, online resources, and GRE preparation materials into your routine. Learn to use the on-screen calculator efficiently, as it can be both a valuable tool and a potential distraction.Enhance your GRE vocabulary by reading analytical non-fiction, and consistently practice with GRE sample papers. Regularly evaluate your progress and refine your strategy to improve your performance.Read MoreGRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverUniversities in USA Without GRE for Masters in 2024GRE Score ValidityGRE Coaching in IndiaGRE Cut Off | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Top MBA Universities Accepting GRE Scores in UK in 2024 | https://www.geeksforgeeks.org/top-mba-universities-accepting-gre-scores-in-uk-in-2024/?ref=lbp | Data Science & ML | Top MBA Universities Accepting GRE Scores in UK in 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Top MBA Universities Accepting GRE Scores in UK in 2024, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [0.00446319394, 0.0379356146, -0.0289173294, 0.0524923056, 0.0699407309, -0.0133436322, -0.00832598563, 0.0182326213, -0.0118242474, -0.00316130137, 0.00376170361, -0.0120509295, 0.0185757093, -0.0278635621, -0.0206954964, -0.00482772384, 0.0174239166, 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07 Oct, 2024 | Average GRE Score for MIT University 2024
07 Oct, 2024
If you're considering applying to MIT University for graduate studies, you're probably wondering about the average GRE score for MIT University in 2024. The Graduate Record Examination (GRE) is a significant part of the admission process for most graduate programs at MIT. Knowing the MIT average GRE score can help you set realistic goals and improve your chances of standing out in the competitive applicant pool.In this blog, we’ll break down everything you need to know about the average GRE score for MIT across various programs, the importance of a strong GRE score, tips to improve your score, and how GRE fits into the overall MIT application process. Table of ContentWhat is the Average GRE Score for MIT University in 2024?Why is the GRE Important for MIT University?MIT GRE Score Breakdown by ProgramHow to Improve Your GRE Score for MIT UniversityGRE Scores and the MIT Application ProcessIs a High GRE Score Enough to Get Into MIT?ConclusionAverage GRE Score for MIT University 2024- FAQsWhat is the Average GRE Score for MIT University in 2024?For 2024, the average GRE score for MIT graduate programs varies depending on the department and program you are applying to. However, we can provide a general overview of the scores expected for different sections of the GRE:Quantitative Reasoning: For most MIT programs, particularly in STEM fields, the average score typically falls between 165-170.Verbal Reasoning: 155-165.Analytical Writing: The average score for this section is usually around 4.0 to 5.0.Keep in mind that these are average scores, and some programs may have higher or lower expectations. For highly competitive programs, especially in engineering, computer science, or business, it’s common for admitted students to score in the top percentiles.Does MIT Require a GRE for Admission?Yes, admittance to several of MIT's programs, including Aeronautics and Astronautics, Biology, Engineering, Chemistry, Microbiology, Physics, and others, needs the GRE.Why is the GRE Important for MIT University?MIT University is one of the most competitive institutions globally, and a strong GRE score can significantly enhance your application. While the GRE is not the only factor MIT considers, it provides a standardized metric for evaluating applicants from diverse educational backgrounds. A high GRE score demonstrates your ability to handle rigorous coursework and problem-solving skills, particularly in the Quantitative Reasoning section, which is crucial for many STEM programs.For non-STEM programs, a solid score in Verbal Reasoning and Analytical Writing is equally important for non-STEM programsMIT GRE Score Breakdown by ProgramEach graduate program at MIT has its own GRE score expectations, so it’s essential to research the specific requirements for your field. Below are some average GRE score ranges for popular MIT graduate programs:MIT School of EngineeringQuantitative: 168-170Verbal: 155-165Analytical Writing: 4.0-5.0MIT Sloan School of Management (MBA)Quantitative: 165-170Verbal: 155-165Analytical Writing: 4.5-5.0MIT Department of EconomicsQuantitative: 165-170Verbal: 160-165Analytical Writing: 4.0-5.0MIT Department of ArchitectureQuantitative: 155-165Verbal: 160-165Analytical Writing: 4.0-5.0MIT Computer Science and Artificial Intelligence Laboratory (CSAIL)Quantitative: 168-170Verbal: 155-165Analytical Writing: 4.0-5.0How to Improve Your GRE Score for MIT UniversityNow that you know the average GRE scores for MIT University, it’s time to focus on improving your own score to meet or exceed these benchmarks. Here are some tips to help you prepare effectively:Understand the GRE Format: Familiarize yourself with the structure of the GRE. Knowing how each section works will help you allocate your time wisely during the test.Targeted Practice: Focus on the areas where you’re weakest. For most STEM applicants to MIT, the Quantitative Reasoning section is critical, so prioritize improving your math skills. For non-STEM applicants, the Verbal Reasoning and Analytical Writing sections may require more attention.Use High-Quality Study Materials: Invest in reliable GRE preparation books and online resources. Practice with sample tests that reflect the actual GRE experience.Take Timed Practice Tests: Simulate the actual GRE test by taking timed practice tests. This will help you build stamina and improve your time management skills, ensuring that you can complete all sections within the allotted time.Consider GRE Prep Courses: If you’re struggling to reach your desired score, enrolling in a GRE prep course could provide you with personalized guidance and study strategies tailored to your needs.Review Test-Taking Strategies: Learn how to approach different types of questions. For example, in Quantitative Reasoning, practice solving problems quickly and accurately, while in Verbal Reasoning, focus on improving your reading comprehension and vocabulary.GRE Scores and the MIT Application ProcessWhile the average GRE score is an essential component of your application to MIT University, it’s just one part of the admissions process. MIT takes a holistic approach to evaluating applicants, which means that other factors are also critical, such as:Undergraduate GPA: Your academic record is a strong indicator of your ability to succeed in graduate school.Letters of Recommendation: Strong, personalized letters from professors or professionals in your field can significantly bolster your application.Statement of Purpose: This is your opportunity to explain why you want to study at MIT and how your background, skills, and goals align with the program you’re applying to.Research Experience: For research-intensive programs, having a strong background in research can be just as important as your GRE score.Work Experience: In some cases, relevant work experience can strengthen your application, especially for programs like the MIT Sloan MBA.Is a High GRE Score Enough to Get Into MIT?While achieving a high GRE score is important, it’s not a guarantee of admission to MIT University. MIT receives thousands of applications each year from highly qualified candidates, and the competition is fierce. In addition to your GRE score, MIT looks at your overall academic performance, professional experience, and fit with the program.For example, an applicant with an average GRE score but exceptional research experience or a compelling statement of purpose could still be a strong contender for admission. On the other hand, a high GRE score alone won’t compensate for a lackluster application in other areas.ConclusionThe average GRE score for MIT University in 2024 is an important factor for anyone looking to apply for graduate studies at this prestigious institution. While it’s not the only criterion MIT uses, a strong GRE score can boost your chances of admission, especially for competitive programs. Remember, the key to success is not just achieving a high GRE score but also building a well-rounded application that highlights your strengths, research experience, and passion for the field.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffAverage GRE Score for MIT University 2024- FAQsWhat is the minimum GRE score required for MIT University?MIT University does not have a strict minimum GRE score requirement. However, competitive applicants typically have scores in the upper percentiles, especially for STEM programs. For example, a score between 165-170 in the Quantitative Reasoning section is common for engineering and computer science applicants. While MIT doesn’t officially set a cutoff, aiming for a score near or above the average GRE score can significantly boost your chances.Does MIT accept GRE scores for all graduate programs?Most graduate programs at MIT require GRE scores as part of the application process, especially in STEM fields. However, some programs, such as certain degrees in the School of Humanities, Arts, and Social Sciences, may either waive the GRE requirement or place less emphasis on it. Always check the specific requirements for the program you're applying to on MIT’s official website.Can a high GRE score guarantee admission to MIT?A high GRE score alone cannot guarantee admission to MIT University. MIT uses a holistic review process, considering other factors like your undergraduate GPA, research experience, letters of recommendation, and statement of purpose. While a strong GRE score can enhance your application, it is essential to submit a well-rounded application to increase your chances of acceptance. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Average GRE Score for MIT University 2024 | https://www.geeksforgeeks.org/average-gre-score-for-mit-university/?ref=lbp | Data Science & ML | Average GRE Score for MIT University 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Average GRE Score for MIT University 2024, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0120697133, -0.0100456988, -0.0215682369, 0.0259243846, 0.0402040444, -0.0217276085, -0.0404165387, 0.015798999, -0.00713983038, -0.019453913, -0.0204632636, -0.0309392642, 0.0306630209, -0.0211644974, -0.0215682369, 0.00834042672, 0.0128346952, -0.00305461488, -0.0270931069, 0.0151615152, -0.0297917929, -0.0367616266, -0.0171802174, 0.00273056, -0.035316661, 0.00778794, -0.00843073707, -0.00905228499, -0.027156854, -0.0110391127, 0.0552486889, -0.00085197197, 0.00996601302, -0.0414577648, -0.0287293177, -0.0133553073, 0.0141309146, 0.00412505819, 0.00335742021, 0.0145665286, 0.012207835, 0.00984382909, 0.0446664393, 0.0163408611, 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04 Oct, 2024 | List of Law Schools That Accept GRE Scores in 2024
04 Oct, 2024
As more students pursue law as a career, the traditional requirement of taking the LSAT is evolving. Over recent years, numerous law schools have started accepting GRE scores as an alternative to the LSAT. This shift has opened doors for students who may already have taken the GRE for other academic pursuits or prefer its structure over the LSAT. In this guide, we will explore law schools that accept GRE scores in 2024, how to leverage your GRE score for law school applications, and key strategies to enhance your chances of getting accepted into top programs. Table of ContentWhy Do Law Schools Accept GRE Scores?Key Advantages of Taking the GRE for Law School ApplicationsLaw Schools That Accept GRE Scores 2023-202International Law Schools That Accept GRE ScoresHow Law Schools Evaluate GRE ScoresShould You Take the GRE or the LSAT?How to Prepare for the GRE to Apply to Law SchoolsGRE vs. LSAT: Which Law Schools Prefer?Why do Law Schools Accept GRE Scores?Traditionally, the Law School Admission Test (LSAT) has been the go-to exam for students pursuing a law degree. However, many law schools in the US and globally have realized that the GRE (Graduate Record Examination) offers a broader range of applicants. The GRE not only tests analytical reasoning, but it also evaluates verbal and quantitative reasoning, which can offer law schools a different perspective on a student's academic potential. Moreover, many applicants to law schools are non-traditional students who may already have GRE scores from previous applications to graduate programs.For applicants, the ability to submit GRE scores for law school adds flexibility, making the admissions process more accessible and reducing the need to prepare for multiple exams. Given the competitive nature of law school admissions, using the GRE score is a great alternative, especially for those more comfortable with its format.Key Advantages of Taking the GRE for Law School ApplicationsFlexibility in Admissions: Students who are considering both graduate school and law school can take the GRE and apply to both programs, streamlining their application process.Broader Career Options: By using GRE scores, law school applicants can keep multiple career paths open. The GRE is widely accepted by various master's and Ph.D. programs in addition to law schools.Test Format Familiarity: The GRE's structure may be more familiar to students from different academic backgrounds, particularly those in sciences or engineering.Cost Efficiency: Taking one test instead of preparing and paying for multiple exams can significantly reduce expenses related to admissions.GRE Frequency: The GRE can be taken more frequently compared to the LSAT, giving students more opportunities to improve their scores and enhance their law school applications.Law Schools That Accept GRE Scores 2023-202Below is a list of some of the top law schools in the US that accept GRE scores for the 2023-2024 admissions cycle:Harvard Law SchoolYale Law SchoolColumbia Law SchoolStanford Law SchoolUniversity of Pennsylvania Carey Law SchoolUniversity of California, Los Angeles (UCLA) School of LawUniversity of Chicago Law SchoolGeorgetown University Law CenterNew York University (NYU) School of LawNorthwestern Pritzker School of LawThese law schools are among the best in the world and have paved the way for accepting GRE scores as part of their admissions process. While most law schools still prioritize LSAT scores, the acceptance of GRE scores provides applicants with increased flexibility and options.International Law Schools That Accept GRE ScoresIn addition to law schools in the US, many international law schools are also accepting GRE scores for admissions. Some of the top law schools outside of the US that accept GRE scores include:University of Toronto Faculty of Law (Canada)McGill University Faculty of Law (Canada)University of Melbourne Law School (Australia)The University of Sydney Law School (Australia)London School of Economics (LSE) Department of Law (UK)University of Cambridge Faculty of Law (UK)These prestigious law schools are known for offering strong global law programs, and the acceptance of GRE scores further opens opportunities for international applicants.How Law Schools Evaluate GRE ScoresLaw schools evaluate GRE scores similarly to how they assess LSAT results, with a focus on the verbal reasoning and analytical writing sections, which are crucial for law studies. However, each law school weighs GRE scores differently, so it’s essential to research the GRE score requirements for law schools that interest you. Most law schools will not provide a specific minimum GRE score, but competitive scores typically range between 315-330 or higher.Should You Take the GRE or the LSAT?Deciding between the GRE and the LSAT can be challenging. Here’s a comparison to help you determine which test is best suited for your application strategy:GRE: Offers flexibility and broader applicability beyond law school admissions. It includes sections on verbal reasoning, quantitative reasoning, and analytical writing. Ideal for students pursuing diverse academic and professional goals.LSAT: Designed specifically for law school admissions, the LSAT focuses on reading comprehension, analytical reasoning, and logical reasoning, skills directly related to legal studies. Law schools may still give more weight to LSAT scores, especially for applicants without a strong quantitative background.If you're considering applying to law schools that accept GRE scores, taking the GRE can simplify your preparation, particularly if you are also applying to graduate programs in other fields.How to Prepare for the GRE to Apply to Law SchoolsTo make the most of your GRE score for law school applications, it's important to focus on specific sections that law schools value. Below are some tips on how to prepare for the GRE:Verbal Reasoning: Since law schools focus on verbal reasoning as an indicator of your ability to comprehend complex texts, this section is crucial. Build your vocabulary and practice reading comprehension to enhance your performance.Analytical Writing: Law schools emphasize analytical writing to assess how well you can construct clear, concise, and logical arguments. Practice writing essays that make strong claims and support them with clear evidence.Quantitative Reasoning: While law schools generally do not prioritize quantitative scores, achieving a good score in this section can help your application stand out, especially if you’re applying to programs with a focus on intellectual property or tech law.Practice Tests: Take full-length GRE practice tests to familiarize yourself with the test format, timing, and types of questions. Analyzing your practice test results will help you focus on areas that need improvement.GRE vs. LSAT: Which Law Schools Prefer?While many law schools now accept GRE scores, it’s important to understand that the LSAT remains the traditional test for law school admissions. Some schools may still give priority to LSAT applicants when evaluating candidates with similar qualifications. Research the specific policies of the schools you're applying to so you can make an informed decision.Some law schools may also have different application requirements for GRE and LSAT applicants, such as essays or recommendation letters, so be sure to check the specific criteria for the schools on your list.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffLaw Schools That Accept GRE Scores in 2024- FAQsDo all law schools accept GRE scores?No, not all law schools accept GRE scores, but many prestigious schools do. It’s important to check each law school's specific admission policies before applying.What is a good GRE score for law school?While there is no definitive answer, a competitive GRE score for law schools typically ranges from 315-330 or higher, with a strong emphasis on verbal reasoning and analytical writing sections.Can I apply to law schools with only a GRE score?Yes, many law schools accept the GRE as an alternative to the LSAT. However, some schools may require additional materials or have different evaluation criteria for GRE applicants. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/List of Law Schools That Accept GRE Scores in 2024 | https://www.geeksforgeeks.org/law-schools-that-accept-gre-scores/?ref=lbp | Data Science & ML | List of Law Schools That Accept GRE Scores in 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, List of Law Schools That Accept GRE Scores in 2024, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [0.0011231699, -0.0398439281, -0.0330025256, 0.0534303673, 0.0513586774, -0.0153329261, 0.00907569472, 0.00908171758, -0.0124662826, 0.00940090232, 0.0229210984, 0.00706422701, 0.0190908778, -0.0181273, -0.00828676578, -0.00730512151, -0.0134539502, -0.00962373, -0.0263056643, 0.0231017694, -0.0164892189, 0.00690764561, 0.0219575204, -0.0116171306, -0.0257756971, -0.00717865163, 0.00302623538, 0.0101657417, -0.0437223278, -0.0296781845, 0.0361100659, 0.0208975859, 0.0210782569, -0.0357487239, -0.00487811072, -0.046083089, -0.00360739301, 0.000728329062, 0.00846743677, 0.0232342612, 0.0436259694, 0.0164289959, 0.0280641932, 0.00752192643, 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12 Aug, 2024 | Minimum GRE Exam Score for Top Universities: List of Top 25
12 Aug, 2024
Candidates must achieve GRE minimum score requirements for top universities to be considered for Master's programs. Depending on the university or program you are applying to, there are different GRE cutoffs. For most programs, scoring 310 or higher is generally regarded as competitive. You will be urged to review the official website's guidelines before submitting your scores. The data indicates that 1,13,304 Indian candidates took the GRE in the testing year of 2022–2023. Moreover, prestigious Indian business schools have begun to accept GRE results for MBA admission. The average GRE cut-off for ISB top programs falls between 319 and 330. Table of ContentMinimum GRE Score for Top Universities in 2024Minimum GRE Score for Top Business SchoolsA Good GRE ScoreGRE Score RangeMinimum GRE Score for Top Universities in 2024-FAQsMinimum GRE Score for Top Universities in 2024The minimum GRE scores varies and are dependent upon the university to which you are applying. High verbal and quantitative GRE scores are frequently required by the world's best colleges. The top US and UK colleges' updated GRE cutoffs are provided below: Universities Accepting GRE ScoresVerbalQuantitativeAnalytical WritingMassachusetts Institute of Technology (MIT)1581595.3Stanford University1591584.8University of California, Berkeley153 – 1561674.5The University of California, Los Angeles (UCLA)1551675.0University of Virginia1631664.5University of Michigan – Ann Arbor1601675.0University of North Carolina – Chapel Hill1581604.5Georgia Institute of Technology1581674.3University of California – San Diego1621605.5University of Illinois – Urbana/Champaign1551654.0University of Wisconsin – Madison1631634.5University of Washington1561674.0Pennsylvania State University1501653.0University of Florida (UFL)1541653.0The University of Texas, Austin1551654.0Ohio State University1561654.0California Institute of Technology1601575.0Duke University1601604.5The University of Chicago1581674.0Northwestern University1601605.0Washington University in St. Louis1611605.0Johns Hopkins University1631644.8Rice University1601675.0Emory University1531634.0-6.0University of Notre Dame1651655.3Vanderbilt University1571664.8College of William and Mary1581604.5Minimum GRE Score for Top Business SchoolsGRE scores are now accepted for MBA programs at practically every business school in the globe. The average GRE cutoff score for MBA programs is typically higher than that of MS programs. Examine the MBA class profile thoroughly before applying to any business school. Business SchoolsGRE Score RangeLondon School of BusinessMIT Management SchoolStanford Graduate School Of BusinessHarvard Business SchoolOxford (Said)320+Owen Graduate School of Management (Vanderbilt University)Imperial College Business SchoolCarroll School of Management - Boston CollegeIESE Business SchoolMcCombs School of Business, University of Texas310-320University of Alabama HuntsvilleRobert H. Smith School of Business, University of MarylandMcGill (Desautels)Miami Herbert Business SchoolEli Broad College of Business, Michigan State University300-310University of DaytonAdams State CollegeEMLyon Business SchoolSORRELL COLLEGE OF BUSINESSAlcorn State University290-300A Good GRE ScoreA strong GRE score varies depending on the particular colleges and programs you are applying to. A competitive score on the GRE is typically defined as falling between 160 and 165 on the verbal and quantitative reasoning portions and 4-5 on the analytical writing component. It is advisable to verify the precise score requirements and range of the colleges you are considering, though, as these can differ significantly. A 160 or higher average on each portion of the GRE may be required by some prestigious universities. Remember that a strong GRE score is only one component of the admissions process; other elements taken into account include your academic history, recommendation letters, and personal statement. Every year, 25% of candidates receive a competitive GRE score and 50% of candidates receive an average GRE score. Furthermore, fewer than 5% of applicants are able to obtain the highest GRE scores.GRE Score RangeThe analytical writing component score varies from 0 to 6, and the verbal and quantitative sections of the GRE range from 260 to 340. A GRE score in the range of 305 to 315 is regarded as typical and is accepted by some of the top colleges in the world. To understand the GRE score range, consult the list below:GRE verbal (score range: 130–170) GRE quantitative reasoning (score range: 130–170) Analytical Writing on the GRE (0–5)GRE Score Ranges based on PerformanceGRE Verbal ReasoningGRE Quantitative ReasoningGRE Analytical Writing AssessmentBest GRE Score Range163 to 170165 to 1705.0 to 6.0Competitive GRE Score Range158 to 162159 to 1644.5Good GRE Score Range152 to 158153 to 1584.0Average GRE Score Range146 to 150150 to 1533.5Poor GRE Score RangeBelow 139Below 141Below 3.0Best GRE Score RangeYou will rank in the top 10% of all GRE exam takers with these scores. GRE Verbal Section: 163 - 170GRE Quantitative Section: 165 - 170GRE Analytical Writing: 5.0 – 6.0Competitive GRE Score RangeThese GRE results (top 25% of all GRE test takers) will place you in a very competitive position for admissions. GRE Verbal Section: 158 - 162GRE Quantitative Section: 159 - 164GRE Analytical Writing: 4.5Good GRE Score RangeAlthough your GRE score of 50% or higher puts you ahead of the competition, it won't help you as much when applying to very competitive schools. GRE Verbal Section: 152 - 158GRE Quantitative Section: 153 -158GRE Analytical Writing: 4.0US university GRE cutoff scores are typically fairly high. A score in the 75th percentile is regarded as favorable. Getting a score of 320 or more is really good and can help you get into any college you wish to attend. Maintain a target score higher than 318 to ensure a smooth admissions process. FAQs on Minimum GRE Score for Top UniversitiesIs 320 a good GRE score?The majority of colleges for master's degrees and the MBA programs at the best business schools accept a GRE score of 320. On their official websites, you can verify the score requirements for universities and business schools. What is the cut off mark for GRE?Universities determine their own requirements for GRE scores; there is no set minimum score needed to be admitted to a university. A GRE score of 310 or above is typically required for admission to most master's programs, and 320 or higher for MBA programs. What is the qualifying score for GRE? The GRE score falls between 260 and 340 on a scale; there is no minimum score required. To apply to and be admitted into some of the top colleges in the world, you must receive a score of 300 or above. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief 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Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [0.0045596608, 0.0154554741, -0.0246813856, 0.0428252853, 0.0453360565, -0.00852715783, -0.0336349, 0.018759748, 0.0091134, -0.0015707144, -0.0103510227, -0.032947991, 0.0306740832, -0.0236391779, -0.0149462139, 0.0189137105, 0.00846794154, -0.00184755097, -0.00874625891, 0.0130986627, -0.0335164703, -0.0346771106, 0.00268102135, -0.00898312405, -0.0579373, 0.0069875326, -0.000588462746, -0.0111386, -0.00710596517, -0.00464552455, 0.0406224355, -0.00625324948, 0.033326976, -0.0251551177, -0.00211254414, -0.030816203, 0.00751455827, -0.0269079208, -0.00929104909, 0.0261262655, 0.0352929607, 0.00562259508, 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14 Aug, 2024 | Top 10 Canadian Universities that Accept SAT Scores in 2024
14 Aug, 2024
If you're considering studying in Canada and wondering which universities accept the SAT, you're not alone. Many students aim to find Canadian universities that recognize SAT scores for admissions. Top institutions like the University of Toronto, McGill University, and the University of British Columbia are known for accepting SAT scores and offering a range of programs for international students. By choosing a university that accepts the SAT, you can streamline your application process and focus on your academic goals. This guide will help you navigate your options and find the best fit for your higher education journey in Canada. Table of ContentSAT Exam HighlightsCanadian Universities That Accept SAT ScoresHow to Apply to Canadian Universities?Student Visa Requirements to Study in CanadaCanadian Universities that Accept SAT- FAQsSAT Exam HighlightsExam NameSATFull formScholastic Assessment TestOfficial Websitehttps://collegereadiness.collegeboard.org/sat Accepted by Undergraduate courses in the US and CanadaConducted byThe College BoardMode of ExamwrittenSAT Fee101$ (INR 7.5K) 103$ (INR 7.6K)Score Range400-1600 pointsCanadian Universities That Accept SAT ScoresThe list of colleges that accept the SAT at the time of admission is given below:University Score Acadia University (SAT – 1,100)Algoma University(SAT – 1,100University of Lethbridge (SAT – 1040)Athabasca University(SAT- 1200)Capilano University(SAT -1,100)Carleton University(SAT – 1380)College of New Caledonia(SAT – 1245)Dalhousie University(SAT – 1,100)McGill Universit(SAT – 1300)ST Mary’s Universit(SAT 1140)University of Manitoba(SAT 1100)How to Apply to Canadian Universities?In Canada, bachelor's degrees take three to five years to complete. In order for an Indian student to apply to Canadian universities, they must possess:A minimum of 65% in Class 12. When applying for a class 11, you must submit your Class 9, 10, and 11 grades; however, once your Class 12 grades are available, you must also submit them.6.5 or above on the IELTS, including sectional scores above 6If you are applying to engineering schools, you ought to have taken classes in English, math, chemistry, and physics in grade 12.A creative portfolio or film must be submitted with your application for a fine arts program.Student Visa Requirements to Study in CanadaAcceptance letter from the university or collegeProof of English proficiency like IELTS or TOEFLValid passportProof of fundsCanadian Universities that Accept SAT- FAQsWhat is the validity of the SAT?SAT scores are valid for 5 years from SAT results.When is the ideal time to take the SAT?In order to be considered for entrance to college programs, students should take the SAT during their eleventh or twelfth grade year. What type of questions are asked on SAT?Reading, Writing & Language, Math, and Essay (Optional) are the four components of the SAT. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Top 10 Canadian Universities that Accept SAT Scores in 2024 | https://www.geeksforgeeks.org/canadian-universities-that-accept-sat-scores/?ref=lbp | Data Science & ML | Top 10 Canadian Universities that Accept SAT Scores in 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Top 10 Canadian Universities that Accept SAT Scores in 2024, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.00862264261, 0.0229475144, -0.0196311139, 0.0472809896, 0.033837188, -0.0184134506, -0.0292239282, -0.00358864293, 0.00503894966, 0.00410837727, -0.0226901229, -0.0513596646, -0.00565273128, -0.0115232561, -0.0365893058, 0.0160672199, 0.0325106308, 0.0268875975, 0.000326690235, 0.0337579921, -0.0403907932, -0.010652082, 0.0116618518, -0.039579019, 0.00210368726, -0.0166117046, 0.0163246132, -0.00878103822, -0.00493500242, -0.0383514538, 0.0419747457, -0.00559333293, -0.0110777691, -0.0207695793, -0.0160771199, -0.0122954333, -0.0266104061, 0.00142308255, -0.0177006721, 0.00242790254, -0.00481620617, 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09 Sep, 2024 | Average Harvard GRE Scores in 2024
09 Sep, 2024
Are you curious about the average Harvard GRE score and how it might impact your application? Understanding the average GRE score for Harvard is crucial for anyone aiming to get into this prestigious institution. Harvard University in Cambridge, Massachusetts, is a top choice for graduate school applicants due to its prestigious Ivy League status and unparalleled academic reputation. Hosting over 14,500 graduate students, Harvard offers diverse programs through its renowned schools, including the Harvard Graduate School of Arts and Sciences, Harvard Law School, Harvard Business School, and School of Engineering and Applied Sciences.With the world’s largest academic library system and elite faculty, Harvard sets high GRE score requirements and a rigorous application process. Aspiring students target Harvard for its exceptional resources, making it a dream destination for many.Average Harvard GRE scoresTable of ContentWhat is a good GRE score to get into Harvard?Average GRE scores for HarvardWhat Are Your Chances of Admission to Harvard?What is a good GRE score to get into Harvard?While a strong GRE score can enhance your chances of admission to Harvard University, it is just one component of a multifaceted application process. Harvard evaluates candidates holistically, considering various elements beyond the GRE, such as the Statement of Purpose (SOP), letters of recommendation, academic transcripts, relevant work experience, and prior research contributions. Each department has its own criteria and focuses on different qualifications, making the selection process highly nuanced.Due to capacity constraints and a highly competitive applicant pool, even well-qualified candidates may face rejection. With acceptance rates for some graduate programs at Harvard dropping as low as 3%, gaining admission to this prestigious institution remains exceptionally challenging.Average Harvard GRE Scores 2024Average GRE scores vary significantly depending on the field of study at Harvard University. For example, in the field of Education, the average verbal score is in the 91st percentile, and the quantitative score is in the 71st percentile, with an analytical writing average of 5.0 for PhD candidates. For a Master of Education, the verbal average is in the 81st percentile, the quantitative average in the 61st percentile, and the analytical writing average is 4.6 (source: gsas.harvard.edu).In contrast, the engineering field has a notably high average quantitative score of 167, while the average verbal score is slightly lower at 160. At the Harvard John A. Paulson School of Engineering and Applied Sciences, GRE quantitative scores typically range from the 90th to 95th percentile, while verbal scores are between the 75th and 80th percentiles (source: seas.harvard.edu).For the Graduate School of Design, which includes architecture, the average GRE scores are 157 for verbal, 159 for quantitative, and 4.0 for analytical writing (source: gsd.harvard.edu).The table below illustrates the average GRE scores for various Harvard graduate programs:DepartmentAverage VerbalAverage QuantitativeEngineering160167Computer Science155161Psychology163154Physics167167Chemistry164163Mathematics165167Education160156Architecture / Design157159All Harvard programs listed below are organized alphabetically by field and include both master’s and doctoral degrees (unless specified otherwise). Most of the GRE scores provided are averages, although some programs have reported recommended or median scores (i.e., the 50th percentile, which is comparable to the average):ProgramUS News RankingGRE Required?Average GRE ScoresAverage GPAAcceptance RateHistory of Art and Architecture PhD—YesUnavailableUnavailableUnavailableBiophysics PhD1YesVerbal: 664, Quantitative: 790, AW: 5.3 (old scale)UnavailableUnavailableChemistry / Chemical Physics4YesVerbal: 163, Quantitative: 166, AW: 4.5Overall: 3.92, Science: 3.95UnavailableGraduate School of Design programs—YesVerbal: 157, Quantitative: 159, AW: 4.0Recommended: 3.4UnavailableEconomics PhD1YesVerbal: 97th percentile, Quantitative: 97th percentileUnavailable4-5%Master of Education (EdM)1YesVerbal: 80th percentile, Quantitative: 60th percentile, AW: 4.6UnavailableUnavailableEducation PhD1YesVerbal: 87th percentile, Quantitative: 58th percentile, AW: 4.9UnavailableUnavailableDoctor of Education Leadership (EdLD)2Either GRE or GMATVerbal: 69th percentile, Quantitative: 37th percentile, AW: 4.5UnavailableUnavailableEngineering and Applied Sciences23YesVerbal: 80-85th percentile, Quantitative: 90-95th percentile3.89% (all programs)English PhD8YesVerbal: Recommended 166Recommended: A- in English courseworkUnavailableFilm and Visual Studies PhD—YesUnavailableRecommended: A- in relevant courseworkUnavailableHealth Policy PhD1Either GRE or GMATVerbal: Above 80th percentile, Quantitative: Above 80th percentile, AW: Above 80th percentileUnavailable8-10%Public Health (SM, MPH, SD, DrPH)2YesMedian Verbal: 160, Quantitative: 161, AW: 4.0Verbal: 50th percentile, Quantitative: 65th percentileSM: 31.3%, MPH: 52.9%, SD: 15.7%, DrPH: 6.9%History PhD4YesUnavailableUnavailable6%JD3Either LSAT or GREUnavailableMedian: 3.8616.5%Medical Sciences PhD programs1YesUnavailableUnavailableUnavailableMiddle Eastern Studies—YesUnavailableUnavailableUnavailablePsychology PhD programs3YesVerbal + Quantitative: 1350 (old scale)UnavailableUnavailableSociology PhD programs1YesUnavailableUnavailableUnavailableTheology (MDiv, MTS, ThM, PhD)—YesUnavailableUnavailableUnavailaWhat Are Your Chances of Admission to Harvard?GRE Score and GPA Estimates for HarvardTo enhance your chances of admission to a Harvard graduate program, aim for the following GRE scores and GPA:Verbal Focus: Aim for around 165 in the Verbal section, 160 in Quantitative, and a 5.0 or higher in Analytical Writing (AW). For programs where verbal skills are crucial, strong scores in Verbal are essential. Aiming for low 160s in Quantitative and a high AW score can differentiate you from other applicants.Quantitative Focus: Strive for a Quantitative score of around 166, with a Verbal score of 161, and an AW score between 4.5 and 5.0. Math-intensive programs require high Quantitative scores, while a strong Verbal score and a solid AW score are also important but not as critical.GPA: A GPA of 3.8 or higher (equivalent to an A or A-) is ideal. A 4.0 GPA can significantly bolster your application, especially if your undergraduate coursework was rigorous and relevant.While achieving these scores and GPA will make you a strong candidate, Harvard's selection process is highly competitive, and even top scores and GPA do not guarantee admission.Key Admission Factors for HarvardMinimum GRE Score or GPA: Most Harvard programs do not have strict minimum GRE score or GPA requirements. However, if a program sets a minimum threshold, it must be met to avoid disqualification. For programs with recommended scores, aim to meet or exceed these to improve your chances.Comparison to Average GRE Scores: Research the average GRE scores for admitted students in your program. Target scores at or above these averages to position yourself as a competitive applicant. If average GRE scores are not available, aim for high scores based on general guidelines.Strength of Application Components: Beyond GRE scores and GPA, the following elements are crucial:A compelling and well-written Statement of Purpose (SOP).Strong letters of recommendation.Relevant research or extracurricular experience.Alignment of your research interests with faculty expertise.Each component of your application should be meticulously crafted to showcase your strengths and fit for the program.GRE Scores and GPA RecommendationsSectionVerbal ScoreQuantitative ScoreAnalytical Writing (AW)Recommended GPAVerbal Focus1651605.0 or higher3.8 or higherQuantitative Focus1611664.5 - 5.03.8 or higherFor a competitive edge, ensure that all aspects of your application are strong and tailored to Harvard’s high standards. Each element, from GRE scores to the Statement of Purpose, plays a crucial role in the admission decision.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffAverage Harvard GRE Scores in 2024- FAQsWhat GRE score is required to get into Harvard?The required GRE score depends on the type of program the student will apply to, but for over 50% of the programs offered at different schools within Harvard University, the average GRE score requirements are in the upper 80th percentile. That's about 162 in Quant, 158 in Verbal, and 4.5 in Analytical Writing.Is a GRE score of 326 good?Most international business schools consider a score of 325 or above to be a good GRE score, and an average GRE score above 330 will allow you to apply to top MBA programs worldwide.Is a 340 GRE good?The highest total GRE score you can get on the general test is 340. Thus, anything above the average score of 300, can be considered as a perfect GRE score. However, a good GRE score depends on the institution you are targeting. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine 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Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Average Harvard GRE Scores in 2024, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for 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22 Aug, 2024 | Top 10 Best GRE Coaching Institutes in India (Online & Offline)
22 Aug, 2024
Preparing for the GRE is a critical step for students aiming to study abroad, and choosing the right GRE coaching in India can make a significant difference in your performance. India offers a range of coaching options, from traditional classroom settings to flexible online programs. When selecting the best GRE coaching in India, consider factors like course content, faculty expertise, and success rates. Many top institutes offer comprehensive programs tailored to individual needs, making it easier to achieve a high score.For those who prefer the convenience of remote learning, GRE coaching online in India provides interactive sessions, personalized study plans, and mock tests that simulate the actual exam environment. The fees for GRE coaching in India vary depending on the institute, course duration, and mode of delivery, but investing in quality coaching can significantly enhance your prospects. Explore the top 10 GRE coaching institutes in India to find the one that aligns best with your academic goals.Table of Content
What are Indian GRE Institutes?10 Best GRE Coaching Institutes in India1. Jamboree2. Manya Group3. Abhyaas4. TIME5. Ivy Aspire6. Mnemonic Education7. Crack Verbal8. Manhattan Review9. Career Launcher10. Endeavor CareersFrequently Asked Questions - Best GRE Coaching Institutes in IndiaWhat are Indian GRE Coaching Institutes?India’s GRE coaching centers are renowned for their comprehensive preparation strategies tailored to help students excel in the Graduate Record Examination (GRE). These centers offer a blend of traditional classroom teaching and modern e-learning methods, ensuring that every student receives personalized attention. Key features include customized study schedules, extensive mock tests, and continuous support systems that guide students through their preparation journey.Beyond test preparation, these institutes provide additional services such as college application guidance, visa assistance, and information on scholarships, making them a one-stop solution for aspiring international students. By choosing a reputed GRE coaching center in India, students can significantly enhance their preparation, boost their test scores, and increase their chances of gaining admission to prestigious graduate programs worldwide.Opting for a well-regarded coaching institute not only ensures thorough GRE preparation but also equips students with the resources needed to navigate the entire application process successfully.10 Best GRE Coaching Institutes in IndiaInstitute NameMode of StudyLocation(s)WebsiteFees (approx.)JamboreeOnline, OfflineDelhi, Mumbai, Bangalore, Chennai, Pune, Hyderabad, Kolkata, Ahmedabadhttps://www.jamboreeindia.com/gmat-online-self-paced₹ 50,000 - ₹ 1,00,000+Manya Group (The Princeton Review)Online, OfflineDelhi, Mumbai, Bangalore, Chennai, Pune, Hyderabad, Kolkata, Ahmedabadhttps://www.manyagroup.com/gre/₹ 45,000 - ₹ 80,000+AbhyaasOnline, OfflineHyderabad, Secunderabad, Warangal, Kukatpallyhttps://abhyaas.in/gre-online-coaching/₹ 35,000 - ₹ 70,000TIMEOnline, OfflineDelhi, Mumbai, Bangalore, Chennai, Pune, Hyderabad, Kolkata, Ahmedabad and other major citieshttps://www.time4education.com/GRE₹ 40,000 - ₹ 80,000+Ivy AspireOnlineNAhttps://www.ivyaspire.com/workshops/₹ 30,000 - ₹ 50,000+Mnemonic EducationOnlineNAhttp://www.mnemoniceducation.com/₹ 25,000 - ₹ 45,000+Crack VerbalOnlineNAhttps://www.crackverbal.com/₹ 20,000 - ₹ 40,000+Manhattan ReviewOnline, In-person (limited locations)Multiple Cities (International), Bangalore, Delhi, Mumbaihttps://www.manhattanprep.com/greUSD 1,000 - USD 2,000+Career LauncherOnline, OfflineDelhi, Mumbai, Bangalore, Chennai, Pune, Hyderabad, Kolkata, Ahmedabad and other major citieshttps://www.careerlauncher.com/gre/₹ 40,000 - ₹ 75,000+Endeavor CareersOnline, OfflineDelhi, Mumbai, Bangalore, Chennai, Pune, Hyderabad, Kolkata, Ahmedabad and other major citieshttps://endeavormagic.com/₹ 35,000 - ₹ 60,000+Here is the listing of 10 best GRE Coaching centres in India along with their essential information:JamboreeJamboree is one of the top GRE training institutes in India known for its personalized approach and exhaustive study materials.Other Features:Personalized study plans: Jamboree customizes study timetables according to your strengths and weaknesses as well as target score.Extensive study material: These include online and offline stuff such as practice tests; video lectures; guidebooks; word builders for vocabulary building.Experienced faculty: Jamboree tutors are highly accomplished professionals having vast experience in coaching GRE candidates.Manya GroupIndia-based Manya Group, in collaboration with The Princeton Review, provides the most thorough GRE coaching services in India focusing on individualized learning and highly efficient techniques to enhance students' scores.Other Features:Tailored tutoring: These are one-on-one personalized sessions offered by Manya Group besides group classes.Comprehensive practice tests: Students will have access to numerous practice tests which mimic the actual format of the GRE exam thereby allowing them to identify weak points that require improvement.Guaranteed Score Improvement Program: There is a guarantee for score improvement under some conditions in this program offered by Manya Group. For further details and eligibility criteria please visit their website.AbhyaasAbhyaas is a coaching center that concentrates on preparations for various entrance exams including GRE and has its physical presence in Hyderabad, India. They offer both online and offline coaching options.Other Features:Customized Prep Solutions: Abhyaas tailors their GRE prep program to your individual needs and target score.Mock tests: They offer comprehensive mock tests to help you assess your progress and identify areas for improvement.Experienced faculty: Abhyaas instructors are experienced professionals with a strong understanding of the GRE.TIMEThere is a popular coaching institute called TIME that offers GRE preparation as well as other entrance exam prep courses. They exist across the country and offer both virtual and traditional types of learning.Other Features:Qualified tutors: TIME consists of experienced, skilled teachers who are responsible for the GRE preparation.Detailed materials: They give students exhaustive learning resources that include mock tests, tutorials and e-books.Possible schedules & delivery methods: TIME has different formats of classes and ensures the convenience for everyone.Ivy AspireIvy Aspire is a GRE and GMAT coaching institute located in Bangalore, specialized for these exams. They have a high success rate and emphasize personalized mentoring and strategic planning.Other Features:Small batch sizes: This allows students to interact more with their tutors so as to ask questions where they are stuck or need some clarifications.Mentorship program: Students are guided by experienced professionals through out the whole process to ensure that they achieve the most out of their efforts during preparation.Strategic study plans: Every student has unique requirements so we customize studies according to his/her desires and target scores at Ivy Aspire.Experienced faculty members: The instructors are competent individuals who possess comprehensive knowledge about admissions processes as well as GRE itself.Mnemonic EducationMnemonic Education offers online and offline GRE preparation classes, with full attention to individual students’ needs and a thorough study.Other Features:Personalized attention: In this respect, mnemonic education stresses its learners’ individual requirements and gives them personal guidance and assistance upon request.Strategic study plans: They construct tailor-made study regimens based on every student’s strengths, weaknesses as well as targets set.Experienced faculty: Trained instructors have expertise in GRE preparation tests.Mock tests: Students take part in periodic mock exams to monitor their progress so that they can identify areas where they need improvement.Crack VerbalCrack Verbal is a leading online GRE coaching platform known for its innovative training practices and emphasis on developing strong verbal reasoning abilities.Other Features:Adaptive learning platform: The learning experience at Crack Verbal’s platform idiosyncratically tailored towards your performance and progress.Expert faculty: Teachers are seasoned GRE tutors and exam preparation specialists.Focus on verbal reasoning: Strong reading comprehension, sentence correction, and critical reasoning skills form the mainstay of Crack Verbal curriculum.Abundant online resources: These incorporate video lessons, practice questions, interactive vocabulary builders and an active community forum.Manhattan ReviewIt is a world-wide test prep firm that does both online and offline GRE training; it is known for its inclusive syllabus and concentration on quantitative reasoning.Other Features:Highly skilled instructors: The faculty consist of experienced and qualified trainers who are experts in GRE preparations.Wide-ranging curriculum: Includes all parts regarding quantitative reasoning, analytical writing as well as verbal reasoning tests for the GRE.Tests and materials: Students receive numerous practice tests in form of books sample questions among other materials.Flexible scheduling: Both online and offline courses offer various scheduling options to fit your needs.Career LauncherCareer Launcher, a renowned coaching institute in India is well known for its GRE preparation and other entrance exams. The institution offers flexible times and a personal approach to education.Other Features:Flexible schedules: Weekdays, weekends and night classes are offered by career launcher that meet the requirements of all students.Personalized coaching: Students receive personalized guidance from experienced teaching faculty who have been there done that before as they aim at meeting their target scores.Comprehensive study material: This includes both online and offline resources such as practice tests, lectures videos, books etc.Doubt clearing sessions: Dedicated sessions are available for students to address any questions or concerns they may have.Endeavor CareersEndeavor Careers is a leading GRE preparation institute in India which aims at empowering students with knowledge and skills essential for success.Other Features:Customized mentoring: Throughout the preparation journey, endeavor careers assigns mentor who is dedicated to each student’s needs.Extensive study material: These study materials provided by them include online and offline resources like vocabulary builders, practice tests, video lectures as well as study materials that would help in your preparation process.Experienced faculty: The team of trainers experienced and qualified is capable of delivering excellent results when it comes to GRE preparation strategies according to Endeavour Career.Conclusion Choosing the right GRE coaching centres can significantly improve your chances of achieving a high score and securing admission to your dream program. Consider the factors mentioned throughout this article, including location, budget, learning style, and institute features, to make an informed decision. Remember, consistent effort and the right guidance are key to GRE success.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffBest GRE Coaching Institutes in India - FAQsWhat is the best coaching for GRE in India?The best GRE coaching program in India will depend on where you live, how much money you have and the way you like to learn. Some of its notable names are Jamboree, Manya Group, and TIME.How much does it cost to get a GRE coach in India?The amount of money payable for GRE coaching services may be between INR 15,000 to INR 50,000 on average depending on the institution and how comprehensive their course materials are as well as the duration.Is online preparation for the General test as good as offline one?Online preparation provides flexibility and wide access to various resources which can be very effective just like an offline preparation one with live sessions, personalized feedbacks, comprehensive study material etc.What is the ideal time frame for preparing the Graduate Record Examination with a tutor?This varies depending upon your initial performance standard and target score but usually candidates discover that three to half a year of concentrated practice at an institute suffices.What should I consider when selecting a GRE coaching institute?Look out for institutions having experienced teachers, books that cover all syllabus, customised training plans, frequent test series and positive feedbacks from the students which prove their good preparation. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Top 10 Best GRE Coaching Institutes in India (Online & Offline) | https://www.geeksforgeeks.org/gre-coaching-in-india/?ref=lbp | Data Science & ML | Top 10 Best GRE Coaching Institutes in India (Online & Offline) | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Top 10 Best GRE Coaching Institutes in India (Online & Offline), Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.00296827033, -0.00937607605, -0.0246746261, 0.00738550629, 0.0442005, 0.0106914, 0.0155869359, 0.0141379694, -0.00827176776, 0.00183582585, -0.0208060276, -0.0387985259, 0.0176689457, -0.0187802874, 0.00107529457, -0.00857422128, 0.0401208848, 0.00981920678, -0.0110290227, 0.0155588007, -0.00815219246, -0.0461418293, 0.0134205204, -0.019357061, -0.0278820451, 0.0162340458, 0.00189209648, 0.000431260822, -0.0171062406, -0.0121966368, 0.030864384, 0.00798338093, 0.0246886928, -0.0494899265, -0.0555671453, -0.00663640536, -0.0183160566, -0.0309487898, -0.0128789162, 0.0177814867, 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18 Sep, 2024 | GRE Quantitative Reasoning Practice Test 2024
18 Sep, 2024
Preparing for the GRE can be a challenging yet rewarding experience, especially when it comes to the Quantitative Reasoning section. This section assesses your mathematical skills, including arithmetic, algebra, geometry, and data analysis. Check out the free GRE Quantitative Reasoning practice test curated by the experts of Geeksforgeeks. GRE Quantitative Reasoning SectionThe GRE Quantitative Reasoning section consists of two parts, each containing 20 questions. The questions are designed to evaluate your ability to:Understand, interpret, and analyze quantitative information.Solve problems using mathematical concepts.Apply basic mathematical skills and concepts to real-life scenarios.The scoring for this section ranges from 130 to 170, with a median score of 150. A strong performance in Quantitative Reasoning can significantly boost your overall GRE score and improve your chances of admission to graduate programs.GRE Quantitative Reasoning Practice TestGRE Quantitative Reasoning Practice Test-1GRE Quantitative Reasoning Practice Test-2GRE Quantitative Reasoning Practice Test-3GRE Quantitative Reasoning Practice Test-4GRE Quantitative Reasoning Practice Test-5GRE Quantitative Reasoning Practice Test-6GRE Quantitative Reasoning Practice Test-7How to Prepare for the GRE Quantitative Reasoning SectionHere are some proven strategies to help you prepare for the GRE Quantitative Reasoning section:1. Focus on Basic Math ConceptsMake sure you’re comfortable with fundamental math concepts like arithmetic, algebra, geometry, and data interpretation. Brushing up on the basics is essential for answering the questions confidently.2. Use Official GRE Practice MaterialsThe best way to practice is by using official GRE materials. The ETS GRE Quantitative Reasoning practice tests provide the most accurate representation of the actual test, ensuring that you’re well-prepared.3. Take Full-Length Practice TestsTaking full-length practice tests under timed conditions helps simulate the real test experience. It allows you to practice pacing yourself and adjusting your strategy as needed.4. Review Your MistakesAfter taking a practice test, review your mistakes thoroughly. Analyze why you made an error and focus on improving that area. This practice will ensure that you don’t repeat the same mistakes on test day.5. Create a Study ScheduleDevelop a study schedule that covers all GRE quantitative topics. Allocate more time to areas where you struggle and keep revising concepts you’re already comfortable with.ConclusionPreparing for the GRE Quantitative Reasoning section can be challenging, but with the right approach and regular practice, you can improve your skills and score well. Make sure to take advantage of GRE practice tests, review your mistakes, and focus on time management. By mastering the basics of arithmetic, algebra, and data interpretation, you’ll be well-prepared to tackle any question the GRE throws at you in 2024. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/GRE Quantitative Reasoning Practice Test 2024 | https://www.geeksforgeeks.org/gre-quantitative-reasoning-practice-test-2024/?ref=lbp | Data Science & ML | GRE Quantitative Reasoning Practice Test 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, GRE Quantitative Reasoning Practice Test 2024, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0228434745, 0.0138978697, -0.0143707655, 0.0281110033, 0.0887992457, -0.00886022, 0.000824693416, 0.0411681719, 0.00974033121, 7.94829612e-05, 0.0218451396, -0.0145678055, 0.0337857492, -0.00966808386, -0.00192934752, 0.0382782556, -0.0128404237, 0.0175365377, -0.0268105417, -0.0490497611, -0.00687668705, 0.00931341201, 0.00118552241, 0.0363078564, -0.0382519811, 0.0177204404, -0.00263704848, 0.00307546207, 0.0105284899, 0.0112181297, 0.0341535546, 0.0168403294, 0.0259698387, -0.0597949959, 0.00560578052, -0.013989822, 0.0152902845, 0.0211226605, -0.027060125, -0.00455161789, -0.00665994314, 0.027217757, 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18 Sep, 2024 | GRE Verbal Reasoning Practice Test 2024
18 Sep, 2024
The GRE (Graduate Record Examination) is a standardized test that plays a crucial role in the admissions process for many graduate programs worldwide. One of the key components of the GRE is the Verbal Reasoning section, which assesses your ability to analyze written material, evaluate arguments, and understand the meanings of words and phrases. This article provides a comprehensive guide to GRE Verbal Reasoning practice tests for 2024, including tips, resources, and sample questions.Understanding GRE Verbal ReasoningThe GRE Verbal Reasoning section consists of two types of questions:Reading Comprehension: These questions test your ability to read and understand passages, including identifying the main idea, drawing inferences, and understanding the author’s tone.Text Completion and Sentence Equivalence: In these questions, you will fill in blanks within sentences or choose words that create a similar meaning. These sections assess your vocabulary and understanding of context.The Verbal Reasoning section is scored on a scale of 130 to 170, with a median score around 150. Scoring well in this section is vital for gaining admission to competitive graduate programs.GRE Verbal Reasoning Practice TestGRE Verbal Reasoning Practice Test- 1GRE Verbal Reasoning Practice Test- 2GRE Verbal Reasoning Practice Test- 3GRE Verbal Reasoning Practice Test- 4GRE Verbal Reasoning Practice Test- 5GRE Verbal Reasoning Practice Test- 6GRE Verbal Reasoning Practice Test- 7GRE Verbal Reasoning Practice Test- 8GRE Verbal Reasoning Practice Test- 9GRE Verbal Reasoning Practice Test- 10Importance of Practice TestsTaking practice tests is an effective way to prepare for the GRE Verbal Reasoning section. Here’s why practice tests are essential:Familiarity with Format: Practice tests help you become familiar with the question types and test format, reducing anxiety on test day.Identify Weak Areas: By taking practice tests, you can identify which areas you need to focus on, whether it’s vocabulary, reading comprehension, or analytical reasoning.Time Management: Regular practice helps you improve your pacing, ensuring you complete each section within the allotted time.Build Confidence: The more you practice, the more confident you will feel in your abilities, leading to a better performance on the actual test.Tips for Effective GRE Verbal Reasoning PreparationTo make the most of your GRE Verbal Reasoning practice, consider these tips:Read Regularly: Engage with a variety of reading materials, including academic articles, opinion pieces, and fiction. This exposure will enhance your reading comprehension skills and vocabulary.Practice Vocabulary: Use flashcards or vocabulary apps to learn new words. Understanding nuanced meanings will help you excel in text completion and sentence equivalence questions.Analyze Practice Questions: After completing practice questions, take the time to review your answers. Understand why you got a question right or wrong to learn from your mistakes.Take Full-Length Practice Tests: Simulate the test environment by taking full-length practice tests under timed conditions. This will help you build stamina and get used to the test format.Use Official GRE Resources: The Educational Testing Service (ETS), which administers the GRE, offers official practice materials, including sample questions and full-length practice tests.ConclusionPreparing for the GRE Verbal Reasoning section requires dedication, practice, and the right resources. By taking advantage of practice tests, improving your vocabulary, and honing your reading comprehension skills, you can significantly enhance your performance. Remember, consistency is key! Stay focused on your goals, and make the most of the resources available to you in 2024. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/GRE Verbal Reasoning Practice Test 2024 | https://www.geeksforgeeks.org/gre-verbal-reasoning-practice-test-2024/?ref=lbp | Data Science & ML | GRE Verbal Reasoning Practice Test 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, GRE Verbal Reasoning Practice Test 2024, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data 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18 Sep, 2024 | GRE Analytical Writing Practice Test 2024
18 Sep, 2024
The GRE (Graduate Record Examination) is a crucial step for students aiming to pursue graduate studies. One of the most important sections of the GRE is the Analytical Writing section, which assesses your critical thinking and analytical writing skills. In this article, we’ll explore everything you need to know about the GRE Analytical Writing practice test for 2024, including tips, sample prompts, and strategies to improve your writing.GRE Analytical Writing Section Mock TestGRE Analytical Writing Practice Test-1 GRE Analytical Writing Practice Test-2GRE Analytical Writing Practice Test-3GRE Analytical Writing Practice Test-4GRE Analytical Writing Practice Test-5GRE Analytical Writing Practice Test-6GRE Analytical Writing Practice Test-7GRE Analytical Writing Practice Test-8GRE Analytical Writing Practice Test-9GRE Analytical Writing Practice Test-10Key Strategies for GRE Analytical Writing SectionTo excel in the GRE Analytical Writing section, consider the following strategies:1. Practice RegularlyConsistent practice is key to improving your writing skills. Set aside time each week to work on both tasks. Use official GRE practice prompts or sample questions available online. This will familiarize you with the format and help you develop a strategy for approaching each task.2. Understand the Scoring CriteriaFamiliarize yourself with the GRE Analytical Writing scoring guidelines. The key criteria include:Clarity: Is your argument clear and easy to follow?Coherence: Are your ideas logically organized?Evidence: Do you provide sufficient examples to support your claims?Language Use: Is your writing free of grammatical errors and appropriate in tone?3. Plan Your ResponsesBefore writing, take a few minutes to plan your response. For the Analyze an Argument task, outline the argument's key points and identify any flaws. For the Analyze an Issue task, list your main arguments and supporting examples. A clear outline will help you stay focused and organized while writing.4. Practice Time ManagementEach task gives you 30 minutes to write your response. Practice managing your time effectively. Allocate time for planning, writing, and revising your response. For example, spend 5 minutes planning, 20 minutes writing, and 5 minutes reviewing your work.5. Review Sample EssaysReading sample essays can help you understand what a high-scoring response looks like. Analyze the structure, argumentation, and language used in these essays. Official GRE resources and test prep books often provide sample essays with scoring explanations.Resources for GRE Analytical Writing PreparationThere are many resources available to help you prepare for the GRE Analytical Writing section:Official GRE Website: The Educational Testing Service (ETS) provides sample prompts, scoring guidelines, and other valuable resources.GRE Prep Books: Consider investing in GRE preparation books that include practice prompts, sample essays, and tips for writing.Online Courses: Many platforms offer online GRE prep courses focused on analytical writing. These courses often include video lectures, practice questions, and personalized feedback.Study Groups: Join or form a study group with fellow GRE test-takers. Sharing feedback and discussing prompts can enhance your learning experience.ConclusionPreparing for the GRE Analytical Writing section requires dedication and practice. By understanding the test format, employing effective strategies, and utilizing available resources, you can improve your writing skills and perform well on test day. Remember, consistent practice is key! With the right approach, you can tackle the GRE Analytical Writing tasks confidently and achieve your desired score in 2024. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief 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Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, GRE Analytical Writing Practice Test 2024, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0331741348, -0.011522688, -0.0210000109, 0.00407672, 0.0769953728, 0.00266878051, -0.00681905, 0.0348272361, -0.00185448735, -0.00799933728, 0.0268279, -0.0188705903, 0.0277525168, -0.0212801974, 0.0141984737, 0.00135365315, 0.0120760575, 0.0197111517, -0.00890294, -0.027906619, -0.00290343724, 0.0117538422, -0.0082935337, 0.0207198244, -0.0263796, 0.0206357688, 0.0053725848, 0.0213502441, -0.00460207043, -0.00398565922, 0.0452782102, 0.0256511141, 0.0326978154, -0.0382455178, -0.0182821974, -0.0263655912, 0.0146677867, 0.0332021527, -0.0161948055, 0.0020926462, -0.000792841485, -0.000987659, 0.0330620594, 0.00266352715, 0.000647932291, -0.0389459841, 0.00204711594, 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04 Oct, 2024 | GRE Analytical Writing Scores and Word Limit
04 Oct, 2024
Understanding GRE Analytical Writing scores is crucial for applicants aiming for top graduate programs. The GRE Analytical Writing Assessment (AWA) measures your ability to articulate complex ideas, construct well-supported arguments, and demonstrate critical thinking. GRE AWA scores range from 0 to 6, with a higher score reflecting superior writing skills and a stronger application. A score of 4.5 or above is often recommended for competitive programs. A strong GRE AWA score can significantly impact your overall GRE performance and improve your chances of admission to prestigious institutions.GRE Analytical Writing Scores and Word LimitTable of ContentTypes of GRE Analytical Writing ExamplesGRE Analytical Writing Score RangeGRE Analytical Writing Examples with Answers GRE Analytical Writing Score PercentilesGRE Analytical Writing Scores- FAQsTypes of GRE Analytical Writing ExamplesIssue Analysis Examples: These examples demonstrate how to critically analyze a given issue, presenting a clear stance and supporting it with relevant evidence. For instance, an essay might argue the impact of technology on education, providing examples of both positive and negative effects.Argument Evaluation Examples: These examples illustrate how to assess the strengths and weaknesses of an argument. For example, evaluating the argument that increased funding in the arts will lead to higher academic performance in schools, highlighting logical fallacies and supporting counterpoints.Key Components of Effective GRE AWA EssaysClear Thesis Statement: Begin with a strong thesis that outlines your main argument or position.Structured Argument: Organize your essay with a clear introduction, body paragraphs, and a conclusion.Relevant Examples: Use specific examples to support your points and illustrate your arguments.Critical Analysis: Demonstrate your ability to evaluate different perspectives and address counterarguments.Resources for GRE Analytical Writing ExamplesOfficial GRE Practice Materials: The ETS website offers official sample questions and scoring guides.GRE Preparation Books: Books like The Official Guide to the GRE General Test include practice essays and critiques.Online Platforms: Websites such as Magoosh and Kaplan provide additional sample essays and analysis.GRE Analytical Writing Score RangeThe GRE Analytical Writing Assessment (AWA) is a crucial part of the GRE exam, designed to evaluate your critical thinking and writing skills. Understanding the GRE analytical writing score range can help you gauge your performance and target your preparation effectively. The GRE AWA score range spans from 0 to 6.0, reflecting various levels of writing proficiency.GRE Analytical Writing Score RangeScoreDescriptionCharacteristics6.0OutstandingClear, insightful, and thorough analysis; exceptional control of language.5.0StrongWell-organized, thoughtful analysis; minor errors may be present.4.0AdequateSatisfactory analysis with some gaps in organization; sufficient language control.3.0LimitedInadequate analysis with poor organization; language issues are prevalent.2.0Seriously FlawedMinimal understanding of the issue; severe language and organization problems.1.0Fundamentally DeficientLittle to no relevant content; severe and frequent errors in language.0.0UnscorableOff-topic, in a non-English language, or not an essay response.GRE Analytical Writing Examples with AnswersExample 1: Analyze an IssuePrompt: "Technological advancements have fundamentally changed the way we interact with each other. Discuss the impact of technology on human relationships."Response: Technology has transformed human interactions profoundly. On one hand, it has made communication more convenient and instantaneous, connecting people across the globe. Platforms like social media and messaging apps enable individuals to stay in touch regardless of geographical barriers. However, these advancements can also lead to superficial relationships and reduced face-to-face interactions, potentially weakening the depth of personal connections. While technology facilitates easy communication, it’s crucial to balance it with meaningful, direct interactions to maintain strong, genuine relationships.Analysis:Score: 5.0Strengths: Clear argument, balanced perspective, and relevant examples.Areas for Improvement: Could include more specific examples and deeper analysis.Example 2: Analyze an IssuePrompt: "The best way to improve education is by increasing teachers' salaries. Do you agree or disagree?"Response: Increasing teachers' salaries is an effective way to enhance education quality. Higher salaries attract and retain talented educators, who are crucial for delivering quality education. With better compensation, teachers can focus more on teaching rather than seeking additional income sources, leading to improved student outcomes. However, while salary increases are beneficial, they should be part of a broader strategy that includes investing in resources, professional development, and reducing class sizes to fully address educational challenges.Analysis:Score: 4.5Strengths: Well-structured argument with clear reasoning.Areas for Improvement: More detailed examples and counterarguments could strengthen the essay.Example 3: Analyze an IssuePrompt: "The success of an organization depends on its leaders rather than its employees. Do you agree or disagree?"Response: The success of an organization is influenced by both its leaders and employees. Leaders provide vision, strategic direction, and motivation, setting the tone for organizational culture and performance. However, employees are the ones executing tasks and driving day-to-day operations. Effective collaboration between leadership and staff is essential for organizational success. Leaders can guide and inspire, but without competent and motivated employees, their vision cannot be realized.Analysis:Score: 4.0Strengths: Balanced perspective and clear argumentation.Areas for Improvement: More examples and a deeper exploration of the interplay between leadership and employee contributions. GRE Analytical Writing Score PercentilesAchieving a strong GRE Analytical Writing score is crucial for graduate school admissions. The GRE Analytical Writing score is measured on a scale from 0 to 6, with percentile rankings indicating how your score compares to other test-takers. Understanding the GRE Analytical Writing score percentiles can help you gauge your performance and set realistic goals for your preparation.GRE Analytical Writing Score PercentilesScorePercentile Rank6.099th percentile5.595th percentile5.090th percentile4.580th percentile4.070th percentile3.550th percentile3.030th percentile2.520th percentile2.010th percentile1.55th percentile1.01st percentileExplanation99th Percentile (6.0): Outstanding writing skills, with a comprehensive understanding of complex issues and exemplary writing ability.90th Percentile (5.0): Strong analytical writing with clear, logical arguments and effective use of language.50th Percentile (3.5): Adequate writing skills, but with room for improvement in argument development and language control.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffGRE Analytical Writing Scores- FAQsWhat is a good GRE score for analytical writing?A good GRE Analytical Writing score typically falls between 4.5 and 6.0. Achieving a score of 4.5 or higher demonstrates strong analytical writing skills and is considered competitive for admission to many graduate programs. Here’s a breakdown of what these scores mean:5.0 – 6.0 (Excellent to Outstanding): Indicates superior critical thinking and writing skills. This range shows a high ability to analyze complex issues and present well-structured arguments.4.5 – 4.9 (Strong): Reflects solid analytical writing with clear argumentation and logical structure. This score is competitive for most top-tier graduate programs.4.0 – 4.4 (Adequate): Shows satisfactory analytical writing but may lack some depth or clarity. This score meets the basic requirements for many programs but may be less competitive for highly selective schools.Is 4.5 a good analytical writing score?We've divided the table into different colors based on whether the GRE analytical writing scores would be considered low (0.0-3.0), average (3.5-4.0), high (4.5-5.0), or excellent (5.5-6.0).What is a 3 on the GRE analytical writing score?A 3 response demonstrates some competence in addressing the specific task directions, in analyzing the issue and in conveying meaning, but is obviously flawed. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/GRE Analytical Writing Scores and Word Limit | https://www.geeksforgeeks.org/gre-analytical-writing-scores/?ref=lbp | Data Science & ML | GRE Analytical Writing Scores and Word Limit | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, GRE Analytical Writing Scores and Word Limit, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0395396277, -0.0024401953, -0.0230647828, 0.00367580866, 0.0450237207, -0.00677048415, -0.00437260466, 0.0334687606, -0.0196908247, -0.0118596321, 0.0213383101, 0.000954215124, 0.0302189291, -0.0198939405, 0.00652787508, 0.00755473226, 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10 Sep, 2024 | GRE Analytical Writing Section (Revised): Tips to Write GRE Issue Essays
10 Sep, 2024
The GRE Analytical Writing section is a crucial part of the GRE that evaluates your analytical writing and critical thinking skills. This section requires you to complete the Analyze an Issue task, where you have 30 minutes to craft a well-organized essay presenting a compelling argument based on the provided prompt. To excel in the GRE Analytical Writing section, aim for a score above 4.5, particularly if you’re targeting top-ranked universities.
Achieving a high score in the Analytical Writing section can significantly enhance your graduate school application and demonstrate your readiness for advanced academic challenges. Understanding the GRE Analytical Writing rubric and practicing effective essay techniques will further boost your performance.
GRE Analytical Writing Section
GRE Analytical Writing Section
Starting September 22, 2023, the GRE General Test’s Analytical Writing measure evaluates your analytical writing and critical thinking abilities by assessing your capacity to:
Articulate and support complex ideas
Construct arguments
Sustain a focused and coherent discussion
This section does not test specific content knowledge. The “Analyze an Issue” task, which is a key component of the Analytical Writing measure, gives you 30 minutes to respond to a presented viewpoint. In this task, you need to assess the issue, consider its nuances, and develop a well-supported argument using facts and examples. Excelling in this section is essential for achieving a competitive score and enhancing your graduate school application. Understanding the GRE Analytical Writing criteria and practicing effectively can boost your performance in this critical part of the test.
GRE Issue Essay Format
An issue-based GRE AWA essay should be between 500 and 600 words long. The common subjects are interesting and can be approached from many angles. Keep your mind that there are no perfect answers in GRE AWA. Examining a problem is an assignment that assesses your ability to think critically on a common subject. You must provide a strong justification for your choice. Go through the guidelines carefully and draft a preliminary plan of action before starting to write your response. The following categories of instructions are possible:
Provide justifications and examples for your position on the suggested course of action.
Write a strong answer outlining how much you agree or disagree with the stated claim.
Write a response outlining your position and supporting it. You must talk about the two points that have been made.
Give a rationale for your stance on the stated claim.
Write a response outlining the policy’s effects and how they affected your choice.
GRE Analytical Writing Section Time
The GRE Analytical Writing Section is a pivotal part of the GRE exam, designed to assess your critical thinking and analytical writing skills. You have 30 minutes to complete the “Analyze an Issue” task, where you’ll need to craft a well-structured essay based on a given prompt. Efficient time management is crucial for success in this section. To maximize your performance, practice writing essays within the 30-minute timeframe to build proficiency and comfort.
Understanding how to effectively use this time can significantly impact your GRE score. For tips and practice, refer to GRE Analytical Writing Section time management strategies and GRE writing practice exercises to enhance your preparation.
Analytical Writing Section GRE Examples
The GRE Analytical Writing Section evaluates your ability to think critically and articulate complex ideas effectively. For a strong performance, reviewing GRE Analytical Writing Section examples can be incredibly beneficial. These examples provide insight into the types of prompts you’ll encounter and illustrate how to structure a high-quality essay.
Typical GRE Analytical Writing Section examples include prompts that require you to analyze and critique arguments, or discuss various perspectives on a given issue. By studying sample essays and understanding how top-scoring responses are crafted, you can improve your writing strategy and meet the GRE writing standards. Use these examples as practice tools to refine your writing skills and enhance your GRE preparation.
GRE Analytical Writing Section Topics
There is currently only one task in GRE AWA: examine a topic. Critical thinking and analytical skills are assessed in this part. The GRE AWA question type is not standardized. To comprehend the most recent modifications, you must refer to the revised GRE pattern. Typical subjects for a GRE analysis include the following:
Technology and Society
Education
Arts
Intellectual Endeavours
Government and power
Cities
Philosophy
Tips for Writing GRE Issue Essay
Aside from picking a side, the fundamental GRE issue tips are to use powerful, declarative phrases, relevant, and precise examples. In their GRE essays, candidates might use the following AWA GRE issue tips:
Start by Practicing GRE Issue Essays: In the GRE issue problem, applicants are asked to share their thoughts on a topic of general interest. GRE AWA advice requests that applicants practice writing three or more essays for the GRE. This will assist applicants with time management, understanding the different kinds of prompts, and gathering the information needed to write.
Pick One Side: Applicants are required to endorse just one side of the question. Speaking from both perspectives will weaken and confuse their essay. The examiner evaluates the candidate’s argumentative style. Those who study the AWA GRE examples and advice will be better able to write.
Give Relevant Examples: GRE AWA advice assists applicants in offering useful examples that will bolster their essays. Candidates must only include examples that bolster their essay; they cannot cover the entirety of it. Examples from a variety of fields, including business, the arts, history, and more, are available.
Follow a Structured Pattern in GRE Issue Essay: A well-structured essay is a crucial GRE AWA recommendation. Examiners like reading well-organized essays over poorly written ones. It raises the GRE AWA score and gives readers more clarity.
GRE Analytical Writing Score Range
After the test, scores for the GRE will be accessible on the official ETS website in eight to ten days. The range of scores for the GRE analytical writing is 0 to 6.0. The GRE score is valid for five years; in order to be admitted, candidates must submit or mail their extra score reports to the universities of their choice during this validity period. Let’s talk about the criteria that ETS looks for in your AWA essay grades:
GRE AWA Score
Explanation
6.0 – Outstanding
Clear identification of the most important features of the argument with deep analysis.Looks for cogent ideas, logical organization, and connecting them properly without sudden transitions.Strongly supports the main points of the critique.Demonstrates superior control of the English language, sentence formation, spelling, grammar, and GRE vocabulary and the variety used in standard written English.Few to no flaws in the writing.
5.0 – Strong
Clearly, identification of the important features of the argument and analyzes them thoughtfully.Develops ideas clearly, and connects them logically, with appropriate transitions.Gives very sensible support to the main points of the critique.Has clear control of language, GRE grammar, including diction and syntactic varietyIt may have minor flaws like spelling errors, but no major flaws.
4.0 – Adequate
Capable of identifying and analyzing the main features of the argument.Develops and organizes ideas satisfactorily, but some important connections and transitions may be missing.Supports the main points of the critique.Demonstrates sufficient control of language, but may lack syntactic variety.May have many minor flaws or some major flaws.
3.0 – Limited
Does not identify or analyze many of the important features of the argument.Has limited logical development and no proper organization of ideas.Offers support of little relevance and value for points of the critiqueUses language imprecisely and/or lacks sentence variety Contains occasional major errors or frequent minor errors in grammar, usage, and mechanics
2.0 – Seriously Flawed
Demonstrates no understanding of the main features of the argument.Almost no analyses of the main points have been made.Does not develop any ideas or is disorganizedProvides zero to few relevant pieces of evidence.Has frequent serious problems in the use of language, grammar, spelling, and sentence structure.
1.0 – Fundamentally Deficient
Provides little to no evidence of the ability to understand and analyze the main idea.Failure to develop an organized response.Contains severe and persistent errors in language and sentence structureHas an unusually frequent pattern of errors in grammar, usage, and logic.A totally incoherent response.
0.0 – Unscorable
The responses are off-topic.The responses are written in a language other than English.The responses are a mere copy of the given topic.The responses consist only of random keystroke characters.No response.
GRE Analytical Writing Section Practice Questions with Answer
GRE Analytical Writing Practice Test FREE- Analytical Writing Section Test-1
GRE Analytical Writing Practice Test FREE- Analytical Writing Section Test-2
GRE Analytical Writing Practice Test FREE- Analytical Writing Section Test-3
GRE Analytical Writing Practice Test FREE- Analytical Writing Section Test-4
GRE Analytical Writing Practice Test FREE- Analytical Writing Section Test-5
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GRE Analytical Writing Section- FAQs
Is a 4 in GRE Analytical Writing good?
A GRE Analytical Writing score of 4 is considered average. While it meets the basic requirements of many graduate programs, top-tier institutions often look for higher scores. For competitive programs, aiming for a score above 4.5 is advisable. A score of 4 reflects competent writing skills but may not stand out among applicants with higher scores. To improve, focus on practicing with GRE Analytical Writing prompts, refining your argumentation, and seeking feedback on your essays to boost your score and enhance your application.
What is analytical writing in GRE?
Analytical Writing in the GRE assesses your ability to think critically and communicate complex ideas effectively. It comprises the Analytical Writing Assessment (AWA) section, where you’ll respond to one “Analyze an Issue” essay prompt. You’ll have 30 minutes to develop and articulate your argument, demonstrating clear reasoning, coherence, and strong writing skills.
Does the GRE have a writing section?
Yes, the GRE includes a writing section known as the Analytical Writing Assessment (AWA). This section evaluates your ability to articulate complex ideas and support arguments effectively. It consists of one “Analyze an Issue” essay and one “Analyze an Argument” essay. 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30 Sep, 2024 | Top 10 Tips for GRE Analytical Writing Section: Advanced Level
30 Sep, 2024
Preparing for the GRE Analytical Writing Test requires a solid understanding of the essay format, along with targeted practice using high-quality resources. The GRE Writing Test includes two tasks: the Issue Essay and the Argument Essay. To excel, start by reviewing GRE essay examples to understand what a high-scoring essay looks like. Familiarize yourself with GRE essay topics with answers PDF to practice writing under timed conditions. Utilize a GRE Issue Essay template to structure your essays effectively, ensuring that your arguments are coherent and well-organized. As you prepare for the GRE essay 2024, focus on analyzing GRE argument essay prompts critically and practice writing essays using various GRE essay prompts to enhance your skills. With these strategies, you’ll be better equipped to achieve a high score on the GRE Writing Test.Tips for GRE Analytical WritingTable of ContentGRE Essay ExamplesGRE Essay Topics with Answers PDFGRE Issue Essay TemplateGRE Analytical Writing Section - StructureGRE Analytical Writing Section - Types and TipsGRE Target Score Or Ideal ScoreTips for GRE Writing Test-FAQsGRE Essay ExamplesThe GRE Analytical Writing section challenges you to showcase your critical thinking and writing skills. High-scoring GRE essay examples can serve as a valuable guide in your preparation. Below, you'll find a breakdown of what makes a strong essay, along with examples to help you succeed.Example 1: GRE Issue EssayPrompt: "Governments should place few, if any, restrictions on scientific research and development."Essay Example: In a rapidly evolving world, scientific research and development are key drivers of progress. While some argue for minimal governmental intervention, it is essential that governments impose certain restrictions to ensure ethical standards, public safety, and environmental protection. For example, unregulated genetic modification research could lead to unintended consequences, highlighting the need for oversight. Therefore, balanced regulation is crucial to foster innovation while safeguarding societal interests.Example 2: GRE Argument EssayPrompt: "The following appeared in a letter to the editor of a local newspaper: 'The new municipal building project should not proceed as planned, as the proposed location is prone to flooding.'"Essay Example: The argument against the municipal building project is based on concerns about flooding. However, the argument lacks evidence and fails to consider possible solutions like advanced drainage systems. Furthermore, it doesn't address the potential economic benefits of the project. A more thorough analysis of the location’s flood risks and mitigation strategies is necessary before making a final decision.Tips for Using GRE Essay ExamplesAnalyze Structure: Notice how high-scoring essays structure their arguments logically.Practice Writing: Use these examples to practice writing your own essays under timed conditions.Focus on Clarity: Ensure your essays are clear, concise, and free from grammatical errors.By studying and practicing with GRE essay examples, you can refine your writing skills and increase your chances of achieving a high score on the GRE.GRE Essay Topics with Answers PDFMaximize your GRE Analytical Writing score with our comprehensive guide to GRE Essay Topics with Answers. Whether you’re preparing for the GRE in 2024 or beyond, understanding the types of essay prompts and learning from detailed sample answers can be crucial for achieving a high score.Here are some GRE Essay Topics that cover both the Issue and Argument tasks, reflecting the types of questions you might encounter on the exam:Issue Essay TopicsTechnology and Society"Technology has made our lives more complex and less enjoyable. Do you agree or disagree?"Education"A college education should be available to everyone, regardless of their financial status. Do you agree or disagree?"Government and Policy"Governments should focus on solving the problems of their own citizens before addressing global issues. Do you agree or disagree?"Arts and Culture"The arts should be funded by the government because they contribute to the cultural enrichment of society. Do you agree or disagree?"Science and Ethics"Scientific advancements are more important than ethical considerations. Do you agree or disagree?"Argument Essay TopicsBusiness and Economics"A company claims that its new product will increase market share by 20% based on a survey. Evaluate the argument's validity."Education"An educational institution asserts that increasing class sizes will improve student performance. Evaluate the argument's logic and evidence."Health and Wellness"A city council argues that building more parks will reduce local healthcare costs. Evaluate the argument's reasoning and evidence."Environmental Policy"A government agency claims that implementing stricter emission regulations will significantly improve air quality. Assess the argument's effectiveness."Social Issues"A community organization argues that introducing more recreational activities for youth will reduce crime rates. Critique the argument's assumptions and evidence."GRE Essay Topics with Answers- DOWNLOAD FREE!!!GRE Issue Essay TemplateIntroductionHook: Start with a compelling statement or question related to the essay prompt.Context: Briefly introduce the issue at hand and its relevance.Thesis Statement: Clearly state your position on the issue.Example: "In the debate over whether technology has made our lives more complex and less enjoyable, it is essential to consider both its advantages and disadvantages. While some argue that technology complicates life, I believe that its benefits far outweigh the drawbacks."Body Paragraph 1: Presenting the ArgumentTopic Sentence: Introduce the main point that supports your thesis.Supporting Details: Provide examples, evidence, or reasoning that supports this point.Explanation: Explain how this point strengthens your overall argument.Example: "One significant advantage of technology is its ability to streamline communication. Tools like smartphones and social media platforms allow us to connect instantly with people worldwide, facilitating both personal and professional interactions."Body Paragraph 2: Addressing CounterargumentsTopic Sentence: Acknowledge an opposing viewpoint.Counterargument Details: Present the opposing argument with supporting details.Refutation: Explain why this counterargument is less convincing or how your position remains stronger.Example: "Critics argue that technology creates a superficial sense of connection and can lead to social isolation. However, studies show that technology, when used appropriately, can enhance relationships by enabling more frequent and meaningful interactions."Body Paragraph 3: Further Support for Your PositionTopic Sentence: Introduce another supporting point.Supporting Details: Provide additional evidence or examples.Explanation: Connect this point back to your thesis.Example: "Moreover, technology has revolutionized access to information and education. Online resources and educational platforms make learning more accessible and flexible, allowing individuals to acquire new skills and knowledge at their own pace."ConclusionSummary: Recap the main points of your essay.Restate Thesis: Reinforce your position based on the arguments presented.Closing Statement: End with a final thought or call to action.Example: "In conclusion, while technology presents certain challenges, its contributions to communication and education underscore its overall positive impact. Embracing technological advancements while addressing potential drawbacks can lead to a more connected and informed society."GRE Analytical Writing Section - StructureThe GRE Analytical Writing section is the first part of the whole GRE entrance examination. The section consists of one writing task. You need to critically analyze the task statement and provide a thoughtful argument in your response. You will get 30 minutes to complete the whole task. GRE Examination No. of sectionsTotal durationNo. of questionsAnalytical Writing130 minutes1GRE Analytical Writing Section - Types and TipsThere are two major types of GRE analytical writing i.e. Issue Task and Argument Task. Let us discuss. GRE Analytical Writing Section - Issue Task TipsIn the GRE Analytical Writing Section's Issue Task, you to create and present a coherent argument on a given topic. Here is a detailed guide to complete the task effectively:Read the Prompt Carefully: Understand the topic and what you are being asked to argue or discuss.Identify Key Components: Identify the specific aspects of the issue you need to address.Develop a Thesis Statement: Clearly state your position on the issue and outline the main points you will use to support it.Plan Your Response: Create an outline with an introduction, body paragraphs, and a conclusion. Consider counterarguments if applicable.Address Counterarguments: Acknowledge opposing viewpoints and refute them with evidence and reasoning if needed.Use Clear and Concise Language: Write in a formal, academic tone. Avoid slang and overly complex sentences.GRE Analytical Writing Section - Structure Of The Issue TaskHere is the proper structure of the Issue Task for GRE Analytical Writing Section as mentioned below. Lets take an example. IntroductionThe question of whether governments should focus on solving poverty and hunger before dealing with environmental issues is a tough one.Body Paragraph 1Environmental problems directly affect poverty and hunger.For example, climate change harms farming and makes food less available.Explain how damage to the environment makes poverty and hunger worse, showing why both issues need attention.Body Paragraph 2Taking care of environmental issues can help prevent future problems.For instance, investing in green practices can provide long-term benefits for communities.Explain how taking proactive steps to protect the environment can help avoid future issues with poverty and hunger.Body Paragraph 3 (Counterarguments)Some people think we should focus only on poverty and hunger right now.Explain that ignoring environmental problems could make it harder to solve poverty and hunger later.ConclusionSummarize why it is important to address both environmental issues and poverty/hunger.Reaffirm that a balanced approach is needed.Highlight how these problems are connected and why a comprehensive approach is necessary.GRE Analytical Writing Section - Argument Task TipsIn the GRE Analytical Writing Section's Argument Task, you to create and present a coherent argument on a given topic. Here is a detailed guide to complete the task effectively:Read the Prompt Carefully: Understand the topic and what you are being asked to argue or discuss.Identify Key Components: Identify the specific aspects of the issue you need to address.Develop a Thesis Statement: Clearly state your position on the issue and outline the main points you will use to support it.Plan Your Response: Create an outline with an introduction, body paragraphs, and a conclusion. Consider counterarguments if applicable.Address Counterarguments: Acknowledge opposing viewpoints and refute them with evidence and reasoning if needed.Use Clear and Concise Language: Write in a formal, academic tone. Avoid slang and overly complex sentences.GRE Analytical Writing Section - Structure Of The Argument TaskHere is the proper structure of the Argument Task for GRE Analytical Writing Section as mentioned below. IntroductionStart by briefly describing the main point or claim made in the prompt. Clearly state what the argument is trying to prove.Paragraph 1: Identify AssumptionsPoint out any hidden assumptions in the argument that are not directly mentioned.Explain why these assumptions are problematic or not well-supported. Discuss how they weaken the argument.Paragraph 2: Evaluate EvidenceLook at the evidence provided in the argument.Check if the evidence is relevant, enough, and trustworthy. Note any missing details, inconsistencies, or unrelated information.Paragraph 3: Analyze ReasoningFocus on the logic behind the argument.Find any mistakes or errors in the reasoning. Explain how these issues affect the strength of the argument.Paragraph 4: Address Counterarguments Consider other viewpoints or opposing arguments.Discuss how these counterarguments might support or challenge the original argument. Explain why they do or do not effectively address the argument.ConclusionRecap the main problems or flaws found in the argument.Reinforce your overall evaluation of the argument.Provide a final comment on how effective the argument is or suggest how it could be improved.GRE Target Score Or Ideal ScoreYour target GRE score should match the average score of admitted students for the program you want.Score Over 160: Ideal for most programs.Score Over 150: Still good for many universities.Score Below 150: Might make it harder to get into top universities.Check the average GRE scores for universities you are interested in to see what score will make you competitive.University NameAverage GRE Verbal ScoreHarvard University164Stanford University162Massachusetts Institute of Technology (MIT)161University of California, Berkeley160University of Chicago163Yale University165Princeton University164Columbia University162University of Pennsylvania161University of Michigan159University of California, Los Angeles (UCLA)160Duke University162Northwestern University161University of Washington159University of California, San Diego (UCSD)158University of Texas at Austin157University of Wisconsin-Madison158New York University162University of Southern California (USC)160University of Florida156Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffTips for GRE Analytical Writing Test-FAQsHow to get better at writing for GRE?Avoid writing in first person.Pay careful attention to the instructions.Create an outline for your time before you enter the exam.Ensure that you write a sufficient amount.Focus on writing the main body paragraphs of your essay first.Is a 4.5 GRE writing score good?Very high and very low GRE writing scores are uncommon. A 4.0, 4.5 or 5.0 is a good GRE writing score, and a 5.5 or 6.0 is exceptionally good.How to get a 6 on GRE writing?Write at least three practice essays. Don't waffle.Choose very specific real-world examples.BUT, make sure your examples are relevant to the topic.Avoid first-person and self-reference. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Top 10 Tips for GRE Analytical Writing Section: Advanced Level | https://www.geeksforgeeks.org/tips-for-gre-analytical-writing/?ref=lbp | Data Science & ML | Top 10 Tips for GRE Analytical Writing Section: Advanced Level | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Top 10 Tips for GRE Analytical Writing Section: Advanced Level, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0126301404, -0.0247219, -0.0229466949, 0.0151910912, 0.0637909397, 0.00507097226, -0.00188433554, 0.0369009636, -0.0243435781, -0.0114078689, 0.0198910162, 0.00456896797, 0.0356786922, -0.0120699331, -0.00133958797, 0.0219572373, 0.00913793594, 0.0100182621, 0.00477995537, -0.00872323662, -0.0250711199, 0.00245, -0.0088687446, 0.0170099474, -0.0167480316, 0.00441618403, 0.00583489193, 0.0212878976, -0.024707349, -0.00862138066, 0.0297273938, 0.0125282845, 0.0471738651, -0.0382687449, -0.0383560508, -0.0198764652, 0.0223501101, -0.0128265768, -0.00817030389, 0.0306440964, 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10 Sep, 2024 | Understanding GRE Analytical Writing Section Question Format (Updated)
10 Sep, 2024
The GRE Analytical Writing Section is a crucial part of the Graduate Record Examination (GRE) that evaluates your ability to think critically, articulate your ideas clearly, and support your arguments with evidence. This section is divided into two tasks: the Issue Task and the Argument Task. Understanding the format and the types of questions you may encounter is key to excelling in this section. Table of ContentUnderstanding the GRE Analytical Writing SectionGRE Analytical Writing: Issue TaskGRE Analytical Writing: Argument TaskTime Management Tips for GRE Analytical WritingLatest Updates and Trends in GRE Analytical WritingCommon Mistakes to AvoidPractice Questions for GRE Analytical WritingGRE Analytical Writing Section Question Format - FAQsUnderstanding the GRE Analytical Writing SectionThe GRE Analytical Writing Section consists of two separately timed tasks:Issue Task: You are required to respond to a general statement or claim, presenting your perspective on the issue. You must support your viewpoint with relevant examples and reasoning.Argument Task: You are asked to critique an argument made by someone else. Here, your task is to evaluate the argument's logic, identify its strengths and weaknesses, and suggest improvements.Both tasks require you to write well-organized essays within a limited time.GRE Analytical Writing: Issue Task1. What to Expect in the Issue TaskIn the Issue Task, you will be presented with a statement or a claim about a general topic. Your job is to construct a compelling argument either supporting or opposing the statement.Key Points to Remember:You have 30 minutes to complete this task.The prompt will often include instructions such as "agree or disagree," "discuss," or "consider both views."You must take a clear stance on the issue and develop your argument with examples and reasoning.2. Structure of the Issue Task EssayAn effective Issue Task essay typically follows this structure:Introduction: Present the topic and your stance.Body Paragraphs: Provide examples, evidence, and reasoning to support your viewpoint.Counterargument: Acknowledge a possible counterargument and refute it.Conclusion: Summarize your points and restate your stance.GRE Analytical Writing: Argument Task1. What to Expect in the Argument TaskIn the Argument Task, you will be asked to evaluate the logic of an argument presented in a short passage. Unlike the Issue Task, you are not supposed to agree or disagree with the argument. Instead, your goal is to critique the reasoning used in the argument and suggest ways to strengthen it.Key Points to Remember:You have 30 minutes to complete this task.The argument is often flawed or incomplete, and your job is to identify these flaws.You should not introduce your own opinions on the subject matter.2. Structure of the Argument Task EssayAn effective Argument Task essay typically follows this structure:Introduction: Briefly summarize the argument and state that you will critique it.Body Paragraphs: Identify and explain the flaws in the argument, using specific examples from the text.Suggestions for Improvement: Offer recommendations on how the argument could be strengthened.Conclusion: Summarize the key points of your critique.Time Management Tips for GRE Analytical WritingOne of the biggest challenges in the GRE Analytical Writing Section is managing your time effectively. Here are some tips:Practice Writing: Regular practice can help you get accustomed to the 30-minute time frame.Outline Before You Write: Spend the first few minutes outlining your essay. This will help you organize your thoughts and ensure a clear structure.Leave Time for Review: Allocate a few minutes at the end to review your essay for any grammatical errors or unclear sentences.Latest Updates and Trends in GRE Analytical WritingThe GRE has maintained a consistent format for the Analytical Writing Section over the years, but it's essential to stay updated with the latest trends:Emphasis on Clarity and Organization: Recent analyses show that essays with clear structure and logical flow tend to score higher.Use of Relevant Examples: Examples that directly support your argument are crucial for a high score.Balanced Argumentation: For the Issue Task, addressing counterarguments is increasingly important in demonstrating critical thinking.Common Mistakes to AvoidHere are some common mistakes students make in the GRE Analytical Writing Section:Ignoring the Task Requirements: Ensure that you fully understand the prompt before starting your essay.Lack of Specific Examples: Vague or general examples can weaken your argument.Poor Organization: A well-structured essay is easier to follow and more likely to score high.Practice Questions for GRE Analytical WritingQuestion 1:Topic: "Governments should prioritize education over military spending."Answer: Introduction: Governments often face difficult choices in allocating resources. One such debate is whether to prioritize education or military spending. Body Paragraphs: Education fosters innovation, economic growth, and social stability. Countries with higher education levels typically have better healthcare, stronger economies, and more stable governments. On the other hand, while military spending is necessary for national security, an overemphasis can lead to economic strain and international tension. Counterargument: Critics might argue that military strength deters aggression and protects national interests. However, education can also be a powerful tool for fostering international understanding and reducing the need for military intervention. Conclusion: While national security is important, investing in education offers long-term benefits that outweigh the immediate advantages of military spending.Question 2:Topic: "Technological advancements have made life better for everyone."Answer: Introduction: Technology has become an integral part of our lives, but the extent to which it has improved life for everyone is debatable. Body Paragraphs: Advancements in healthcare, communication, and transportation have undeniably improved living standards for many. However, the benefits of technology are not evenly distributed; the digital divide has left some communities behind. Counterargument: Some might argue that technology has created new problems, such as job displacement and privacy concerns. While these issues are real, they are challenges to be managed rather than reasons to reject technological progress. Conclusion: On balance, technological advancements have made life better for most people, but efforts must be made to ensure these benefits are shared more equitably.Question 3:Topic: "In order to be successful, businesses must focus on innovation."Answer: Introduction: In today's fast-paced world, innovation is often touted as the key to business success. Body Paragraphs: Innovative companies are better able to adapt to changing market conditions, attract top talent, and differentiate themselves from competitors. Examples include companies like Apple and Tesla, which have thrived through continuous innovation. Counterargument: While innovation is important, some argue that maintaining quality and customer service are equally vital. Businesses must strike a balance between innovation and reliability. Conclusion: Success in business requires a focus on innovation, but it should not come at the expense of other crucial factors like quality and customer satisfaction.Question 4:Topic: "Public funding should support the arts, even during economic downturns."Answer: Introduction: During economic downturns, public funding is often redirected away from the arts toward more essential services. Body Paragraphs: The arts play a crucial role in cultural preservation, education, and community well-being. Cutting funding can have long-term negative effects on society. Moreover, the arts can be a source of economic growth through tourism and local businesses. Counterargument: Some argue that during tough economic times, funding should prioritize essential services. However, the arts are not just a luxury but a necessary component of a healthy society. Conclusion: Public funding should continue to support the arts, as they are vital to both the cultural and economic health of a community.Question 5:Topic: "Universities should require every student to take a variety of courses outside their major."Answer: Introduction: The debate over whether universities should require students to take courses outside their major is ongoing. Body Paragraphs: A well-rounded education helps students develop critical thinking skills, gain diverse perspectives, and become more adaptable in their careers. For instance, a science major may benefit from courses in philosophy or literature. Counterargument: Opponents argue that this requirement can detract from a student's focus on their major and increase the time and cost of their education. However, the long-term benefits of a broad education often outweigh these concerns. Conclusion: Universities should encourage students to explore a variety of subjects, as it prepares them better for the complexities of the real world.Argument Task Practice QuestionsQuestion 6:Topic: "The following is a letter to the editor of a local newspaper: 'Our town should invest more in public transportation to reduce traffic congestion.'"Answer: The argument that increased investment in public transportation will reduce traffic congestion seems logical but requires closer examination. The argument assumes that current public transportation is underutilized due to lack of investment, without considering other factors like convenience, coverage, or public preference. Additionally, it fails to address whether the town's population would actually use improved public transportation or if they are more reliant on personal vehicles. The argument could be strengthened by providing data on current transportation usage and public opinion surveys. While investing in public transportation could help, the argument needs more evidence to support its claim.Question 7:Topic: "A recent study suggests that people who eat breakfast are more productive at work."Answer: The claim that eating breakfast leads to higher productivity is appealing but may be overly simplistic. The study likely establishes correlation, not causation. Other factors, such as overall diet, sleep quality, and work environment, may also influence productivity. Additionally, the study may not account for individual differences in metabolism and work habits. The argument could be strengthened by controlling for these variables and examining a more diverse sample population. While there may be some truth to the claim, it is premature to suggest that eating breakfast alone significantly boosts productivity.Question 8:Topic: "The following is a recommendation from the board of a large company: 'Our company should focus on developing new products rather than improving existing ones.'"Answer: Introduction: The recommendation to focus on new product development over improving existing ones is bold but requires further analysis. Body Paragraphs: The argument assumes that new products will generate more revenue than improving current offerings, without considering the costs, risks, or market demand. It also overlooks the potential benefits of enhancing existing products, such as customer loyalty and brand strength. Suggestions for Improvement: The recommendation would be stronger if supported by market research and an analysis of the company's product portfolio. Conclusion: While new products are important, the company should not disregard the potential of improving existing products without careful consideration.Question 9:Topic: "A survey suggests that most people prefer online shopping to in-store shopping."Answer: Introduction: The claim that most people prefer online shopping based on a survey requires deeper scrutiny. Body Paragraphs: The survey's sample size, demographic, and question framing could significantly influence the results. The argument also fails to consider the context, such as the type of products being purchased or the impact of current events like a pandemic. Suggestions for Improvement: The argument could be improved by providing more detailed information about the survey and considering factors that might affect shopping preferences. Conclusion: While online shopping may be growing, the survey results should be interpreted with caution.Question 10:Topic: "The following is an advertisement: 'Our company's organic cleaning products are better for the environment than conventional products.'"Answer: Introduction: The advertisement's claim that organic cleaning products are better for the environment needs to be critically evaluated. Body Paragraphs: The argument assumes that 'organic' automatically means 'better for the environment' without providing any evidence or comparison to conventional products. It also fails to consider the full lifecycle of the product, including production, packaging, and disposal. Suggestions for Improvement: To make a more convincing case, the advertisement should include specific data on the environmental impact of both organic and conventional products. Conclusion: While organic products may offer environmental benefits, the argument requires more substantial evidence to be credible.ConclusionThe GRE Analytical Writing Section is your chance to showcase your ability to think critically and communicate your ideas effectively. By understanding the question format and following a structured approach, you can maximize your score. Practice regularly, stay updated with the latest trends, and focus on clear, logical argumentation to excel in this section.Also Read: GRE Exam Syllabus 2024GRE 2024: Exam Dates, Registration, Syllabus, and Score ValidityGRE Accepting Universities in USA in 2024: GRE Score Required for US UniversitiesMS in Data Science in USA Without GRE: Universities & RequirementsGRE Analytical Writing Section Question Format - FAQsHow do you write an analytical section in GRE?The "Analyze an Issue" task, which lasts 30 minutes, is the Analytical Writing measure. In this activity, a viewpoint on a matter is presented along with guidelines for how to react. You must assess the problem, take into account all of its nuances, and create a case for your position that is supported by facts and examples. Is a 4 on the GRE analytical writing good?A solid GRE writing score is 4.0, 4.5, or 5.0; an exceptionally outstanding score is 5.5 or 6.0. A somewhat lower score might not have a significant impact on your applications if you have other ways to showcase your writing abilities. Is awa score of 3 good in GRE?Every GRE AWA score corresponds to a particular performance level. A candidate with a GRE AWA score of 6 to 5 is considered to have adequate writing skills. For US universities, the average AWA cutoff is between 4.5 and above. In the GRE, the average AWA score is 3.5. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Understanding GRE Analytical Writing Section Question Format (Updated) | https://www.geeksforgeeks.org/gre-analytical-writing-section-question-format/?ref=lbp | Data Science & ML | Understanding GRE Analytical Writing Section Question Format (Updated) | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Understanding GRE Analytical Writing Section Question Format (Updated), Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0226321891, -0.0285682827, -0.0243607592, 0.00732966699, 0.0473547429, -0.0167094972, -0.00976842269, 0.0356701538, -0.0207160246, 0.00730286771, 0.0360721461, -0.0159993097, 0.0479443297, -0.00645868294, -0.00619068788, 0.0266923159, 0.0133327581, 0.025807932, 0.00884384, -0.010719806, -0.0176340807, 0.00898453686, -0.00668312889, 0.0302298516, -0.0256605353, 0.010277614, -0.0122741777, 0.0115036918, -0.0262769237, -0.0170444902, 0.0233423766, 0.0102173146, 0.0465507545, -0.0346785709, -0.03915409, -0.0303638503, 0.0471939445, -0.00789915677, -0.00986222085, 0.0469259508, 0.0133930575, 0.0133997574, 0.0342229791, -0.0187194608, 0.00871654227, 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24 Sep, 2024 | GRE Analytical Writing Section Overview | Syllabus, Examples & More
24 Sep, 2024
The GRE Analytical Writing Assessment (AWA) is a vital part of the GRE, assessing your ability to think critically and write analytically. Aiming for a GRE Analytical Writing score above 4.5 is crucial if you're targeting top universities. The updated format features just one task: Analyze an Issue, giving you 30 minutes to write a concise, well-structured essay.To excel, focus on writing between 500 and 600 words across 4 to 5 paragraphs, ensuring clarity and adherence to the GRE Analytical Writing word limit. Reviewing GRE Analytical Writing examples and GRE Analytical Writing PDFs can provide essential practice and insight, helping you achieve a strong score and boost your overall GRE performance.Table of ContentGRE Analytical Writing SectionGRE Analytical Writing Topics PDFGRE Issue Essay FormatGRE Analytical Writing SamplesGRE Analytical Writing ScoreGRE Analytical Writing Section- FAQsGRE Analytical Writing SectionThe GRE Analytical Writing Assessment (AWA) now exclusively features the Analyze an Issue task. This section is designed to evaluate your critical thinking and analytical writing abilities. Unlike other sections, there is no fixed pattern for GRE AWA topics, making it essential to familiarize yourself with a wide range of issues. Staying updated on the latest GRE exam pattern is crucial to understanding the recent changes in this section.Common GRE AWA TopicsThe following are some frequently encountered themes for the GRE Analyze an Issue task:Topic CategorySample TopicsTechnology and SocietyThe impact of technology on society, the role of the internet in shaping modern culture.EducationThe importance of standardized testing, the value of a liberal arts education.ArtsThe relevance of art in contemporary society, government funding for the arts.Intellectual EndeavoursThe pursuit of knowledge for its own sake, the value of curiosity-driven research.Government and PowerThe role of government in society, the balance of power between different branches of government.CitiesThe challenges of urbanization, the importance of sustainable city planning.PhilosophyThe role of ethics in decision-making, the relevance of ancient philosophical ideas in modern times.GRE Analytical Writing Topics PDFUnlock your potential for success in the GRE with our comprehensive GRE Analytical Writing PDF guide. Designed to help you excel in the Analytical Writing Assessment (AWA), this resource offers essential insights and strategies to master the GRE essay tasks. The GRE AWA section assesses your ability to think critically, develop well-structured arguments, and express your ideas clearly and effectively. Our PDF guide includes detailed explanations of the GRE Analytical Writing format, tips for crafting compelling essays, and sample prompts with high-scoring responses. Whether you're aiming for a top score or simply looking to improve your writing skills, this PDF provides the tools and knowledge you need to succeed in the GRE Analytical Writing section. Download now to start your journey towards GRE success!GRE Analytical Writing PDF- Free DOWNLOAD!!!!GRE Issue Essay FormatImportant GRE Issue Essay Format are as follows:GRE AWA Essay: Essential Tips for SuccessThe GRE AWA essay on an issue should be approximately 500-600 words in length, focusing on topics of general interest that can be analyzed from multiple perspectives. Remember, there are no absolute correct answers in the GRE AWA; instead, the test evaluates your critical thinking skills and your ability to present a well-reasoned argument. The GRE Analyze an Issue task challenges you to take a stance on a given topic, providing compelling reasons and evidence to support your position.Before you begin writing, carefully review the instructions and plan your response. Instructions typically fall into the following categories:Agree/Disagree with a Statement: Explain why you agree or disagree with the given statement, considering different perspectives that may support or challenge the statement.Position on a Recommendation: Articulate your stance on the provided recommendation, backing it up with reasons and examples.Extent of Agreement/Disagreement: Craft a response that discusses the extent to which you agree or disagree with a given claim.Balanced Argument: Write a response that discusses both sides of the argument, then explain your position.Consequences of a Policy: Discuss the consequences of a policy and how they influenced your decision.Tips for Writing a Strong GRE Issue EssayTo excel in the GRE Issue Essay, consider the following tips:Practice Regularly: Start by practicing writing GRE Issue Essays. Writing at least three essays will help you manage your time, familiarize yourself with different prompts, and understand the factual support needed for a strong argument.Pick One Side: Choose one side of the argument to support. Avoid trying to argue both sides, as this can weaken your essay and make your position unclear. The examiners assess your ability to defend your chosen stance effectively.Use Relevant Examples: Provide relevant examples to bolster your argument. Use examples from diverse fields such as business, arts, or history, but ensure they serve to support your essay rather than dominate it.Follow a Structured Pattern: Organize your essay in a clear, structured manner. A well-structured essay not only provides clarity to the reader but also helps to increase your GRE AWA score.By following these tips and practicing regularly, you'll improve your ability to write a compelling GRE AWA essay, enhancing your chances of achieving a high score. Incorporate these strategies into your preparation to present clear, well-supported arguments that will impress GRE examiners.GRE Analytical Writing SamplesHere are some examples of high-quality GRE Analytical Writing essays for the "Analyze an Issue" task. These examples illustrate how to effectively develop and present arguments, supporting a high score in the GRE AWA section:Example 1: Technology and SocietyPrompt: "Technology has made our lives easier but has also made us more isolated from each other."Essay: In today’s fast-paced world, technology undeniably simplifies many aspects of life, from communication to information access. However, it also contributes to a sense of isolation. For instance, while social media platforms facilitate instant communication, they often replace face-to-face interactions with impersonal digital exchanges. This shift can lead to superficial relationships and a lack of genuine human connection. Moreover, the rise of remote work, enabled by technology, has reduced daily interpersonal interactions, potentially weakening social bonds. Nonetheless, technology also fosters global connections and allows for virtual communities that can provide support and shared experiences. Balancing the benefits of technology with its potential to isolate individuals is crucial for maintaining meaningful personal connections.Example 2: EducationPrompt: "A college education should emphasize practical skills rather than theoretical knowledge."Essay: The debate between practical skills and theoretical knowledge in higher education is crucial for preparing students for the workforce. Advocates for practical skills argue that such training equips students with job-ready abilities, making them more competitive in the job market. For instance, courses in coding, data analysis, and project management directly align with industry demands and provide tangible benefits. Conversely, theoretical knowledge fosters critical thinking and problem-solving skills that are also essential in any profession. For example, understanding foundational theories in economics or psychology can enhance analytical abilities and adaptability. A balanced approach, integrating both practical skills and theoretical knowledge, ensures that students are well-rounded and prepared for diverse challenges.Example 3: Government and PowerPrompt: "Governments should prioritize economic development over environmental protection."Essay: The debate over whether governments should prioritize economic development or environmental protection is complex and multifaceted. Economic development fosters job creation, infrastructure improvement, and overall societal prosperity. For example, industrial growth often leads to higher employment rates and improved living standards. However, prioritizing economic growth at the expense of environmental protection can lead to long-term damage, such as climate change and loss of biodiversity. Sustainable development practices, which balance economic growth with environmental stewardship, are crucial. For instance, investing in green technologies can stimulate economic growth while preserving natural resources. Hence, a strategic approach that integrates both priorities is essential for achieving long-term prosperity and ecological balance.GRE Analytical Writing ScoreGRE scores will be accessible on the official ETS website within 8-10 days following the exam date. The Analytical Writing GRE score falls between 0 and 6.0. Valid for five years, candidates must submit or send their additional score reports to their chosen institutions within this timeframe for a successful admission process. Now, let's explore the criteria ETS considers when evaluating your AWA essays.Here’s a brief table summarizing the GRE AWA score and its corresponding explanation:GRE AWA ScoreExplanation6.0 – OutstandingClear identification and deep analysis of key features; well-organized ideas with logical connections; strong language control with few to no errors.5.0 – StrongThoughtful analysis with clear identification of important features; logical idea development with minor flaws; good control of language and syntax.4.0 – AdequateIdentifies main features with satisfactory analysis; organized ideas but may miss connections; sufficient language control with some flaws.3.0 – LimitedLimited analysis and poor organization; minimal support for critique; imprecise language with frequent errors.2.0 – Seriously FlawedNo clear understanding or analysis; disorganized with irrelevant evidence; serious language, grammar, and structural issues.1.0 – Fundamentally DeficientLacks understanding and organization; severe errors in grammar and sentence structure; incoherent response.0.0 – UnscorableOff-topic, non-English, copied, random characters, or no response.Read More:GRE Exam Pattern 2024GRE SyllabusGRE Exam Fee in IndiaGRE Eligibility CriteriaGRE Exam Dates 2024How to Register for GREFree GRE Practice TestDocuments Required GREBest Books GREGRE Full FormGRE Exam Fee WaiverGRE Total ScoreGRE Score ValidityGRE Coaching in IndiaGRE Cut OffGRE Analytical Writing Section- FAQsHow to write analytical writing in GRE?The Analytical Writing section of the GRE includes a 30-minute "Analyze an Issue" task. In this task, you are given a statement or opinion on a particular topic along with guidelines for your response. Your goal is to assess the issue, explore its various aspects, and construct a well-reasoned argument supported by relevant examples and explanations.Is 3.5 a good score in analytical writing in GRE?A score of 3.5 in GRE Analytical Writing is considered below average. Top-ranked universities generally look for higher scores, typically 4.0 or above, to meet their competitive admissions standards.How many words should your GRE Analytical Writing essay be? For the GRE Analytical Writing section, it's recommended that your essay be between 500 and 600 words. Aiming for this word count ensures that you have enough space to develop your arguments fully while adhering to the GRE Analytical Writing guidelines. Keeping within this range helps demonstrate a well-structured, coherent argument and allows for a thorough analysis of the issue. Properly managing your word count is crucial for scoring well on the GRE Analytical Writing Assessment.What is a good AWA score in GRE?A GRE AWA score of 6 to 5 means the candidate has proper writing skills. The average AWA cutoff for US universities ranges from 4.5 and above. The average AWA score in GRE is 3.5. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson 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Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, GRE Analytical Writing Section Overview | Syllabus, Examples & More, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0358050428, -0.023463957, -0.0257017724, 0.000124346057, 0.0489141382, -0.00257216347, -0.00376720959, 0.0281514507, -0.0176509339, -0.00419093808, 0.0263108816, -0.0153071862, 0.0331302583, -0.0213188324, -0.000637661491, 0.0155720161, 0.0184983891, 0.0170550644, 0.0185513552, -0.0104012061, -0.0169623755, 0.0111162476, -0.0107454853, 0.0289194584, -0.0209613107, 0.0156779476, -0.0143935215, 0.01271185, -0.0277277231, -0.0140492423, 0.0278071724, 0.00534294965, 0.0466366, -0.0228416063, -0.0529130772, -0.0244967937, 0.0413664766, -0.00869305152, -0.0111162476, 0.0187764615, 0.0268140584, 0.0053628115, 0.0381355509, -0.0167107861, -0.0012273225, -0.0213188324, 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10 Sep, 2024 | Recent GRE Verbal Reasoning Question and Answers Practice FREE!
10 Sep, 2024
The GRE (Graduate Record Examination) is a crucial step for anyone looking to pursue graduate studies, particularly in the United States. Among its sections, the Verbal Reasoning part often poses a significant challenge to test-takers. This section assesses your ability to understand, interpret, and analyze written material, as well as evaluate arguments and identify relationships among words and concepts. To help you excel, this article provides an in-depth overview of GRE Verbal Reasoning questions and answers, with effective strategies and practice examples. Table of ContentUnderstanding the GRE Verbal Reasoning SectionGRE Verbal Reasoning Question TypesGRE Verbal Reasoning Practice Question and AnswersTips for Mastering GRE Verbal ReasoningCommon Pitfalls to AvoidResources for GRE Verbal Reasoning PreparationGRE Verbal Reasoning Question and Answers- FAQs Understanding the GRE Verbal Reasoning SectionThe GRE Verbal Reasoning section is designed to measure your ability to:Analyze and conclude discourse.Reason from incomplete data.Identify an author's assumptions and/or perspective.Understand multiple levels of meaning, such as literal, figurative, and author's intent.The section consists of three types of questions:Reading ComprehensionText CompletionSentence EquivalenceEach type requires a different strategy, and understanding these differences is key to scoring well.GRE Verbal Reasoning Question Types1. Reading ComprehensionReading Comprehension questions test your ability to understand, interpret, and analyze passages. The passages may range from one paragraph to several, and the questions will ask you to find the main idea, infer meaning, or evaluate an argument.Key Strategies:Skim the Passage: Quickly read the passage to get a general idea. Focus on the first and last sentences of each paragraph as they often contain the main ideas.Understand the Question: Read the question carefully to determine what it is asking. Look for keywords that will help you locate the answer in the passage.Refer Back to the Text: Always refer back to the passage to confirm your answer, rather than relying on memory.Example Question:Passage:"In recent years, there has been a shift in the approach to studying economic trends. Traditional models focused heavily on quantitative data, while newer models integrate qualitative analysis to provide a more comprehensive understanding."Question:Which of the following best describes the main idea of the passage?A) The importance of economic modelsB) The integration of qualitative analysis in economic studiesC) The limitations of traditional economic modelsD) The use of quantitative data in economicsAnswer: B) The integration of qualitative analysis in economic studiesExplanation: The passage discusses the shift towards integrating qualitative analysis in economic models, making B the correct answer.2. Text CompletionText Completion questions test your ability to understand the context of a passage and choose words that best complete it. Each passage has one to three blanks, and you need to select the correct words from multiple choices.Key Strategies:Read the Entire Sentence: Before filling in the blanks, read the entire sentence to understand the overall context.Predict the Answer: Try to predict what type of word fits in the blank before looking at the answer choices.Eliminate Incorrect Choices: Use the process of elimination to narrow down your options.Example Question:Sentence:The scientist's new theory was (1) _______________ by her peers, who found her arguments both (2) _______________ and groundbreaking.A) dismissed B) acclaimed C) misunderstoodA) uninspired B) controversial C) compellingAnswer: 1) B) acclaimed, 2) C) compellingExplanation: The scientist's theory was well-received ("acclaimed") because her arguments were both convincing ("compelling") and innovative.3. Sentence EquivalenceSentence Equivalence questions test your ability to find two words that fit into a single sentence, creating sentences that are alike in meaning. These questions assess both your vocabulary and your ability to understand the context of a sentence.Key Strategies:Focus on Sentence Structure: Pay attention to clues in the sentence that indicate what type of word is needed.Consider Synonyms: Look for two words in the answer choices that are synonyms or close in meaning.Check for Equivalence: Ensure that the two sentences formed by the chosen words have the same meaning.Example Question:Sentence:The teacher's lecture was so __________ that many students fell asleep.A) engaging B) monotonous C) fascinating D) tedious E) lively F) boringAnswer: B) monotonous, D) tediousExplanation: Both "monotonous" and "tedious" convey a sense of boredom, making them the correct choices.GRE Verbal Reasoning Practice Question and AnswersReading ComprehensionQuestion 1:Passage:"Climate change is a pressing issue that demands immediate action. However, despite widespread recognition of the problem, the global response has been sluggish, with many countries failing to meet their carbon reduction targets."Question:Which of the following best describes the author's tone in the passage?A) OptimisticB) NeutralC) CriticalD) IndifferentAnswer: C) CriticalExplanation: The author criticizes the global response to climate change, indicating a critical tone.Question 2:Passage:"Recent studies suggest that a diet rich in omega-3 fatty acids can significantly reduce the risk of heart disease. Omega-3s, found in fish and certain plant oils, help lower blood pressure and reduce inflammation."Question:What is the primary purpose of the passage?A) To argue against the consumption of fishB) To explain the benefits of omega-3 fatty acidsC) To discuss the causes of heart diseaseD) To promote plant-based dietsAnswer: B) To explain the benefits of omega-3 fatty acidsExplanation: The passage focuses on the health benefits of omega-3 fatty acids.Question 3:Passage:"The advent of artificial intelligence has revolutionized various industries. From healthcare to finance, AI technologies are being integrated to enhance efficiency and accuracy in decision-making processes."Question:What can be inferred from the passage?A) AI is only beneficial in healthcare.B) AI has limited applications.C) AI is improving decision-making across industries.D) AI technologies are outdated.Answer: C) AI is improving decision-making across industriesExplanation: The passage suggests that AI is positively impacting multiple industries.Question 4:Passage:"In Shakespeare's plays, the characters often grapple with complex moral dilemmas, reflecting the playwright's deep understanding of human nature. His works continue to resonate with audiences because of their timeless exploration of ethical conflicts."Question:What is the author's main argument in the passage?A) Shakespeare's plays are outdated.B) Shakespeare had little understanding of human nature.C) Shakespeare's works remain relevant due to their moral exploration.D) Ethical conflicts are irrelevant in modern times.Answer: C) Shakespeare's works remain relevant due to their moral explorationExplanation: The author argues that the moral dilemmas in Shakespeare's plays keep them relevant.Question 5:Passage:"With the increasing reliance on digital media, the art of letter writing has become a rarity. While emails and instant messaging offer convenience, they lack the personal touch and emotional depth of handwritten letters."Question:Which of the following best describes the author's view on digital communication?A) EnthusiasticB) CriticalC) IndifferentD) SupportiveAnswer: B) CriticalExplanation: The author suggests that digital communication lacks the emotional depth of handwritten letters, indicating a critical view.Text CompletionQuestion 1:Sentence:The scientist's groundbreaking research was met with widespread ________ from the academic community, leading to numerous awards and recognition.A) skepticismB) indifferenceC) acclaimD) controversyAnswer: C) acclaimExplanation: The sentence suggests that the research was well-received, so "acclaim" is the correct choice.Question 2:Sentence:Although the novel was initially met with ________, it eventually gained widespread popularity and critical acclaim.A) enthusiasmB) indifferenceC) excitementD) praiseAnswer: B) indifferenceExplanation: The use of "eventually" suggests that the novel was not popular at first, making "indifference" the best fit.Question 3:Sentence:The politician's speech was so ________ that even his most ardent supporters found it difficult to stay engaged.A) captivatingB) inspiringC) monotonousD) rivetingAnswer: C) monotonousExplanation: The sentence indicates that the speech was not engaging, so "monotonous" is the correct choice.Question 4:Sentence:The artist was known for her ________ use of color, which made her paintings instantly recognizable.A) subtleB) boldC) mutedD) timidAnswer: B) boldExplanation: The sentence describes the artist's distinctive style, making "bold" the appropriate choice.Question 5:Sentence:Despite the company's ________ start, it managed to become a leader in the industry within a few years.A) auspiciousB) turbulentC) promisingD) smoothAnswer: B) turbulentExplanation: The contrast with the company becoming a leader suggests it had a difficult beginning, so "turbulent" fits best.Sentence EquivalenceQuestion 1:Sentence:The professor's lectures were so ________ that students found it difficult to stay awake.A) engagingB) boringC) tediousD) fascinatingE) stimulatingF) monotonousAnswer: B) boring, C) tediousExplanation: Both "boring" and "tedious" suggest the lectures were not interesting.Question 2:Sentence:The CEO's decision to ________ the company's expansion was met with surprise, as most had expected a more cautious approach.A) delayB) accelerateC) hinderD) postponeE) speed upF) slow downAnswer: B) accelerate, E) speed upExplanation: Both "accelerate" and "speed up" convey the idea of hastening the expansion.Question 3:Sentence:The new policy was designed to ________ innovation within the company, encouraging employees to think creatively.A) fosterB) stifleC) promoteD) hinderE) discourageF) cultivateAnswer: A) foster, C) promoteExplanation: Both "foster" and "promote" suggest encouraging innovation.Question 4:Sentence:Her response to the criticism was surprisingly ________, as she calmly addressed each point without becoming defensive.A) measuredB) erraticC) composedD) volatileE) thoughtfulF) hastyAnswer: A) measured, C) composedExplanation: Both "measured" and "composed" indicate a calm and controlled response.Question 5:Sentence:The scientist's findings were ________ by the academic community, leading to further research and exploration in the field.A) ignoredB) laudedC) dismissedD) celebratedE) overlookedF) praisedAnswer: B) lauded, D) celebratedExplanation: Both "lauded" and "celebrated" suggest that the findings were highly regarded.Tips for Mastering GRE Verbal ReasoningSuccess in the GRE Verbal Reasoning section requires not only understanding the types of questions but also developing effective test-taking strategies. Here are some tips to help you master this section:Expand Your Vocabulary:A strong vocabulary is essential for doing well in the Verbal Reasoning section. Use flashcards, vocabulary apps, and read widely to enhance your word knowledge.Practice Reading Comprehension:Regularly practice reading academic articles, essays, and complex texts. Focus on identifying main ideas, understanding arguments, and making inferences.Time Management:Practice completing questions within the allotted time. The Verbal Reasoning section is time-pressured, so developing a pace that allows you to answer all questions is crucial.Take Practice Tests:Simulate test conditions by taking full-length practice tests. This will help you become familiar with the test format and improve your endurance.Review Your Mistakes:After each practice test, review your incorrect answers to understand your mistakes. This will help you avoid similar errors in the future.Learn to Skim:Not every passage needs to be read in detail. Learn to skim for main ideas and key points to save time.Use Process of Elimination:Eliminate obviously incorrect answers to increase your chances of selecting the right one.Stay Calm and Focused:On test day, remain calm and focused. Anxiety can affect your performance, so practice relaxation techniques if necessary.Common Pitfalls to AvoidEven with the best preparation, there are common pitfalls that can trip up test-takers. Here’s what to watch out for:Overthinking Questions: Sometimes, the simplest answer is the correct one. Avoid reading too much into questions.Ignoring Context: Always consider the broader context of a passage or sentence. Don’t focus solely on individual words.Skipping Hard Questions: If you encounter a difficult question, it’s better to move on and return to it later. Don’t let one question consume too much time.Resources for GRE Verbal Reasoning PreparationTo enhance your preparation, consider using the following resources:Official GRE Guide:The official guide from ETS provides authentic practice questions and valuable tips.Vocabulary Apps:Apps like Magoosh and Quizlet offer extensive GRE vocabulary lists to help you build your word knowledge.GRE Prep Books:Books like "The Princeton Review's Cracking the GRE" and "Kaplan's GRE Prep Plus" are great for comprehensive review and practice.Online Practice Tests:Websites like ETS, Manhattan Prep, and Kaplan offer free GRE practice tests that mimic the real exam.GRE Forums:Engage with other test-takers on forums like Reddit’s GRE subreddit. Sharing tips and strategies can be very helpful.ConclusionThe GRE Verbal Reasoning section may be challenging, but with the right strategies and preparation, you can achieve a high score. Focus on expanding your vocabulary, practicing different question types, and taking full-length practice tests. Remember to manage your time effectively and stay calm on test day. By following the tips and using the resources provided in this guide, you’ll be well-prepared to tackle the GRE Verbal Reasoning section and move closer to your graduate school goals.Also Read: GRE Exam Syllabus 2024GRE 2024: Exam Dates, Registration, Syllabus, and Score ValidityGRE Accepting Universities in USA in 2024: GRE Score Required for US UniversitiesMS in Data Science in USA Without GRE: Universities & RequirementsGRE Verbal Reasoning Question and Answers- FAQs Q1: How many questions are there in the GRE Verbal Reasoning section?A: The GRE Verbal Reasoning section consists of two parts, each containing 20 questions. These include a mix of Reading Comprehension, Text Completion, and Sentence Equivalence questions. You will have 30 minutes to complete each part.Q2: How can I improve my vocabulary for the GRE Verbal Reasoning section?A: Improving your vocabulary is key to success in the GRE Verbal Reasoning section. You can enhance your vocabulary by reading widely, using flashcards, and regularly practicing with GRE-specific vocabulary lists. Additionally, learning the roots, prefixes, and suffixes of words can help you deduce the meanings of unfamiliar words.Q3: Is it possible to prepare for the GRE Verbal Reasoning section in a short time?A: Yes, it is possible to prepare for the GRE Verbal Reasoning section in a short time, but it requires focused and consistent effort. Prioritize high-frequency GRE words, practice with sample questions, and take timed practice tests to get familiar with the test format. Additionally, review your mistakes to understand your weak areas and improve upon them | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in 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Series Data, Data Science & ML, Recent GRE Verbal Reasoning Question and Answers Practice FREE!, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [0.00591764506, -0.00496102078, -0.0259530526, 0.0216700602, 0.0593979843, 0.0118755689, -0.0073441905, 0.0087271, -0.0175213311, 0.0170111321, 0.0042427131, 0.0107276198, 0.0121239554, -0.0335926227, -0.0120702507, 0.0215089452, 0.0173333641, 0.025872495, -0.00876737852, -0.0174810532, -0.026543811, 0.0188371092, -0.021361256, -0.0100361649, -0.0283563621, 0.0178032834, 0.00250568474, 0.00513891922, -0.0334583595, 0.0274970774, 0.0231201015, 0.00412523327, 0.017360216, -0.0571960695, -0.0445484892, -0.0174273476, 0.0179509725, -0.0159504544, -0.0183269102, 0.0238988269, 0.0219788663, 0.0291350875, 0.0131175024, -0.019696394, 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25 Sep, 2024 | Latest GRE Verbal Reasoning Topics and Format 2024
25 Sep, 2024
Are you gearing up for the GRE and feeling a bit anxious about the Verbal Reasoning section? You’re in the right place! The GRE Verbal Reasoning section assesses your ability to understand and analyze written material, focusing on essential topics like reading comprehension, text completion, and sentence equivalence. In this article, we’ll explore the key GRE Verbal Reasoning topics you need to master, offer effective study strategies, and answer common questions about what to expect on test day. Whether you're aiming for a top score to enhance your graduate school application or just want to improve your verbal skills, this guide will equip you with the knowledge and confidence to succeed! Table of ContentUnderstanding GRE Verbal ReasoningTopics Covered in GRE Verbal ReasoningFormat of GRE Verbal ReasoningTips for Mastering GRE Verbal ReasoningGRE Verbal Reasoning Practice QuestionsCommon Challenges and How to Overcome ThemGRE Verbal Reasoning Topics and Format 2024- FAQsUnderstanding GRE Verbal Reasoning SectionThe GRE Verbal Reasoning section is crafted to measure a range of skills that are essential for success in graduate school. These skills include:Reading Comprehension: The ability to read and understand complex passages.Text Completion: The skill of filling in the blanks with appropriate words or phrases to complete sentences or paragraphs meaningfully.Sentence Equivalence: The ability to find two words that fit a sentence and give it a similar meaning.Each of these question types is designed to test your understanding of vocabulary, grammar, and overall comprehension of written English.GRE Verbal Reasoning TopicsReading ComprehensionReading Comprehension forms the backbone of the Verbal Reasoning section. Here, you will encounter passages that cover a wide range of subjects, from the arts and humanities to sciences and social studies. The key topics include:Humanities: Literature, philosophy, history, and art.Social Sciences: Sociology, psychology, anthropology, and economics.Natural Sciences: Biology, chemistry, physics, and environmental science.Business and Law: Business practices, ethics, legal principles, and economics.In each passage, your task is to understand the main idea, infer meanings, draw conclusions, and analyze the author's intent and tone.Text CompletionText Completion questions assess your ability to choose the correct words that best complete a sentence or paragraph. These questions test your vocabulary and contextual understanding. Key areas include:Vocabulary in Context: Understanding the meaning of words as used in specific contexts.Logical Consistency: Identifying words that maintain the logical flow of the sentence or paragraph.Complex Sentence Structures: Navigating through sentences with multiple clauses and intricate structures.Sentence EquivalenceSentence Equivalence questions require you to find two words that can complete a sentence and provide a similar meaning. These questions focus on:Synonyms and Antonyms: Identifying words with similar or opposite meanings.Contextual Understanding: Choosing words that maintain the sentence's intended meaning.Vocabulary Breadth: A wide-ranging vocabulary is essential for success in these questions.Format of GRE Verbal ReasoningThe GRE Verbal Reasoning section consists of two 30-minute sections, each containing 20 questions. The questions are divided among Reading Comprehension, Text Completion, and Sentence Equivalence. The section is adaptive, meaning the difficulty level of the second section is based on your performance in the first section.Reading Comprehension:Passages range from one paragraph to several paragraphs.Questions may ask about specific details, main ideas, inferences, and the structure of the passage.Typically, 10 questions per section.Text Completion:Usually, 6 questions per section.Sentences may have one, two, or three blanks.Each blank has three answer choices, and you must choose the correct word for each blank.Sentence Equivalence:Typically, 4 questions per section.Sentences have one blank, and you must select two correct answer choices that give the sentence a similar meaning.Tips for Mastering GRE Verbal ReasoningBuild a Strong Vocabulary:Regularly read a variety of texts to encounter new words.Use flashcards or apps to reinforce your vocabulary knowledge.Practice using new words in sentences to solidify your understanding.Practice Active Reading:When reading passages, summarize each paragraph in your own words.Identify the main idea and tone of the passage.Practice making inferences and drawing conclusions based on the text.Understand the Context:For Text Completion and Sentence Equivalence, pay close attention to the context surrounding the blanks.Eliminate answer choices that do not fit the overall tone or logical flow of the sentence.Practice with Official GRE Material:Use official GRE practice tests and questions to familiarize yourself with the question format and difficulty level.Review explanations for any questions you get wrong to understand your mistakes.Time Management:Practice completing sections within the allotted time to ensure you can manage the pressure of the exam.If stuck on a question, move on and return to it later to avoid wasting time.Use Process of Elimination:Narrow down answer choices by eliminating those that are clearly incorrect.For Reading Comprehension, return to the passage to verify your answers.GRE Verbal Reasoning Practice QuestionsTo give you a better understanding of what to expect, here are some sample questions based on each topic:Reading ComprehensionSample Passage: "The Renaissance was a period of great cultural change and achievement in Europe..."Sample Question: What is the primary purpose of the passage?Answer Choices: a) To discuss the causes of the Renaissance, b) To describe the impact of the Renaissance on art, c) To explain the economic factors during the Renaissance.Text CompletionSample Sentence: "The scientist's hypothesis was so ______________ that it inspired a generation of researchers."Answer Choices: a) revolutionaryb) enigmaticc) mundane.Sentence EquivalenceSample Sentence: "The artist's work was both ___________ and ___________, captivating audiences around the world."Answer Choices: a) innovativeb) derivativec) transformatived) conventionalCommon Challenges and How to Overcome ThemVocabulary OverloadChallenge: Encountering too many unfamiliar words.Solution: Focus on learning high-frequency GRE words and practice using them in sentences.Complex PassagesChallenge: Difficulty in understanding dense or abstract passages.Solution: Practice reading academic journals or articles to build familiarity with complex texts.Time PressureChallenge: Running out of time before completing all questions.Solution: Practice under timed conditions and learn to skim passages effectively.Also Read: GRE Exam Syllabus 2024GRE 2024: Exam Dates, Registration, Syllabus, and Score ValidityGRE Accepting Universities in USA in 2024: GRE Score Required for US UniversitiesMS in Data Science in USA Without GRE: Universities & RequirementsConclusionMastering the GRE Verbal Reasoning section requires a combination of strong vocabulary, sharp analytical skills, and effective time management. By understanding the key topics and format, and implementing the strategies outlined in this guide, you can approach the GRE with confidence and achieve your desired score. Whether it's Reading Comprehension, Text Completion, or Sentence Equivalence, each question type can be tackled with practice and preparation. Start incorporating these tips into your study routine today, and take one step closer to acing the GRE Verbal Reasoning section!GRE Verbal Reasoning Topics and Format 2024- FAQsWhat is the structure of the GRE Verbal Reasoning test?There are three different sorts of questions in each GRE Verbal section: Text Completion, Sentence Equivalency, and Reading Comprehension. The GRE Verbal section consists of two sections with roughly 27 questions to answer in 41 minutes.What is a good GRE score out of 340?The optimal score varies depending on which university you want to apply to. In order to gain easy entrance to the world's most prestigious colleges, you must score 320 or higher out of 340. Remember that a score of at least the 75th percentile is regarded as sufficient to submit an application for admission. What is a 165 on the GRE verbal exam? It's at or above the 75th percentile for most programs: 165+ in quantitative reasoning and 157+ in verbal reasoning. A score in the 90th percentile or above is required for elite programs: 169+ in Quant and 162+ in Verbal | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024 | https://www.geeksforgeeks.org/gre-verbal-reasoning-topics/?ref=lbp | Data Science & ML | Latest GRE Verbal Reasoning Topics and Format 2024 | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Latest GRE Verbal Reasoning Topics and Format 2024, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [0.00498431688, -0.00126846379, -0.0271268878, 0.0241555311, 0.0636719093, -0.0052065053, -0.0285462402, 0.0185975041, -0.0228290334, 0.0153210536, 0.0215953905, 0.00440065749, 0.0288115405, -0.0253759101, -0.0182526149, 0.0432438403, 0.00767379161, 0.0288115405, -0.0344624221, -0.0181464944, -0.0302972179, -0.00113001058, -0.0230014771, -0.00433433289, -0.039370466, -0.00575700169, -0.000478782924, 0.00660927687, -0.0258799791, -0.00474886317, 0.0379909053, 0.0145516843, 0.042633649, -0.0434295498, -0.0302441567, -0.0158914477, 0.0229086224, 0.00230644853, -0.000603142136, 0.0299257971, 0.0295809079, 0.0332951024, 0.0145649491, 0.0102007706, 0.00170620822, -0.0357358605, 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27 Sep, 2024 | Updated 300+ GRE Vocabulary List of Words With Usage and Definition
27 Sep, 2024
Preparing for the GRE can feel overwhelming, especially when it comes to mastering the extensive vocabulary required for the Verbal Reasoning section. A well-curated GRE vocabulary list is essential for boosting your score and understanding complex passages. In this article, we provide a comprehensive GRE vocabulary list with high-frequency words you’re likely to encounter on the exam, along with tips on how to study effectively.
Whether you’re aiming for a top score or just want to improve your verbal skills, this guide will help you build a strong vocabulary foundation for the GRE!
Table of Content
Why GRE Vocabulary List Matters
How to Use GRE Vocabulary List of Words
Top 300+ GRE Vocabulary Words with Usage
GRE Vocabulary Flashcards
Tips for Mastering GRE Vocabulary Words
GRE Vocabulary Words With Usage and Definition- FAQs
Why GRE Vocabulary List Matters
The GRE (Graduate Record Examination) is a standardized test used for admission to graduate schools. The verbal reasoning section of the GRE assesses your ability to understand, interpret, and analyze written material. A significant portion of this section involves understanding and using sophisticated vocabulary. By expanding your vocabulary, you’ll improve your reading comprehension, critical thinking, and overall performance on the test.
How to Use GRE Vocabulary List of Words
The list of GRE vocabulary words is designed to be practical and easy to use. Each word is accompanied by its definition and an example sentence to help you understand its usage. We recommend regularly studying these words and incorporating them into your practice tests to reinforce learning. To maximize your study time, try using flashcards or vocabulary apps that feature these words.
Top 300+ GRE Vocabulary Words with Usage
Here’s a curated list of 200 GRE vocabulary words to help you get started:
Word
Definition
Example Sentence
Abate
To reduce in amount or intensity
The storm suddenly abated, leaving behind only light rain.
Benevolent
Showing kindness and goodwill
Her benevolent nature made her popular among the community.
Cacophony
Harsh, discordant mixture of sounds
The cacophony of city traffic was overwhelming.
Deference
Respectful submission or yielding to the judgment of another
He showed deference to his mentor’s opinions.
Ebullient
Cheerful and full of energy
Her ebullient personality brightened everyone’s day.
Furtive
Secretive or sly
He cast a furtive glance around the room.
Garrulous
Excessively talkative
The garrulous host took over the conversation.
Hapless
Unfortunate or unlucky
The hapless student failed to notice the errors in his essay.
Iconoclast
One who attacks or undermines traditional beliefs
The artist was known as an iconoclast, challenging conventional styles.
Juxtapose
To place side by side for comparison
The artist juxtaposed bright colors with dark backgrounds.
Keen
Having a sharp edge or point; enthusiastic
She had a keen interest in marine biology.
Lethargic
Sluggish or lacking energy
After the long flight, he felt lethargic and needed rest.
Mellifluous
Sweet or musical; pleasant to hear
The singer’s mellifluous voice captivated the audience.
Nefarious
Wicked or villainous
The nefarious plot was uncovered by the detectives.
Obfuscate
To deliberately make something unclear or difficult to understand
The politician’s speech was designed to obfuscate the real issues.
Perpetuate
To make something continue indefinitely
The documentary sought to perpetuate the memory of the historical event.
Quintessential
Representing the most perfect example of something
She was the quintessential scholar, known for her diligence and expertise.
Recalcitrant
Stubbornly resistant to authority
The recalcitrant student refused to follow the rules.
Sanguine
Optimistic or positive, especially in a difficult situation
Despite the challenges, she remained sanguine about the future.
Trepidation
A feeling of fear or anxiety about something that may happen
He approached the new project with trepidation.
Ubiquitous
Present or existing everywhere
Smartphones have become ubiquitous in modern society.
Verbose
Using more words than needed
The professor’s verbose lecture was hard to follow.
Warrant
To justify or necessitate
The evidence did not warrant further investigation.
Xenophobia
Fear or hatred of strangers or foreigners
Xenophobia can lead to social and cultural tensions.
Yoke
A device used for joining two animals; something that burdens
The yoke of responsibility weighed heavily on his shoulders.
Zealous
Showing great enthusiasm or devotion
The zealous fan attended every game.
Abstruse
Difficult to understand
The professor’s lecture was so abstruse that many students were confused.
Aplomb
Self-confidence or assurance, especially in a demanding situation
She handled the difficult situation with aplomb.
Bolster
To support or strengthen
The new evidence bolstered the defense’s case.
Candid
Truthful and straightforward; frank
Her candid remarks surprised everyone at the meeting.
Disparate
Essentially different or distinct
The two cultures were so disparate that finding common ground was challenging.
Enervate
To weaken or drain energy
The long lecture enervated the students.
Facilitate
To make an action or process easier
The new software will facilitate the data entry process.
Gregarious
Sociable and outgoing
He was known for his gregarious personality and love of social gatherings.
Hapless
Unlucky or unfortunate
The hapless traveler lost his luggage on the first day of his trip.
Insidious
Proceeding in a gradual, subtle way, but with harmful effects
The insidious effects of the disease were not immediately noticeable.
Kaleidoscope
A constantly changing pattern of colors and shapes
Her mood was like a kaleidoscope, changing rapidly throughout the day.
Luminous
Emitting light; bright or shining
The luminous stars were visible even through the city lights.
Maverick
An independent-minded person
The maverick scientist pursued unconventional theories.
Nostalgia
A sentimental longing for the past
He felt a sense of nostalgia when he visited his childhood home.
Obsolete
No longer produced or used; out of date
The technology quickly became obsolete.
Plausible
Seemingly reasonable or probable
The explanation seemed plausible given the evidence.
Pristine
In its original condition; unspoiled
The pristine beaches were untouched by tourists.
Quixotic
Exceedingly idealistic; unrealistic and impractical
His quixotic plans were unlikely to succeed.
Rescind
To revoke, cancel, or repeal
The company decided to rescind the job offer.
Skeptical
Doubtful or questioning
She was skeptical about the new product’s claims.
Tangible
Perceptible by touch; capable of being touched or felt
The progress was tangible and visible.
Unprecedented
Never done or known before
The research made unprecedented advances in the field.
Venerable
Accorded a great deal of respect, especially because of age or wisdom
The venerable professor was admired by all his students.
Wistful
Having or showing a feeling of vague or regretful longing
She looked wistful as she remembered her childhood home.
Zephyr
A gentle, mild breeze
A zephyr blew through the open window, bringing a cool respite.
Abide
To accept or act in accordance with
You must abide by the rules of the competition.
Brevity
Concise and exact use of words in writing or speech
The brevity of his speech made it impactful.
Concur
To agree or have the same opinion
I concur with your assessment of the situation.
Diligent
Having or showing care and conscientiousness in one’s work
Her diligent efforts were evident in the final report.
Empathy
The ability to understand and share the feelings of another
She showed great empathy towards her friend’s situation.
Fortuitous
Happening by accident or chance
It was a fortuitous meeting that led to the new partnership.
Guile
Sly or cunning intelligence
The con artist used guile to trick his victims.
Homogeneous
Of the same kind; alike
The group was quite homogeneous in their interests.
Impetuous
Acting quickly without thought or care
His impetuous decision led to unexpected consequences.
Judicious
Having, showing, or done with good judgment or sense
Her judicious choice of words helped defuse the situation.
Keen
Having a sharp edge or point; enthusiastic
She has a keen sense of observation.
Lethargic
Sluggish and apathetic
He felt lethargic after staying up all night.
Meticulous
Showing great attention to detail; very careful and precise
The artist was meticulous in his work.
Nefarious
Wicked or villainous
The villain’s nefarious plans were eventually thwarted.
Obsolete
No longer produced or used; out of date
The technology quickly became obsolete.
Pragmatic
Dealing with things sensibly and realistically
Her pragmatic approach helped solve the problem efficiently.
Quell
To put an end to, typically by the use of force
The police quelled the disturbance quickly.
Reverent
Feeling or showing deep and solemn respect
The students listened with reverent attention.
Substantiate
To provide evidence to support or prove the truth of
You need to substantiate your claims with data.
Tactile
Related to the sense of touch
The tactile feedback from the keyboard was satisfying.
Uplift
To raise or elevate
The speech aimed to uplift the audience’s spirits.
Vivid
Producing powerful feelings or strong, clear images in the mind
She gave a vivid description of the scene.
Whimsical
Playfully quaint or fanciful
The whimsical decorations made the party unique.
Yearn
To have an intense feeling of longing
He yearned for a simpler life.
Zenith
The highest point; peak
The company reached its zenith during the 1990s.
Abyss
A deep or seemingly bottomless chasm
He stared into the abyss, overwhelmed by its vastness.
Chide
To scold or rebuke
She chided her children for being late.
Dilatory
Slow to act; intended to cause delay
His dilatory tactics frustrated the committee.
Egregious
Outstandingly bad; shocking
The error was so egregious that it had to be corrected immediately.
Fervent
Having or displaying a passionate intensity
She was a fervent supporter of the cause.
Genuine
Truly what something is said to be; authentic
The signature was verified as genuine.
Hubris
Excessive pride or self-confidence
His hubris led to his downfall.
Innocuous
Not harmful or offensive
The comment was intended to be innocuous.
Mundane
Lacking interest or excitement; dull
He found the daily routine quite mundane.
Noxious
Harmful, poisonous, or very unpleasant
The noxious fumes were dangerous to inhale.
Opaque
Not able to be seen through; not transparent
The opaque material blocked out the sunlight.
Pristine
In its original condition; unspoiled
The pristine beaches were untouched by tourists.
Quixotic
Exceedingly idealistic; unrealistic and impractical
His quixotic plans were unlikely to succeed.
Resilient
Able to withstand or recover quickly from difficult conditions
The resilient community rebuilt after the disaster.
Sage
A profoundly wise person
The sage offered valuable advice.
Tactile
Related to the sense of touch
The tactile feedback from the keyboard was satisfying.
Ubiquitous
Present, appearing, or found everywhere
Smartphones are ubiquitous in modern society.
Vex
To make someone feel annoyed, frustrated, or worried
The constant interruptions vexed the speaker.
Wary
Feeling or showing caution about possible dangers or problems
She was wary of the new proposal.
GRE Vocabulary Flashcards
GRE vocabulary flashcards are an essential tool for students aiming to enhance their verbal reasoning skills. Flashcards make it easier to memorize the challenging words commonly seen on the GRE. They help you retain definitions, identify usage in context, and improve recall. Whether you’re on the go or sitting at your desk, flashcards offer the flexibility to learn anytime, anywhere.
Here’s how to make the most of GRE vocabulary flashcards:
Prioritize High-Frequency Words: Focus on words that appear often on the GRE. By mastering these, you’ll maximize your chances of success.
Daily Practice: Set aside time each day to review your flashcards. Consistency is key to building a strong vocabulary.
Contextual Learning: Write sentences or look up examples that use the word in context to understand its meaning better.
Use Spaced Repetition: Digital flashcard apps like Anki use spaced repetition to help you focus on words you struggle with while reinforcing those you know well.
Tips for Mastering GRE Vocabulary Words
Regular Review: Consistent review is key to retaining vocabulary. Set aside time each day to review and practice these words.
Use Flashcards: Create flashcards with the vocabulary words and their definitions. Review them regularly to reinforce your memory.
Practice in Context: Use the words in sentences and practice questions to understand how they fit into different contexts.
Join Study Groups: Collaborate with others preparing for the GRE to discuss and quiz each other on vocabulary.
Leverage Online Resources: Utilize apps and online platforms that offer GRE vocabulary practice and quizzes.
Conclusion
Building a strong GRE vocabulary is essential for success on the verbal reasoning section of the GRE. By familiarizing yourself with these 200 GRE vocabulary words and incorporating them into your study routine, you’ll be well-equipped to tackle the test with confidence. Remember, consistent practice and review are key to mastering vocabulary and achieving a high GRE score. Good luck with your preparation!
Also Read:
Books for GRE Exam
GRE Coaching Institutes in India
Best Tips for GRE General Test 2024 – Best 10 Strategies
How to Prepare GRE Exam in 1 month – Step-by-Step Study Plan
GRE Vocabulary Words With Usage and Definition- FAQs
How can I improve my GRE vocabulary?
Go for Long Term. If you have the opportunity, spread out your vocabulary studying over a long time.
Use Flashcards
Write Down Unfamiliar Words.
Find a Study Buddy.
Learn Your Word Roots
Repeat.
Use the Words.
What are GRE vocabulary words?
On the other hand, the nearly 3500 advanced terms in the GRE® Vocabulary may be words you can read or spell with ease, but you may not be familiar with their definitions. The GRE® favors evaluating applicants based on their use of words that have many meanings and may be incorporated into various speech segments.
How many vocab is enough for GRE?
To be prepared for anything that could come your way on test day, you might need to master more than 1,000 GRE vocabulary words. During your GRE exam preparation, you will likely need to study at least a few hundred vocabulary words, even if you already have a large vocabulary. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic 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10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.00990516786, 0.0139800385, -0.0246013179, 0.00411606301, 0.0542978086, 0.0314329043, -0.0157798249, 0.0125668244, -0.0153108668, 0.00983545743, 0.00360908057, 0.0277319346, 0.00743996585, -0.0196455661, -0.00299594877, 0.0370604098, 0.0180485714, 0.00420478499, -0.0267940164, -0.0141574824, -0.043423038, -0.0232958384, 6.35708348e-05, -0.0192526542, -0.0239168927, 0.00626440067, 0.0169712342, 0.00338093843, -0.0319398865, 0.0242971294, 0.0244112, 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22 May, 2020 | GRE | List of words to enhance your vocabulary with alphabet ‘B’
22 May, 2020
Please refer for Set-1: List of words to enhance your vocabulary
Set-2 :
The list of 10 most common root words with alphabet ‘B’ with their meaning and examples is as follows:
No
Root
Meaning
Examples
Meaning
1
bio
life
amphibious
living on both
autobiography
written account of one’s life
biopsy
medical check up
biome
a large naturally occurring community of flora and fauna occupying a major habitat
2
bi
two
binary
consisting of two
bipartisan
having two of something
bipolar
having two poles as earth
biannual
occurring twice a year
bisexual
attracted to both men and women
3
bel
beautiful / fair / fine
embellish
make beautiful / decorate
belle
women / girl admired for her beauty and charm
4
bas
low
abase
to lower / disgrace oneself
baseness
lack of moral principles; bad character
5
bell
war
rebel
one who makes war against established authority
belligerent
ready to fight / quarrelsome / warlike
antebellum
before the war
6
bibl
book
bible
collection of books – 66 in all
bibliotheca
library
bibliophile
a person who collects or has a great love of books
7
brev
short / brief
abbreviation
shortform
brevity
briefness / conciseness / shortness
breviloquent
laconic; concise in one’s speech
8
bene
good
benefactor
A person who helps institutions or people
benediction
act of praying
benevolent
charitable / kind
beneficent
doing good
benign
having a kindly disposition
9
burs
purse/money
bursar
treasurer
bursary
treasury
disburse
to pay
10
bon / boun
god / generous
bonafide
in good faith; without fraud
bountiful
generous | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’ | https://www.geeksforgeeks.org/gre-list-of-words-to-enhance-your-vocabulary-with-alphabet-b/?ref=ml_lbp | Data Science & ML | GRE | List of words to enhance your vocabulary with alphabet ‘B’ | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Latest GRE Verbal Reasoning Topics and Format 2024, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [0.0318227857, 0.0214404482, -0.0148209408, -0.00864682812, 0.0501608215, -0.00530635752, -0.0038377021, -0.00530251767, -0.0106971869, -0.0082321493, 0.0171400718, 0.0021117921, -0.019643506, -0.00763700809, -0.00597829139, 0.027338108, 0.0343415774, 0.00947618671, -0.00850092247, 0.00714169675, -0.0483178, 0.00483408384, 0.0352323689, -0.0203960706, -0.006957395, 0.0143678654, 0.0203192793, 0.00321568339, -0.0109198848, 0.00120276154, 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23 Jun, 2020 | GRE | List of words to enhance your vocabulary with root alphabet ‘E’
23 Jun, 2020
The list of 10 most common root words with root alphabet ‘E’ with their meaning and examples is as follows :
S.No
Root
Meaning
Examples
Meaning
1
eu
good
eulogy
a praising speech
sacrifice
holy offering
2
ex
out
exclude
to remove or to make “out” something
excommunicate
officially exclude someone from participating within the sacraments and services of the Christian Church.
3
en
into, in
encircle
put in or on
endear
cause to be, make into
4
enni
year
centennial
a 100th anniversary.
perennial
forever
5
epi
on
epidermis
the layer of the skin on the dermis.
epitaph
writing on the tomb.
6
equ
equal
equivalence
the condition of being equal
equilateral
triangle with all sides equal
7
err
to wander or to make a mistake
error
a wandering from the correct answer
erratic
of wandering behavior or attitude instead of a normal or right behavior
8
extra
outside of.
extraterrestrial
outside of Earth.
extracellular
something situated or some activity taking place outside a cell or cells.
9
esce
becoming
obsolescent
becoming obsolete
convalesce
begin to be well
10
em
to put in or within
embrace
to put your arms around the person to show a sign of love or friendship
embark
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Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0185974538, 0.0334336236, -0.0118967975, -0.0269697886, 0.0295608956, 0.0178034045, 0.00370207732, -0.00557575328, -0.0119943125, -0.037445657, -0.010009191, 0.017928781, -0.0355789475, 0.00860915799, 0.0260642953, 0.00361849321, 0.0151147842, 0.0217179246, -0.00225851079, 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22 Mar, 2022 | GRE | List of words to enhance your vocabulary with root alphabet ‘G’
22 Mar, 2022
The list of 10 most common root words with root alphabet ‘G’ with their meaning and examples is as follows :
S.No
Root
Meaning
Examples
Meaning
1
gen
type, race, kind
gender
Belonging to one or another sex
genre
A particular kind in literature, music or art
2
gn/gno
know
ignore
knowingly refuse to take notice of
recognize
identify someone or something from having encountered them before; know again
3
grand
one generation more remote
grandfather
the father of one’s father or mother. (one generation more remote)
grandnephew
a son of one’s nephew or niece. (one generation more remote)
4
grat
pleasing
grateful
feeling or showing an appreciation for something done or received.
ingratiate
to bring oneself in favor
5
grav
heavy
grave
serious, weighty
Gravidate
To make heavy; impregnate
6
greg
group
congregrate
to group together
gregarious
living in flocks or loosely organized communities.
7
gest
carry/ bring
suggest
to bring an idea for consideration
ingest
to bring into the body, as food or liquid:
8
grad/gress
to step or go
egress
going out
progress
to step up
degrade
to step down
9
graph
to write
epigraph
to write on building, statue
autograph
a signature, especially that of a celebrity written as a memento for an admirer.
10
gyn
related to woman
misogyny
hatred of woman
gynecology
the branch of physiology and medicine which deals with the functions and diseases specific to women and girls, especially those affecting the reproductive system. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’/GRE | List of words to enhance your vocabulary with root alphabet ‘E’/GRE | List of words to enhance your vocabulary with root alphabet ‘G’ | 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13 Sep, 2021 | GRE | List of words to enhance your vocabulary with root alphabet ‘H’
13 Sep, 2021
The list of 10 most common words starting with root alphabet “H”
S.No.
Root
Meaning
Example
Meaning
1
Hypo
less than normal
hypothetical
based on or serving as a hypothesis.
2
Homo
Same
Homogeneous
o alike.
3
Hyst
exaggerated
Hysteria
uncontrollable emotion
4
Hind
situated at the back; posterior.
Hinder
Delay or obstruct
5
Hocus
deceive
Hocus-pocus
Meaningless talk
6
Hyper
hyperactive or unusually energetic.
Hyperbole
statements that are exaggerated on purpose
7
Huma
Human like characteristics
Humane
Showing concern and kindness, tender
8
Hulla
exhausted
Hullabaloo
Informal-an uproar,
9
Hetero
different
Heterogeneous
not same/can’t be mixed
10
Hein
evil
Heinous
wicked | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation 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alphabet ‘H’ | Artificial Intelligence – Boon or Bane, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0148962708, 0.0226117019, -0.0125484103, -0.0203722045, 0.0457724407, -0.0073217121, -0.0296480581, -0.00905190501, 0.0156331379, 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11 Jan, 2025 | ACID Properties in DBMS
11 Jan, 2025
A transaction is a single logical unit of work that interacts with the database, potentially modifying its content through read and write operations. To maintain database consistency both before and after a transaction, specific properties, known as ACID properties must be followed.
This article focuses on the ACID properties in DBMS, which are essential for ensuring data consistency, integrity, and reliability during database transactions.
Atomicity:
By this, we mean that either the entire transaction takes place at once or doesn’t happen at all. There is no midway i.e. transactions do not occur partially. Each transaction is considered as one unit and either runs to completion or is not executed at all. It involves the following two operations. — Abort : If a transaction aborts, changes made to the database are not visible. — Commit : If a transaction commits, changes made are visible. Atomicity is also known as the ‘All or nothing rule’.
Consider the following transaction T consisting of T1 and T2 : Transfer of 100 from account X to account Y .
Example
If the transaction fails after completion of T1 but before completion of T2 ( say, after write(X) but before write(Y) ), then the amount has been deducted from X but not added to Y . This results in an inconsistent database state. Therefore, the transaction must be executed in its entirety in order to ensure the correctness of the database state.
Consistency:
Consistency ensures that a database remains in a valid state before and after a transaction. It guarantees that any transaction will take the database from one consistent state to another, maintaining the rules and constraints defined for the data. Referring to the example above, The total amount before and after the transaction must be maintained. Total before T occurs = 500 + 200 = 700 . Total after T occurs = 400 + 300 = 700 . Therefore, the database is consistent . Inconsistency occurs in case T1 completes but T2 fails.
Isolation:
This property ensures that multiple transactions can occur concurrently without leading to the inconsistency of the database state. Transactions occur independently without interference. Changes occurring in a particular transaction will not be visible to any other transaction until that particular change in that transaction is written to memory or has been committed. This property ensures that when multiple transactions run at the same time, the result will be the same as if they were run one after another in a specific order.Let X = 500, Y = 500. Consider two transactions T and T”.
Suppose T has been executed till Read (Y) and then T’’ starts. As a result, interleaving of operations takes place due to which T’’ reads the correct value of X but the incorrect value of Y and sum computed by T’’: (X+Y = 50, 000+500=50, 500) . is thus not consistent with the sum at end of the transaction: T: (X+Y = 50, 000 + 450 = 50, 450) . This results in database inconsistency, due to a loss of 50 units. Hence, transactions must take place in isolation and changes should be visible only after they have been made to the main memory.
Durability:
This property ensures that once the transaction has completed execution, the updates and modifications to the database are stored in and written to disk and they persist even if a system failure occurs. These updates now become permanent and are stored in non-volatile memory. The effects of the transaction, thus, are never lost.
Some important points:
Property
Responsibility for maintaining properties
Atomicity
Transaction Manager
Consistency
Application programmer
Isolation
Concurrency Control Manager
Durability
Recovery Manager
The ACID properties, in totality, provide a mechanism to ensure the correctness and consistency of a database in a way such that each transaction is a group of operations that acts as a single unit, produces consistent results, acts in isolation from other operations, and updates that it makes are durably stored.
ACID properties are the four key characteristics that define the reliability and consistency of a transaction in a Database Management System (DBMS). The acronym ACID stands for Atomicity, Consistency, Isolation, and Durability. Here is a brief description of each of these properties:
Atomicity: Atomicity ensures that a transaction is treated as a single, indivisible unit of work. Either all the operations within the transaction are completed successfully, or none of them are. If any part of the transaction fails, the entire transaction is rolled back to its original state, ensuring data consistency and integrity.
Consistency: Consistency ensures that a transaction takes the database from one consistent state to another consistent state. The database is in a consistent state both before and after the transaction is executed. Constraints, such as unique keys and foreign keys, must be maintained to ensure data consistency.
Isolation: Isolation ensures that multiple transactions can execute concurrently without interfering with each other. Each transaction must be isolated from other transactions until it is completed. This isolation prevents dirty reads, non-repeatable reads, and phantom reads.
Durability: Durability ensures that once a transaction is committed, its changes are permanent and will survive any subsequent system failures. The transaction’s changes are saved to the database permanently, and even if the system crashes, the changes remain intact and can be recovered.
Overall, ACID properties provide a framework for ensuring data consistency, integrity, and reliability in DBMS. They ensure that transactions are executed in a reliable and consistent manner, even in the presence of system failures, network issues, or other problems. These properties make DBMS a reliable and efficient tool for managing data in modern organizations.
Advantages of ACID Properties in DBMS
Data Consistency: ACID properties ensure that the data remains consistent and accurate after any transaction execution.
Data Integrity: ACID properties maintain the integrity of the data by ensuring that any changes to the database are permanent and cannot be lost.
Concurrency Control: ACID properties help to manage multiple transactions occurring concurrently by preventing interference between them.
Recovery: ACID properties ensure that in case of any failure or crash, the system can recover the data up to the point of failure or crash.
Disadvantages of ACID Properties in DBMS
Performance: The ACID properties can cause a performance overhead in the system, as they require additional processing to ensure data consistency and integrity.
Scalability: The ACID properties may cause scalability issues in large distributed systems where multiple transactions occur concurrently.
Complexity: Implementing the ACID properties can increase the complexity of the system and require significant expertise and resources. Overall, the advantages of ACID properties in DBMS outweigh the disadvantages. They provide a reliable and consistent approach to data management, ensuring data integrity, accuracy, and reliability. However, in some cases, the overhead of implementing ACID properties can cause performance and scalability issues. Therefore, it’s important to balance the benefits of ACID properties against the specific needs and requirements of the system.
Conclusion
In conclusion, ACID properties involve four properties i.e. Atomicity, Consistency, Isolation and Durability that are responsible for data consistency, integrity and reliability in DBMS. Atomicity ensures that a transaction is rolled back if any part of it fails. Consistency ensures that the database remains consistent before and after the transaction. Isolation ensures that one transaction is not affected by the other. Durability ensures that the changes introduced by a particular transaction persist even after a system failure.
ACID Properties in DBMS – FAQs
What is the importance of ACID properties?
ACID properties ensure data consistency, integrity and reliability in DBMS. They manage multiple transactions that are occurring concurrently and help to recover data if any system failures occur. Thus, they play an important role.
How can we achieve Atomicity in transactions?
To achieve atomicity, a transaction should be treated as a single unit. If at any point of transaction, execution fails then the whole transaction should be rolled back by undoing the changes made.
What are some drawbacks of ACID Properties in DBMS?
ACID properties cause performance overhead because of additional processing required for maintaining data integrity and consistency. 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19 Sep, 2023 | File Organization in DBMS | Set 3
19 Sep, 2023
B+ Tree, as the name suggests, uses a tree-like structure to store records in a File. It uses the concept of Key indexing where the primary key is used to sort the records. For each primary key, an index value is generated and mapped with the record. An index of a record is the address of the record in the file.
B+ Tree is very similar to a binary search tree, with the only difference being that instead of just two children, it can have more than two. All the information is stored in a leaf node and the intermediate nodes act as a pointer to the leaf nodes. The information in leaf nodes always remains a sorted sequential linked list.
B+ Tree File Organization
In the above diagram, 56 is the root node which is also called the main node of the tree. The intermediate nodes here, just consist of the address of leaf nodes. They do not contain any actual records. Leaf nodes consist of the actual record. All leaf nodes are balanced.
Advantages of B+ Tree File Organization
Tree traversal is easier and faster.
Searching becomes easy as all records are stored only in leaf nodes and are sorted in sequentially linked lists.
There is no restriction on B+ tree size. It may grow/shrink as the size of the data increases/decreases.
Disadvantages of B+ Tree File Organization
Inefficient for static tables.
Cluster File Organization
In Cluster file organization, two or more related tables/records are stored within the same file known as clusters. These files will have two or more tables in the same data block and the key attributes which are used to map these tables together are stored only once.
Thus it lowers the cost of searching and retrieving various records in different files as they are now combined and kept in a single cluster. For example, we have two tables or relation Employee and Department. These tables are related to each other.
Cluster File Organization
Therefore this table is allowed to combine using a join operation and can be seen in a cluster file.
Cluster File Organization
If we have to insert, update or delete any record we can directly do so. Data is sorted based on the primary key or the key with which searching is done. The cluster key is the key with which the joining of the table is performed.
Types of Cluster File Organization
There are two ways to implement this method.
Indexed Clusters: In Indexed clustering, the records are grouped based on the cluster key and stored together. The above-mentioned example of the Employee and Department relationship is an example of an Indexed Cluster where the records are based on the Department ID.
Hash Clusters: This is very much similar to an indexed cluster with the only difference that instead of storing the records based on cluster key, we generate a hash key value and store the records with the same hash key value.
Advantages of Cluster File Organization
It is basically used when multiple tables have to be joined with the same joining condition.
It gives the best output when the cardinality is 1:m.
Disadvantages of Cluster File Organization
It gives a low performance in the case of a large database.
In the case of a 1:1 cardinality, it becomes ineffective.
ISAM (Indexed Sequential Access Method):
A combination of sequential and indexed methods. Data is stored sequentially, but an index is maintained for faster access. Think of it like having a bookmark in a book that guides you to specific pages.
Advantages of ISAM :
Faster retrieval compared to pure sequential methods.
Suitable for applications with a mix of sequential and random access.
Disadvantages of ISAM :
Index maintenance can add overhead in terms of storage and update operations.
Not as efficient as fully indexed methods for random access.
FAQs on File Organization in DBMS
Q.1: What do you mean by B+ Tree?
Answer:
B+ Tree is a self-balancing search tree where each node has more than two children and can hold multiple values.
Q.2: Where do we use B+ Tree?
Answer:
We use B+ Tree where we have to store a large amount of data that can’t be stored in the main memory.
Q.3: What are the advantages of the Cluster File Organization?
Answer:
Cluster File Organization shares available storage that remains underutilized if they come across separately. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief 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25 Jan, 2025 | Last Minute Notes – DBMS
25 Jan, 2025
Database Management System is an organized collection of interrelated data that helps in accessing data quickly, along with efficient insertion, and deletion of data into the DBMS. DBMS organizes data in the form of tables, schemas, records, etc.
DBMS over File System (Limitations of File System)
The file system has numerous issues, which were resolved with the help of DBMS, the issues with the file system are:
Physical Access Management: Users are responsible for managing the physical details required to access the database.File System Suitability: File systems are effective for handling small databases but lack efficiency for larger ones.Concurrency Issues: For large databases, the operating system struggles to manage concurrency effectively, leading to potential conflicts.Single-User Access: In a file system, only one user can access the entire dataset at a time, limiting scalability and multi-user functionality.Data access: In a file system, accessing data was difficult and insecure as well. Accessing data concurrently was not possible.No Backup and Recovery: There is no backup and recovery in the file system that can lead to data loss.ER-ModelER DiagramAn ER diagram is a model of a logical view of the database which is represented using the following components:
Entity: The entity is a real-world object, represented using a rectangular box.Strong Entity: A strong entity set has a primary key and all the tuples of the set can be identified using that primary keyWeak entity: When an entity does not have sufficient attributes to form a primary key. Weak entities are associated with another strong entity set also known as identifying an entity. A weak entity’s existence depends upon the existence of its identifying entity. The weak entity is represented using a double-lined or bold-lined rectangle. Attribute: Attribute is the properties or characteristics of the real-world object. It is represented using an oval. Key attribute: The attribute which determines each entity uniquely is known as the Key attribute. It is represented by an oval with an underlying line. Composite Attribute: An attribute that is composed of many other attributes. E.g. address is an attribute it is formed of other attributes like state, district, city, street, etc. It is represented using an oval comprises of many other ovals. Multivalued Attribute: An attribute that can have multiple values, like a mobile number. It is represented using a double-lined oval. Derived attribute: An attribute that can be derived from other attributes. E.g. Age is an attribute that can be derived from another attribute Data of Birth. It is represented using a dashed oval.Relationship: A relationship is an association between two or more entities. Entities are connected or related to each other and this relationship is represented using a diamond. Participation Constraint: It specifies the maximum or a minimum number of relationship instances in which any entity can participate. In simple words, participation means how an entity is linked to a relationship.Total Participation: Every entity in the entity set participates in at least one relationship in the relationship set.Example: In the “Manages” relationship between Emp (Employee) and Dept (Department): If every department must have a manager, then Dept has total participation in the “Manages” relationship.Partial Participation: Some entities in the entity set participate in the relationship, but not all. Example: In the same “Manages” relationship: If not all employees are managers, then Emp has partial participation in the “Manages” relationship.Cardinality in DBMSCardinality of relation expresses the maximum number of possible relationship occurrences for an entity participating in a relationship. Cardinality of a relationship can be defined as the number of times an entity of an entity set participates in a relationship set. Let’s suppose a binary relationship R between two entity sets A and B. The relationship must have one of the following mapping cardinalities:
One-to-One: When one entity of A is related to at most one entity of B, and vice-versa.One-to-Many: When one entity of A is related to one or more than one entity of B. Whereas B is associated with at most one entity in A. Many-to-One: When one entity of B is related to one or more than one entity of A. Whereas A is associated with at most one entity in B. Many-to-Many: Any number of entities of A is related to any number of entities of B, and vice-versa. The most commonly asked question in ER diagram is the minimum number of tables required for a given ER diagram. Generally, the following criteria are used:
CardinalityMinimum No. of tables1:1 cardinality with partial participation of both entities21:1 cardinality with a total participation of at least 1 entity11:n cardinality2m:n cardinality3If the relation is one-to-many or many-to-one then two or more relational tables can be combined.If the relation is many-to-many two tables cannot be combined. If the relation is one-to-one and there is total participation of one entity then that entity can be combined with a relational table. If there is total participation of both entities then one table can be obtained by combining one table and both entities of the relation. Note: This is a general observation. Special cases need to be taken care of. We may need an extra table if the attribute of a relationship can’t be moved to any entity side.
Specialization: It is a top-down approach in which one entity is divided/specialized into two or more sub-entities based on its characteristics.
Generalization: It is a bottom-up approach in which common properties of two or more sub-entities are combined/generalized to form one entity. It is exactly the reverse of Specialization. In this, two or lower level entities are generalized to one higher level entity.
Aggregation: Aggregation is an abstraction process through which relationships are represented as higher-level entity sets.
Read more about Introduction to ER Model.
Database DesignDatabase design Goals: The prime goal of designing a database is:
To have zero redundancy in the systemLoss-less joinDependency preservationOvercome all the shortcomings of conventional file systemAccording to E.F. Codd (Codd’s Rule in DBMS), “All the records of the table must be unique”.
Integrity Constraints Of RDBMSIntegrity constraints are rules that ensure data in a database is accurate and consistent. The main types are:
Entity Integrity: Each record must have a unique identifier (primary key).Referential Integrity: Relationships between tables must be consistent (using foreign keys).Domain Integrity: Data in each field must meet certain rules (e.g., correct type or range).User-Defined Integrity: Custom rules set by users for specific needs.Key Terms in Relational DatabasesTable: A collection of rows (records) in a database.Record: A single row in a table, containing data fields.Field: A column in a table, also called an attribute.Domain: The set of possible values a field can have.Key: A method for identifying specific records in a table.Index: A tool that speeds up database queries and searches.View: A virtual table created from data in actual tables.Tuple: Another word for a record or row in a table.Relation: Another term for a table.Cardinality: The total number of rows in a table.Degree: The number of columns in a table.Schema: The structure of a table, including its name, fields, and allowed values.Prime Attributes: Unique attributes used to identify rows, part of the primary or candidate key (e.g., student ID).Non-Prime Attributes: Attributes not part of any key, may have duplicates, and provide additional information (e.g., student’s first name, date of birth).Keys in databaseKeys of a relation: There are various types of keys in a relation which are: primary key, candidate key, super key, and alternate key. Let’s take a table called STUDENT
[email protected]@[email protected]. Primary Key
The primary key is the unique identifier for each record. In this case, student_id is the primary key because each student has a unique ID. Primary Key: student_id
2. Candidate Key
The minimal set of attributes that can determine a tuple uniquely. There can be more than 1 candidate key of a relation and its proper subset can’t determine tuple uniquely and it can’t be NULL. In this case, both student_id and email can uniquely identify a student. Candidate Keys: student_id, email, phone.
3. Super Key
A super key is any combination of columns that uniquely identifies a record. It can include extra attributes beyond what is necessary for uniqueness. A candidate key is always a super key but vice versa is not true. For example, student_id combined with phone or email would still uniquely identify a student. Super Keys: student_id, student_id + phone, email + phone etc.
4. Alternate Key
An alternate key is any candidate key that is not chosen as the primary key. In this case, since student_id is the primary key, email becomes the alternate key. Alternate Key: email, phone.
5. Foreign Key
Foreign Key is a set of attributes in a table that is used to refer to the primary key or alternative key of the same or another table.
Functional DependencyIt is a constraint that specifies the association/ relationship between a set of attributes. It is represented as A->B, where set A can determine the values of set B correctly. The A is known as the Determinant, and B is known as the Dependent.
Types of Functional Dependencies in DBMS:
Trivial Functional Dependency: A functional dependency where the right-hand side is a subset of the left-hand side.Example: A → A (any attribute depends on itself).Non-Trivial Functional Dependency: A functional dependency where the right-hand side is not a subset of the left-hand side.Example: Student_ID → Student_Name (Student_ID determines Student_Name).Multivalued Functional Dependency: When one attribute determines a set of values for another attribute, but not directly.Example: Student_ID →→ Student_Courses (A student may have multiple courses).Transitive Functional Dependency: When one attribute depends on another through a third attribute.Example: Student_ID → Student_Name and Student_Name → Department, so Student_ID → Department.All dependencies can relate to a Student table where Student_ID is the key.
Armstrong’s Axioms: It is a statement that is always considered true and used as a starting point for further arguments. Armstrong axiom is used to generate a closure set in a relational database.
Armstrong AxiomAttribute Closure(X+): All attributes of the set are functionally determined by X.
Prime Attribute: An attribute that is part of one candidate key. Non-prime Attribute: An attribute that is not a part of any candidate key. Example: If the relation R(ABCD) {A->B, B->C, C->D}, then the attribute closure of
A will be (A+)={ABCD} [A can determine B, B can determine C, C can determine D]B will be (B+)={BCD} [B can determine C, C can determine D]C will be (C+)={CD} [C can determine D] D will be (D+)={D} [D can determine itself]
Note: With the help of Attribute closure, we can easily determine the Superkey [The set of attributes whose closure contains all attributes of a relation] of a relation, So in the above example A is the superkey of the given relation. There can be more than one superkey in a relationship.
Example: If the relation R(ABCDE) {A->BC, CD->E, B->D, E->A}, then the attribute closure will be
A+= {ABCDE}B+= {BD}C+= {C}D+= {D}E+= {ABCDE}
Steps to Find a Candidate Key (Minimal Super Key)Identify all Super Keys:A super key is any set of attributes that can uniquely identify a record. Start by considering combinations of attributes that can act as super keys.Remove Redundant Attributes:Check if any attribute in the super key is unnecessary. If removing an attribute still allows the set to uniquely identify records, it is redundant. Continue removing until no more attributes can be removed without losing uniqueness.Minimal Super Key = Candidate Key:After eliminating unnecessary attributes, the resulting set is a Candidate Key.Equivalence sets of Functional DependencyIf two sets of a functional dependency are equivalent, i.e. if A+= B+. Every FD in A can be inferred from B, and every FD in B can be inferred from A, then A and B are functionally equivalent.
Minimal Cover or Canonical CoverA minimal cover is the smallest set of functional dependencies that preserves the same information.Steps:
Single attribute on the right-hand side: Break dependencies like AB → C into AB → B and AB → C.Remove unnecessary attributes: Eliminate attributes on the left-hand side if not needed.Remove redundant dependencies: If a dependency is implied by others, remove it.Example: Given: AB → C, A → B, BC → A, Minimal cover could be: A → B, B → C, BC → A.
Normalization: Normalization is used to eliminate the following anomalies:
Insertion AnomalyDeletion AnomalyUpdation AnomalyJoin AnomalyNormalization was introduced to achieve integrity in the database and make the database more maintainable.
Normal Forms1. First Normal Form: A relation is in first normal form if it does not contain any multi-valued or composite attribute. If the data is in 1NF then it will have high redundancy. First Normal Form (1NF) is considered the default state for any relational table.
2. Second Normal Form: A relation is in the second normal form if it is in the first normal form and if it does not contain any partial dependency.
Partial Dependency: A dependency is called partial dependency if any proper subset of candidate key determines non-prime (which are not part of candidate key) attribute.Let R be the relational schema and X, Y, A is the set of attributes. Suppose X is any candidate key, Y is a proper subset of candidate key, and A is a Non-prime attribute. Partial Dependency Y->A will be partial dependency iff, Y is a proper subset of candidate key, and A is a non-prime attribute.
Full Functional Dependency: If A and B are an attribute set of a relation, B is fully functional dependent on A, if B is functionally dependent on A but not on any proper subset of A.3. Third Normal Form: A relation is in the third normal form if it is in the second normal form and it does not contain any transitive dependency. For a relation to be in Third Normal Form, either LHS of FD should be super key or RHS should be the prime attribute.
4. Boyce-Codd Normal Form: A relation is in Boyce-Codd Normal Form if the LHS of every FD is super key. The relationship between Normal Forms can be represented as 1NF, 2NF, 3NF or BCNF.
Read more about Normal Forms.
Design Goal1NF2NF3NFBCNFZero RedundancyHigh redundancyLess than 1NFLess than 2NFNo redundancyLoss-less decompositionAlwaysAlwaysAlwaysAlwaysDependency preservationAlwaysAlwaysAlwaysSometimes Not possibleProperties of Decomposition:Loss-less Join Decomposition: There should not be the generation of any new tuple because of the decomposition. If [R1 ⋈ R2 ⋈ R3…….⋈ Rn] = R then loss-less join decomposition , If [R1 ⋈ R2 ⋈ R3 …….. ⋈ Rn] ⊃ R then lossy join decomposition.
Consider the relation R(A,B,C) with the functional dependencies: A→B , B→C . Decompose R into R1(A,B) and R2(B,C) :
To check for a lossless join, ensure the common attribute B is a candidate key in at least one of the decomposed relations:
In R1(A,B), A→B, so A is a key.In R2(B,C), B→C, so B is a key.When R1 and R2 are joined on B, no information is lost. Therefore, the decomposition is lossless.
Dependency Preserving Decomposition: There should not be the loss of any tuple because of the decomposition. Let R be a relation with Functional dependency F. After decomposition R is decomposed into R1, R2, R3……Rn with FD set F1, F2, F3……Fn respectively. If F1, F2, F3…..Fn ≣ F, then the decomposition is dependency preserving otherwise not.
Suppose we have a relation R(A,B,C) with the functional dependencies: A→B , B→C. If we decompose R into R1(A,B) and R2(B,C) :
R1 preserves the dependency A→B.R2 preserves the dependency B→C.Since all original functional dependencies are preserved in at least one of the decomposed relations, dependency preservation is achieved.
Data Retrieval (SQL, RA)Commands to Access Database: For efficient data retrieval, insertion, deletion, updation, etc. The commands in the Database are categorized into three categories, which are as follows:
DDL [Data Definition language]: It deals with how data should store in the database. DDL commands include CREATE, ALTER, DROP, COMMENT, and TRUNCATE DML [Data Manipulation language]: It deals with data manipulation like modifying, updating, deleting, etc. DML commands include SELECT, INSERT, DELETE, UPDATE, LOCK TABLE, MERGE, CALL, AND EXPLAIN PLAN.DCL [Data Control Language]: It acts as an access specifier, and includes GRANT, AND REVOKE.Query Language: Language using which any user can retrieve some data from the database.
Note: Relational model is a theoretical framework RDBMS is its implementation.
Relational Algebra: Procedural language with basic and extended operators.
Basic OperatorSemanticσ(Selection)Select rows based on a given conditionπ (Projection)Project some columnsX (Cross Product/ Cartesian Product)Cross product of relations, returns m*n rows where m and n are numbers of rows in R1 and R2 respectively.U (Union)Return those tuples which are either in R1 or R2. Maximum number of rows returned = m+n Minimum number of rows returned = max(m,n)– (Minus)R1-R2 returns those tuples which are in R1 but not in R2. Maximum number of rows returned = m Minimum number of rows returned = m-nρ(Rename)Renaming a relation to another relation.Extended OperatorSemantic (Intersection)Returns those tuples which are in both relation R1 and R2. Maximum number of rows returned = min(m,n) Minimum number of rows returned = 0⋈(Conditional Join)Selection from two or more tables based on some condition (Cross product followed by selection)⋈(Equi Join)It is a special case of conditional join when only an equality condition is applied between attributes.⋈(Natural Join)In natural join, equality condition on common attributes holds, and duplicate attributes are removed by default. Note: Natural Join is equivalent to the cross product of two relations have no attribute in common and the natural join of a relation R with itself will return R only.⟕(Left Outer Join)When applying join on two relations R and S, Left Outer Joins gives all tuples of R in the result set. The tuples of R which do not satisfy the join condition will have values as NULL for attributes of S.⟖(Right Outer Join)When applying join on two relations R and S, Right Outer Joins gives all tuples of S in the result set. The tuples of S which do not satisfy the join condition will have values as NULL for attributes of R.⟗(Full Outer Join)When applying join on two relations R and S, Full Outer Joins gives all tuples of S and all tuples of R in the result set. The tuples of S which do not satisfy the join condition will have values as NULL for attributes of R and vice versa./ (Division Operator)Division operator A/B will return those tuples in A which is associated with every tuple of B.Note: Attributes of B should be a proper subset of attributes of A. The attributes in A/B will be Attributes of A- Attribute of B.Read more about Relational Algebra.
Relational Calculus: Relational calculus is a non-procedural query language. It explains what to do but not how to do it. It is of two types:
Tuple Relational Calculus: The tuple relational calculus is based on specifying the number of tuple variables. Each variable usually ranges over a particular database relation. It is of the form {t| cond(t)} where t is the tuple variable and cond(t) is a conditional expression involving t. The result of such query is the set of tuples of t that satisfy cond(t). Domain Relational Calculus: It is a non-procedural query language equivalent in power to Tuple Relational Calculus. Domain Relational Calculus provides only the description of the query but it does not provide the methods to solve it{x1, x2, ……, xn | cond (x1, x2, ……., xn, xn+1, xn+2, …….., xn+m)}where, x1, x2, ……., xn, xn+1, xn+2, …….., xn+m are domain variables ranging over domains, and cond is a condition. SQL: Structured Query Language, lets you access or modify databases. SQL can execute queries, retrieve data, insert records, update records, delete records, create a new database, create new tables, create views, and set permissions on tables, procedures, or views.
SQL Commands:
OperatorMeaningSELECTSelects columns from a relation or set of relations. It defines WHAT is to be returned. Note: As opposed to Relational Algebra, it may give duplicate tuples for the repeated values of an attribute.FROMFROM is used to define the Table(s) or View(s) used by the SELECT or WHERE statementsWHEREWHERE is used to define what records are to be included in the query. It uses conditional operators. EXISTSEXISTS is used to check whether the result of a correlated nested query is empty (contains no tuples) or not.GROUP BYGROUP BY is used to group the tuples based on some attribute or set of attributes like counting the number of students GROUP BY the department.ORDER BYORDER BY is used to sort the fetched data in either ascending or descending according to one or more columns.Aggregate functionsFind the aggregated value of an attribute. Used mostly with GROUP BY. e.g.; count, sum, min max. select count(*) from the student group by dept_idNote: we can select only those columns which are part of GROUP BY.Nested QueriesWhen one query is a part of another query. UPDATEIt is used to update records in a table.DELETEIt is used to delete rows in a table.LIKELIKE operator is used with the WHERE clause to search a specified pattern in a column.IN IN operator is used to specify multiple values in the WHERE clause.BETWEENIt selects values within a range. AliasesIt is used to temporarily rename a table or a column heading. HAVINGThe HAVING clause was added because the WHERE keyword could be used with aggregate functions. Read more about SQL
SQL Subqueries: A subquery in SQL is a query nested inside another query to provide intermediate results for the outer query.
Execution FlowFROM –> Cross-product of relations (tables)
↓
WHERE –> Apply selection condition (σ) to filter rows
↓
GROUP BY –> Group rows based on specified column(s)
↓
HAVING –> Filter groups based on aggregate conditions
↓
SELECT –> Choose and project the required columns
↓
DISTINCT –> Remove duplicate rows (if specified)
↓
ORDER BY –> Sort the result set (ascending/descending)
File StructureFile organization: It is the logical relation between records and it defines how file records are mapped into disk blocks(memory). A database is a collection of files, each file is a collection of records, and each record contains a sequence of fields. The blocking Factor is the average number of records per block.
Strategies for storing files of records in block:
Spanned Strategy: It allows a partial part of the record to be stored in the block. It is suitable for variable-length records. No wastage of memory in spanned strategy but block access time gets increases. Unspanned Strategy: Data cannot be stored partially, the whole block will be occupied, this can lead to internal fragmentation and wastage of memory but block access time is reduced. This is suitable for fixed-length records. File organizations is of following types:
Sequential File OrganizationHeap File Organization Hash File Organization B+ Tree File Organization Clustered File Organization Sequential File: In this method, files are stored in sequential order one after another.
Blocking factor: [Tex]\left \lfloor \frac{Block\ Size}{Record\ Size} \right \rfloor
[/Tex]Number of record blocks: [Tex]\left \lceil \frac{Total\ number\ of\ records}{Blocking\ factor} \right \rceil
[/Tex]Average number of blocks accessed by linear search: [Tex]\left \lfloor \frac{number\ of\ record\ blocks}{2} \right \rfloor
[/Tex]Average number of blocks accessed by binary search: [Tex]\left \lfloor { log_2 \ number\ of\ record\ blocks} \right \rfloor
[/Tex]Index File:
Index blocking factor: [Tex]\left \lfloor \frac{number\ of\ record\ blocks \ +\ 1}{2} \right \rfloor
[/Tex]First level index block: [Tex]\left \lfloor \frac{number\ of\ record\ blocks}{index\ blocking\ factor} \right \rfloor
[/Tex]Number of block accesses: [Tex]\left \lfloor { log_2 \ (first\ level\ index\ blocks)} \right \rfloor + 1
[/Tex]Indexing Type:1. Single level IndexPrimary Index(Sparse): A primary index is an ordered file(ordered with key field), records of fixed length with two fields. The first field is the same as the primary key of the data file and the second field is a pointer to a data block, where the key is available. In Sparse indexing, for a set of database records there exists a single entry in the index file.Number of index file entries ≤ Number of database records.Secondary Index (Dense): Secondary index provides secondary means of accessing a file for which primary access already exists. In Dense indexing, for every database record, there exists an entry in the index file. The index blocking factor is the same for all indexes. Number of database records = Number of entries in the index fileNumber of block accesses= [Tex]\left \lceil{log_2\ ( single\ level\ index\ block)} \right \rceil + 1
[/Tex]Clustered Index(Sparse): A clustering index is created on a data file whose records are physically ordered on a non-key field (called a Clustering field). Almost one clustering index is possible. Single-level index blocks= [Tex]\left \lceil \frac{Number\ of\ distinct\ values\ over\ non\ key\ field}{Index\ blocking\ factor} \right \rceil + 1
[/Tex]Number of block accesses= [Tex]\left \lceil{log_2\ ( single\ level\ index\ block)} \right \rceil + 1
[/Tex]2. Multilevel IndexIndexed sequential access method: Second level index is always sparse. Level 1 = “first-level index blocks” computed by indexLevel 2 = [Tex]\left \lceil \frac{Number\ of\ blocks\ in\ level\ (1)}{index\ blocking\ factor} \right \rceil
[/Tex]Level n = [Tex]\left \lceil \frac{Number\ of\ blocks\ in\ level\ (n-1)}{index\ blocking\ factor} \right \rceil =1
[/Tex]Number of blocks = [Tex]\sum_{i=1}^{n} (Number\ of\ blocks\ in\ level\ i)
[/Tex]Number of block access = n+1B-Tree: Also known as Baye’s or balanced Search Tree. At every level, we have Key and Data pointers, and data pointer points either block or record. Root node: B-tree can have children between 2 and p, where p is the Order of the tree.Internal Node: [Tex]\left \lceil \frac {n}{2} \right \rceil
[/Tex] to n children.Leaf nodes all are at the same level.Block size = p × (size of block pointer) + (p-1)× (Size of key field + size of record pointer)Minimum number of nodes = [Tex]1 + (\frac{2[(\frac{p}{2})^h -1]}{(\frac{p}{2}) -2})
[/Tex]Maximum number of nodes = [Tex]\frac{p^{h+1}-1}{p-1}[/Tex]Minimum height = [Tex]\left ( \left \lceil log_p \ l \right \rceil \right )[/Tex] l is the number of leavesMaximum height = [Tex]\left \lfloor 1 +log_{\frac {p}{2}} \frac{l}{2} \right \rfloor[/Tex]B+ Tree: It is the same as B-tree. All the records are available at the leaf (last) level. B+ tree allows both sequential and random access whereas in B-tree only random access was allowed. Each leaf node has one block pointer and all the leaf nodes are connected to the next leaf node using a block pointer.Order of non-leaf node= [p × size of block pointer] + [(p-1) × size of key field] <= Block size.Order of Leaf node= [(pleaf -1) × (size of key field + size of record pointer) + p × (size of block pointer) <= Block size]Transaction and Concurrency ControlA transaction is a unit of instruction or set of instructions that performs a logical unit of work. Transaction processes are always atomic in nature either they will execute completely or do not execute.
Transaction Properties:Atomicity: Either execute all operations or none of them. It is managed by the transaction Management Component.Consistency: Database must be consistent before and after the execution of the transaction. If atomicity, isolation, and durability are implemented accurately, consistency will be achieved automatically. Isolation: In concurrent transactions, the execution of one transaction must not affect the execution of another transaction. It is managed by the Concurrency Control component. Durability: After the commit operation, the changes should be durable and persist always in the database. It is managed by the Recovery Management component. Read more about Transaction Properties.
Transaction States:A transaction in DBMS goes through various states during its execution to ensure consistency and reliability in the database.
States of Transactions:
Active:Transaction is executing its operations.Partially Committed:Transaction has completed its final step but is yet to be made permanent.Committed:All changes are successfully saved in the database.Failed:An error or issue prevents the transaction from completing.Aborted:Changes are rolled back, and the transaction is terminated.Flow: Active → Partially Committed → Committed Active → Failed → Aborted
Read more about Transaction States.
Schedule: Sequences in which instructions of the concurrent transactions get executed. Schedules are of two types:
Serial Schedule: Transactions execute one by one, another transaction will begin after the commit of the first transaction. It is inconsistent and the system’s efficiency is so poor due to no concurrency. The number of possible serial schedules with n transactions = n!Non-Serial Schedule: When two or more transactions can execute simultaneously. This may lead to inconsistency, but have better throughput and less response time. The number of possible non-serial schedules with n transactions = Total Schedule – Serial Schedule[Tex](\frac {n_1 + n_2 +n_3+ ……..+n_n}{n_1!\ n_2!\ n_3!…….n_n!} )-n!
[/Tex]Serializability: A schedule is said to be serializable if it is equivalent to a serial schedule. It is categorized into two categories: Conflict Serializability, and View Serializability.
Conflict Serializability: A schedule will be conflict serializable if it can be transformed into a serial schedule by swapping non-conflicting operations. It is a polynomial-time problem.
Conflicting operations: Two operations will be conflicting if They belong to different transactions.They are working on the same data item.At least one of them is the Write operation.View Serializability: A schedule will be view serializable if it is view equivalent to a serial schedule. It is an NP-Complete Problem.
Check whether it is conflict serializable or not, if Yes then it is view serializable.If the schedule does not conflict with serializable then check whether it has blind write or not. If it does not have blind write then it is not view serializable. [To be view serializable a schedule must have a blind write]If the schedule has blind write, Now check whether the schedule is view-equivalent to any other serial schedule. Now, draw a precedence graph using given dependencies. If no cycle/loop exists in the graph, then the schedule would be a View-Serializable otherwise not.Types of Schedule based recoverability:
Irrecoverable Schedule: A transaction is impossible to roll back once the commit operation is done. Recoverable Schedule: A schedule is recoverable if a transaction Ti reads a data item previously written by Transaction Tj, the commit operation Tj appears before the commit operation of Ti. Cascadeless Recoverable Schedule: Cascadeless Schedule avoids cascading aborts/rollbacks (ACA). Schedules in which transactions read values only after all transactions whose changes they are going to read commit are called cascadeless schedules. Avoids that a single transaction abort leads to a series of transaction rollbacks.Cascading rollback: When failure of a single transaction leads to a series of transaction rollbacks.Strict Recoverable Schedule: If there is no read or write in the schedule before the commit, then such schedule are known as a Strict recoverable schedule. Concurrency Control with Locks:
To achieve consistency, isolation is the most important concept. Isolation can be achieved using locking very easily. A schedule acquires a lock prior to accessing the transaction and the lock is released when the transaction is completed. A locking protocol is a set of rules followed by all transactions while requesting and releasing locks. Locking protocols restrict the set of possible schedules.
Lock Types:
Binary Locks
It is in two states: Locked(1) or Unlocked(0)When an object is locked it is unavailable to other objects.When an object is unlocked then it is open to transactions.An object is unlocked when the transaction is unlocked. Every transaction locks a data item before use and unlocks/releases it after use.Issues with binary locks: Irrecoverability, Deadlock, and Low concurrency.Shared/Exclusive Locks:
Shared (S Mode): It is denoted by lock-S(Q), the transaction can perform a read operation, and any other transaction can also obtain the same lock on same data item at the same time and can also perform a read operation only. Exclusive (X Mode): It is denoted by lock- X(Q), the transaction can perform both read and write operations, any other transaction can not obtain either shared/exclusive lock.Two-Phase Locking: This protocol requires that each transaction in a schedule will be two phases: i.e. Growing phase and the shrinking phase.
In the growing phase, transactions can only obtain locks but cannot release any lock. In the shrinking phase, transactions can only release locks but can not obtain any lock.The transaction can perform read/write operations in both the growing as well as in shrinking phase.Rules for 2-PL:Two transactions cannot have conflicting locks.No unlock operation can precede a lock operation in the same transaction.No data are affected until all locks are obtained.Basic 2-PL:Rule: A transaction must acquire a lock before accessing a data item and release it after use.Phases:Growing Phase: Locks are acquired but not released.Shrinking Phase: Locks are released but no new locks are acquired.Ensures: Serializability but not deadlock-free.Strict 2-PL:Rule: A transaction holds all exclusive (write) locks until it commits or aborts.Phases: Growing Phase: Locks are acquired.Release Phase: Locks are released only after commit/abort.Ensures: Serializability and prevents cascading rollbacks.Rigorous 2-PL:Rule: A transaction holds all locks (read and write) until it commits or aborts.Phases:Growing Phase: Locks are acquired.Release Phase: All locks are released only after commit/abort. Ensures: Serializability and strict schedules (stronger than Strict 2PL).Conservative 2-PL:Rule: A transaction acquires all required locks upfront before executing.Key Feature: If all locks cannot be acquired at the start, the transaction waits and does not proceed.Prevents: Deadlocks completely.Trade-off: May cause delays if locks are unavailable.Timestamp Ordering Protocol: Each transaction gets a unique timestamp when it starts.
Rules:
Read Rule: A transaction can read an item only if its timestamp ≥ last write timestamp of the item.Write Rule: A transaction can write an item only if its timestamp ≥ last read and last write timestamps of the item.Ensures serializability by executing transactions in timestamp order.
Conflict Resolution: Abort and restart conflicting transactions with a new timestamp.
Thomas Write Rule: A protocol in timestamp ordering where outdated write operations (with a timestamp older than the current write timestamp of a data item) are ignored instead of aborting the transaction.
Rule: Ignore a write if the transaction’s timestamp (TS) is older than the data’s write timestamp (WTS).Logic: The outdated write is discarded because a newer write has already been performed.Prevents: Unnecessary aborts of transactions.Allows: Greater concurrency compared to basic timestamp ordering.Used in timestamp ordering protocols to optimize write operations.
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15 Jun, 2024 | Commonly asked DBMS interview questions
15 Jun, 2024
1. What are the advantages of DBMS over traditional file-based systems?
Database management systems were developed to handle the following difficulties of typical File-processing systems supported by conventional operating systems. 1. Data redundancy and inconsistency 2. Difficulty in accessing data 3. Data isolation – multiple files and formats 4. Integrity problems 5. Atomicity of updates 6. Concurrent access by multiple users 7. Security problems
2. What are super, primary, candidate, and foreign keys? A super key is a set of attributes of a relation schema upon which all attributes of the schema are functionally dependent. No two rows can have the same value of super key attributes. A Candidate key is a minimal superkey, i.e., no proper subset of Candidate key attributes can be a superkey. A Primary Key is one of the candidate keys. One of the candidate keys is selected as most important and becomes the primary key. There cannot be more than one primary key in a table..A Foreign key is a field (or collection of fields) in one table that uniquely identifies a row of another table.
3. What is the difference between primary key and unique constraints? The primary key cannot have NULL value, the unique constraints can have NULL values. There is only one primary key in a table, but there can be multiple unique constrains.
4.What is database normalization? It is a process of analyzing the given relation schemas based on their functional dependencies and primary keys to achieve the following desirable properties: 1. Minimizing Redundancy 2. Minimizing the Insertion, Deletion, And Update Anomalies Relation schemas that do not meet the properties are decomposed into smaller relation schemas that could meet desirable properties.
5. Why is the use of DBMS recommended? Explain by listing some of its major advantages?
Some of the major advantages of DBMS are as follows:
Controlled Redundancy: DBMS supports a mechanism to control the redundancy of data inside the database by integrating all the data into a single database and as data is stored in only one place, the duplicity of data does not happen.
Data Sharing: Sharing of data among multiple users simultaneously can also be done in DBMS as the same database will be shared among all the users and by different application programs.
Backup and Recovery Facility: DBMS minimizes the pain of creating the backup of data again and again by providing a feature of ‘backup and recovery’ which automatically creates the data backup and restores the data whenever required.
Enforcement of Integrity Constraints: Integrity Constraints are very important to be enforced on the data so that the refined data after putting some constraints are stored in the database and this is followed by DBMS.
Independence of Data: It simply means that you can change the structure of the data without affecting the structure of any of the application programs.
6. What are the differences between DDL, DML, and DCL in SQL? Following are some details of three :DDL stands for Data Definition Language. SQL queries like CREATE, ALTER, DROP, TRUNCATE and RENAME come under this. DML stands for Data Manipulation Language. SQL queries like SELECT, INSERT, DELETE and UPDATE come under this. DCL stands for Data Control Language. SQL queries like GRANT and REVOKE come under this.
7. What is the difference between having and where clause? HAVING is used to specify a condition for a group or an aggregate function used in a select statement. The WHERE clause selects before grouping. The HAVING clause selects rows after grouping. Unlike the HAVING clause, the WHERE clause cannot contain aggregate functions. (See this for examples). See Having vs Where Clause? for more details
8.How to print duplicate rows in a table? See https://www.geeksforgeeks.org/how-to-print-duplicate-rows-in-a-table/
9. What is Join? An SQL Join is used to combine data from two or more tables, based on a common field between them. For example, consider the following two tables.
Table – Student Table
EnrollNo
StudentName
Address
1000
geek1
geeksquiz1
1001
geek2
geeksquiz2
1002
geek3
geeksquiz3
Table – StudentCourse Table
CourseID
EnrollNo
1
1000
2
1000
3
1000
1
1002
2
1003
Following is a join query that shows the names of students enrolled in different courseIDs.
SELECT StudentCourse.CourseID, Student.StudentName FROM StudentCourse INNER JOIN Student ON StudentCourse.EnrollNo = Student.EnrollNo ORDER BY StudentCourse.CourseID;
The above query would produce the following result.
CourseID
StudentName
1
geek1
1
geek3
2
geek1
3
geek1
9. What is Identity? Identity (or AutoNumber) is a column that automatically generates numeric values. A start and increment value can be set, but most DBA leave these at 1. A GUID column also generates numbers; the value of this cannot be controlled. Identity/GUID columns do not need to be indexed.
10.What is a view in SQL? How to create a view? A view is a virtual table based on the result-set of an SQL statement. We can create it using create view syntax.
CREATE VIEW view_name ASSELECT column_name(s)FROM table_nameWHERE condition
11.What are the uses of view? 1. Views can represent a subset of the data contained in a table; consequently, a view can limit the degree of exposure of the underlying tables to the outer world: a given user may have permission to query the view, while denied access to the rest of the base table. 2. Views can join and simplify multiple tables into a single virtual table.3. Views can act as aggregated tables, where the database engine aggregates data (sum, average, etc.) and presents the calculated results as part of the data.4. Views can hide the complexity of data.5. Views take very little space to store; the database contains only the definition of a view, not a copy of all the data which it presents. 6. Depending on the SQL engine used, views can provide extra security.
12. What is a Trigger? A Trigger is a code associated with insert, update or delete operations. The code is executed automatically whenever the associated query is executed on a table. Triggers can be useful to maintain integrity in the database.
13. What is a stored procedure? A stored procedure is like a function that contains a set of operations compiled together. It contains a set of operations that are commonly used in an application to do some common database tasks.
14. What is the difference between Trigger and Stored Procedure? Unlike Stored Procedures, Triggers cannot be called directly. They can only be associated with queries.
15. What is a transaction? What are ACID properties? A Database Transaction is a set of database operations that must be treated as a whole, which means either all operations are executed or none of them. An example can be a bank transaction from one account to another account. Either both debit and credit operations must be executed or none of them. ACID (Atomicity, Consistency, Isolation, Durability) is a set of properties that guarantee that database transactions are processed reliably.
16. What are indexes? A database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and the use of more storage space to maintain the extra copy of data. Data can be stored only in one order on a disk. To support faster access according to different values, faster search like binary search for different values is desired, For this purpose, indexes are created on tables. These indexes need extra space on the disk, but they allow faster search according to different frequently searched values.
17. What are clustered and non-clustered Indexes? Clustered indexes are the index according to which data is physically stored on a disk. Therefore, only one clustered index can be created on a given database table. Non-clustered indexes don’t define the physical ordering of data, but logical ordering. Typically, a tree is created whose leaf point to disk records. B-Tree or B+ tree are used for this purpose.
18. What is Denormalization?
Denormalization is a database optimization technique in which we add redundant data to one or more tables.
19. What is CLAUSE in SQL?
A clause in SQL is a part of a query that lets you filter or customize how you want your data to be queried to you.
20. What is a Live Lock?
Livelock situation can be defined as when two or more processes continually repeat the same interaction in response to changes in the other processes without doing any useful work These processes are not in the waiting state, and they are running concurrently. This is different from a deadlock because in a deadlock all processes are in the waiting state.
21. What is QBE?
Query-by-example represents a visual/graphical approach for accessing information in a database through the use of query templates called skeleton tables. It is used by entering example values directly into a query template to represent what is to be achieved. QBE is used by many database systems for personal computers. QBE is a very powerful facility that gives the user the capability to access the information a user wants without the knowledge of any programming language. Queries in QBE are expressed by skeleton tables. QBE has two distinct features:
QBE has the two-dimensional syntax: Queries look like tables.
22. Why are cursors necessary in embedded SQL?
A cursor is an object used to store the output of a query for row-by-row processing by the application programs. SQL statements operate on a set of data and return a set of data. On other hand, host language programs operate on a row at a time. The cursors are used to navigate through a set of rows returned by an embedded SQL SELECT statement. A cursor can be compared to a pointer.
23. What is the purpose of normalization in DBMS?
Database normalization is the process of organizing the attributes of the database to reduce or eliminate data redundancy (having the same data but at different places).
Purpose of normalization:
It is used to remove duplicate data and database anomalies from the relational table.
Normalization helps to reduce redundancy and complexity by examining new data types used in the table.
It is helpful to divide the large database table into smaller tables and link them using relationships.
It avoids duplicate data or no repeating groups into a table.
It reduces the chances for anomalies to occur in a database.
24. What is the difference between a database schema and a database state?
The collection of information stored in a database at a particular moment in time is called database state while the overall design of the database is called the database schema.
25. What is the purpose of SQL?
SQL stands for Structured Query Language whose main purpose is to interact with the relational databases in the form of inserting, deleting and updating/modifying the data in the database.
26. Explain the concepts of a Primary key and Foreign Key.
Primary Key is used to uniquely identify the records in a database table while Foreign Key is mainly used to link two or more tables together, as this is a particular field(s) in one of the database tables which are the primary key of some other table.
Example: There are 2 tables – Employee and Department. Both have one common field/column as ‘ID’ where ID is the primary key of the Employee table while this is the foreign key for the Department table.
27.What are the main differences between Primary key and Unique Key?
Given below are few differences:
The main difference between the Primary key and the Unique key is that the Primary key can never have a null value while the Unique key may consist of a null value.
In each table, there can be only one primary key while there can be more than one unique key in a table.
28. What is the concept of sub-query in terms of SQL?
Sub-query is basically the query that is included inside some other query and can also be called an inner query which is found inside the outer query.
29. What is the use of the DROP command and what are the differences between DROP, TRUNCATE and DELETE commands?
DROP command is a DDL command which is used to drop/delete the existing table, database, index, or view from the database.
The major difference between DROP, TRUNCATE and DELETE commands are:
DROP and TRUNCATE commands are the DDL commands which are used to delete tables from the database.
And when we make use of a DROP command, the tables get deleted permanently all the privileges and indexes that are related to the table also get deleted. This operation cannot be rolled back and so should be used only when necessary.
However in case of TRUNCATE, only the data stored in a table is deleted and the structure of the table is preserved and you can re-insert data by the use of “INSERT INTO clause”. It can be rolled back until the commit has been made.
DELETE command, on the other hand, is a DML Command which is used to delete rows from the table and this can be rolled back, however its considered slower than truncate. Using the delete command, we can delete 1 or more specific rows from the table.
30. What is the main difference between UNION and UNION ALL?
UNION and UNION ALL are used to join the data from 2 or more tables but UNION removes duplicate rows and picks the rows which are distinct after combining the data from the tables whereas UNION ALL does not remove the duplicate rows, it just picks all the data from the tables.
31. What is Correlated Subquery in DBMS?
A Subquery is also known as a nested query i.e. a query written inside some query. When a Subquery is executed for each of the rows of the outer query then it is termed as a Correlated Subquery.
An example of Non-Correlated Subquery is:
SELECT * from EMP WHERE ‘RIYA’ IN (SELECT Name from DEPT WHERE EMP.EMPID=DEPT.EMPID);
Here, the inner query is not executed for each of the rows of the outer query.
32. Explain Entity, Entity Type, and Entity Set in DBMS?
The entity is an object, place, or thing which has its independent existence in the real world and about which data can be stored in a database. For Example, any person, book, etc.
Entity Type is a collection of entities that have the same attributes. For Example, the STUDENT table contains rows in which each row is an entity holding the attributes like name, age, and id of the students, hence STUDENT is an Entity Type that holds the entities having the same attributes.
Entity Set is a collection of entities of the same type. For Example, A collection of the employees of a firm.
33. What are the different levels of abstraction in the DBMS?
There are 3 levels of data abstraction in the DBMS.
They include:
Physical Level: This is the lowest level of the data abstraction which states how the data is stored in the database.
Logical Level: This is the next level of the data abstraction which states the type of the data and the relationship among the data that is stored in the database.
View Level: This is the highest level in the data abstraction which shows/states only a part of the database.
34 . What integrity rules exist in the DBMS?
There are two major integrity rules that exist in the DBMS.
Entity Integrity: This states a very important rule that the value of a Primary key can never have a NULL value.
Referential Integrity: This rule is related to the Foreign key which states that either the value of a Foreign key is a NULL value or it should be the primary key of any other relation.
35. What is E-R model in the DBMS?
E-R model is known as an Entity-Relationship model in the DBMS which is based on the concept of the Entities and the relationship that exists among these entities.
36. What is a functional dependency in the DBMS?
This is basically a constraint that is useful in describing the relationship among the different attributes in a relation.
Example: If there is some relation ‘R1’ which has 2 attributes as Y and Z then the functional dependency among these 2 attributes can be shown as Y->Z which states that Z is functionally dependent on Y.
37. What is 1NF in the DBMS?
1NF is known as the First Normal Form.
This is the easiest form of the normalization process which states that the domain of an attribute should have only atomic values. The objective of this is to remove the duplicate columns that are present in the table.
38. What is 2NF in the DBMS?
2NF is the Second Normal Form.
Any table is said to have in the 2NF if it satisfies the following 2 conditions:
A table is in the 1NF.
Each non-prime attribute of a table is said to be functionally dependent in totality on the primary key.
39. What is 3NF in the DBMS?
3NF is the Third Normal Form.
Any table is said to have in the 3NF if it satisfies the following 2 conditions:
A table is in the 2NF.
Each non-prime attribute of a table is said to be non-transitively dependent on every key of the table.
40. What is BCNF in the DBMS?
BCNF is the Boyce Codd Normal Form which is stricter than the 3NF.
Any table is said to have in the BCNF if it satisfies the following 2 conditions:
A table is in the 3NF.
For each of the functional dependencies X->Y that exists, X is the super key of a table.
41. What is a CLAUSE in terms of SQL?
This is used with the SQL queries to fetch specific data as per the requirements on the basis of the conditions that are put in the SQL. This is very helpful in picking the selective records from the complete set of records.
For Example, There is a query that has a WHERE condition or the query with the HAVING clause.
42.How can you get the alternate records from the table in the SQL?
If you want to fetch the odd numbers then the following query can be used:
SELECT EmpId from (SELECT rowno,EmpId from Emp) WHERE mod(rowno,2)=1;
If you want to fetch the even numbers, then the following query can be used:
SELECT EmpId from (SELECT rowno,EmpId from Emp) WHERE mod(rowno,2)=0;
43. How is the pattern matching done in the SQL?
Answer: With the help of the LIKE operator, pattern matching is possible in the SQL.’%’ is used with the LIKE operator when it matches with the 0 or more characters, and ‘_’ is used to match the one particular character.
Example:
SELECT * from Emp WHERE name like ‘b%’;
SELECT * from Emp WHERE name like ‘hans_’;
44. What is a join in the SQL?
A Join is one of the SQL statements which is used to join the data or the rows from 2 or more tables on the basis of a common field/column among them.
45. What are the different types of joins in SQL?
There are 4 types of SQL Joins:
Inner Join: This type of join is used to fetch the data among the tables which are common in both tables.
Left Join: This returns all the rows from the table which is on the left side of the join but only the matching rows from the table which is on the right side of the join.
Right Join: This returns all the rows from the table which is on the right side of the join but only the matching rows from the table which is on the left side of the join.
Full Join: This returns the rows from all the tables on which the join condition has been put and the rows which do not match hold null values.
46. Explain the Stored Procedure.
A Stored Procedure is a group of SQL statements in the form of a function that has some unique name and is stored in relational database management systems(RDBMS) and can be accessed whenever required.
47. What is RDBMS?
RDBMS is the Relational Database Management System which contains data in the form of the tables and data is accessed on the basis of the common fields among the tables.
48. What are the different types of relationships in the DBMS?
A Relationship in DBMS depicts an association between the tables.
Different types of relationships are:
One-to-One: This basically states that there should be a one-to-one relationship between the tables i.e. there should be one record in both the tables.
One-to-Many: This states that there can be many relationships for one i.e. a primary key table hold only one record which can have many, one, or none records in the related table.
Many-to-Many: This states that both the tables can be related to many other tables.
49. What do you mean by Entity type extension?
Compilation of similar entity types into one particular type which is grouped together as an entity set is known as entity type extension.
50. What is conceptual design in dbms?
Conceptual design is the first stage in the database design process. The goal at this stage is to design a database that is independent of database software and physical details. The output of this process is a conceptual data model that describes the main data entities, attributes, relationships, and constraints of a given problem domain.
51. Differentiate between logical database design and physical database design. Show how this separation leads to data independence.
Parameters
Logical Database Design
Physical Database Design
Task
Maps or transforms the conceptual schema (or an ER schema) from the high-level data model into a relational database schema.
The specifications for the stored database in terms of physical storage structures, record placement, and indexes are designed.
Choice of criteria
The mapping can proceed in two stages:
System-independent mapping but data model-dependent
Tailoring the schemas to a specific DBMS
The following criteria are often used to guide the choice of physical database design options:
Response Time
Space Utilization
Transaction Throughput
Result
DDL statements in the language of the chosen DBMS that specify the conceptual and external level schemas of the database system. But if the DDL statements include some physical design parameters, a complete DDL specification must wait until after the physical database design phase is completed.
An initial determination of storage structures and the access paths for the database files. This corresponds to defining the internal schema in terms of Data Storage Definition Language.
The database design is divided into several phases. The logical database design and physical database design are two of them. This separation is generally based on the concept of the three-level architecture of DBMS, which provides data independence. Therefore, we can say that this separation leads to data independence because the output of the logical database design is the conceptual and external level schemas of the database system which is independent of the output of the physical database design that is an internal schema.
52. What are temporary tables? When are they useful? Temporary tables exist solely for a particular session, or whose data persists for the duration of the transaction. The temporary tables are generally used to support specialized rollups or specific application processing requirements. Unlike a permanent table, space is not allocated to a temporary table when it is created. Space will be dynamically allocated for the table as rows are inserted. The CREATE GLOBAL TEMPORARY TABLE command is used to create a temporary table in Oracle.
53. Explain different types of failures that occur in the Oracle database.Types of Failures – In the Oracle database following types of failures can occur:
Statement Failure·
Bad data type
Insufficient space
Insufficient Privileges (e.g., object privileges to a role)
User Process Failure
The user performed an abnormal disconnect
The user’s session was abnormally terminated
The user’s program raised an address exception
User Error
The user drops a table
User damages data by modification
Instance Failure
Media Failure
The user drops a table
User damages data by modification
Alert Logs
Records informational and error messages
All Instance startups and shutdowns are recorded in the log
54. What is the main goal of RAID technology?
RAID stands for Redundant Array of Inexpensive (or sometimes “Independent”)Disks.
RAID is a method of combining several hard disk drives into one logical unit (two or more disks grouped together to appear as a single device to the host system). RAID technology was developed to address the fault-tolerance and performance limitations of conventional disk storage. It can offer fault tolerance and higher throughput levels than a single hard drive or group of independent hard drives. 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25 Oct, 2024 | Commonly asked DBMS Interview Questions | Set 2
25 Oct, 2024
This article is an extension of Commonly asked DBMS interview questions | Set 1.
Q1. There is a table where only one row is fully repeated. Write a Query to find the Repeated row
Name
Section
abc
CS1
bcd
CS2
abc
CS1
In the above table, we can find duplicate rows using the below query.
SELECT name, section FROM tblGROUP BY name, sectionHAVING COUNT(*) > 1
Q2. Query to find 2nd highest salary of an employee?
SELECT max(salary) FROM EMPLOYEES WHERE salary IN(SELECT salary FROM EMPLOYEEs MINUS SELECT max(salary)FROM EMPLOYEES);
OR
SELECT max(salary) FROM EMPLOYEES WHERE salary <> (SELECT max(salary) FROM EMPLOYEES);
Q3. Consider the following Employee table. How many rows are there in the result of the following query?
ID
Salary
DeptName
1
10000
EC
2
40000
EC
3
30000
CS
4
40000
ME
5
50000
ME
6
60000
ME
7
70000
CS
How many rows are there in the result of the following query?
SELECT E.IDFROM Employee EWHERE EXISTS (SELECT E2.salaryFROM Employee E2WHERE E2.DeptName = 'CS'AND E.salary > E2.salary)
Following 5 rows will be the result of the query as 3000 is the minimum salary of CS Employees and all these rows are greater than 30000. 2 4 5 6 7
Q4. Write a trigger to update Emp table such that, If an updation is done in Dep table then salary of all employees of that department should be incremented by some amount (updation)
Assuming Table name are Dept and Emp, trigger can be written as follows:
CREATE OR REPLACE TRIGGER update_trigAFTER UPDATE ON DeptFOR EACH ROWDECLARECURSOR emp_cur IS SELECT * FROM Emp;BEGINFOR i IN emp_cur LOOPIF i.dept_no = :NEW.dept_no THENDBMS_OUTPUT.PUT_LINE(i.emp_no); -- for printing thoseUPDATE Emp -- emp number which areSET sal = i.sal + 100 -- updatedWHERE emp_no = i.emp_no;END IF;END LOOP;END;
Q5. There is a table which contains two columns Student and Marks, you need to find all the students, whose marks are greater than average marks i.e. list of above-average students.
SELECT student, marks FROM tableWHERE marks > SELECT AVG(marks) from table;
Q6. Name the Employee who has the third-highest salary using sub queries.
SELECT Emp1.NameFROM Employee Emp1WHERE 2 = (SELECT COUNT(DISTINCT(Emp2.Salary)) FROM Employee Emp2 WHERE Emp2.Salary > Emp1.Salary )
Logic: Number of people with a salary higher than this person will be 2.
Q7. Why we cannot use WHERE clause with aggregate functions like HAVING ?
The difference between the having and where clause in SQL is that the where clause canNOT be used with aggregates, but the having clause can.
Note: It is not a predefined rule but by and large you’ll see that in a good number of the SQL queries, we use WHERE prior to GROUP BY and HAVING after GROUP BY. The Where clause acts as a pre filter where as Having as a post filter. The where clause works on row’s data, not on aggregated data.
Let us consider below table ‘Marks’.
Student
Course
Score
a
c1
40
a
c2
50
b
c3
60
d
c1
70
e
c2
80
SELECT Student, sum(Score) AS total FROM Marks
This would select data row by row basis. The having clause works on aggregated data. For example, the output of the below query
SELECT Student, sum(score) AS total FROM Marks
Student
Total
a
90
b
60
d
70
e
80
When we apply to have in above query, we get
SELECT Student, sum(score) AS totalFROM Marks having total > 70
Student
Total
a
90
e
80
Q8. Difference between primary key and unique key and why one should use a unique key if it allows only one null ?
Primary key:
Only one in a row(tuple).
Never allows null value(only key field).
Unique key identifier can not be null and must be unique.
Unique Key:
Can be more than one unique key in one row.
Unique key can have null values(only single null is allowed).
It can be a candidate key.
Unique key can be null and may not be unique.
Q9. What’s the difference between materialized and dynamic view?
Materialized views:
Disk-based and are updated periodically based upon the query definition.
A materialized table is created or updated infrequently and it must be synchronized with its associated base tables.
Dynamic views:
Virtual only and run the query definition each time they are accessed.
A dynamic view may be created every time that a specific view is requested by the user.
Q10. What is embedded and dynamic SQL?
Static or Embedded SQL:
SQL statements in an application that do not change at runtime and, therefore, can be hard-coded into the application.
Dynamic SQL:
SQL statements that are constructed at runtime; for example, the application may allow users to enter their own queries.
Dynamic SQL is a programming technique that enables you to buildSQL statements dynamically at runtime. You can create more general purpose, flexible applications by using dynamic SQL because the full text of a SQL statement may be unknown at compilation.
Static (embedded) SQL
Dynamic (interactive) SQL
In static SQL how database will be accessed is predetermined in the embedded SQL statement.
In dynamic SQL, how database will be accessed is determined at run time.
It is more swift and efficient.
It is less swift and efficient.
SQL statements are compiled at compile time.
SQL statements are compiled at run time.
Parsing, validation, optimization, and generation of application plan are done at compile time.
Parsing, validation, optimization, and generation of application plan are done at run time.
It is generally used for situations where data is distributed uniformly.
It is generally used for situations where data is distributed non-uniformly.
EXECUTE IMMEDIATE, EXECUTE and PREPARE statements are not used.
EXECUTE IMMEDIATE, EXECUTE and PREPARE statements are used.
It is less flexible.
It is more flexible.
Q11. What is the difference between CHAR and VARCHAR?
CHAR and VARCHAR differ in storage and retrieval.
CHAR column length is fixed while VARCHAR length is variable.
The maximum no. of characters CHAR data type can hold is 255 characters while VARCHAR can hold up to 4000 characters.
CHAR is 50% faster than VARCHAR.
CHAR uses static memory allocation while VARCHAR uses dynamic memory allocation.
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06 Jan, 2025 | Database Management System – GATE CSE Previous Year Questions
06 Jan, 2025
In this article, we are mainly focusing on the DBMS GATE Questions that are asked in Previous Years, with their solutions, and where an explanation is required, we have also provided the reason.
Topic-Wise Quizzes to Practice Previous Year’s Questions
ER and Relational Models
Database Design (Normal Forms)
SQL
Transaction and Concurrency Control
File Structures (Sequential Files, Indexing, B and B+ Trees)
Below mentioned are the links to the Database Management Systems PYQ’s pages. On each page, you will get the questions asked in DBMS along with the years asked.
GATE DBMS Previous Year Questions
Database Management Systems | Set 1,2
Database Management Systems | Set 3
Database Management Systems | Set 4
Database Management Systems | Set 5
Database Management Systems | Set 6
Database Management Systems | Set 7
Database Management Systems | Set 8
Database Management Systems | Set 9
Database Management Systems | Set 10
GATE CSE Previous Year Question Papers
These previous year’s questions help you understand the question patterns followed by GATE that directly help a candidate in scoring good marks in GATE. Below is the links to year-wise GATE Previous Question Papers.
GATE CSE Previous Year Question Papers
These GATE CSE question papers span over 15 years, along with their official answer keys. We’ve also provided Quiz tests to help you practice key topics, improve speed, track your progress, and build confidence for the GATE exam 2025.
These previous year’s questions help you in understanding the question patterns followed by GATE that directly help a candidate in scoring good marks in GATE. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’/GRE | List of words to enhance your vocabulary with root alphabet ‘E’/GRE | List of words to enhance your vocabulary with root alphabet ‘H’/ACID Properties in DBMS/File Organization in DBMS | Set 3/Last Minute Notes – DBMS/Commonly asked DBMS interview questions/Commonly asked DBMS Interview Questions | Set 2/Database Management System – GATE CSE Previous Year Questions | https://www.geeksforgeeks.org/database-management-system-gate-questions/?ref=next_article | Data Science & ML | Database Management System – GATE CSE Previous Year Questions | Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0369870551, 0.0376394726, -0.0143782785, 0.0390446782, 0.0685038418, 0.0222825669, 0.00702603487, 0.0324703194, -0.0427835323, -0.0240139831, 0.0413532332, -0.0488309413, 0.018531166, -0.0184935275, -0.0428086258, -0.0191459451, -0.0229977164, 0.0241269022, -0.0212663021, -0.0507129133, -0.0110785514, -0.0173894353, -0.0121575492, 0.015595288, -0.0355065688, 0.0205009654, 0.00659318082, -0.026021421, -0.00754044065, 0.00317426212, -0.00535735162, 0.0214419533, 0.00497154705, -0.0156705659, -0.0736228079, 0.0159465894, -0.0317426212, 0.0102755763, 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31 Jan, 2025 | GATE CSE and IT Previous Years Papers PDF Download Link
31 Jan, 2025
Practicing Year Wise Questions of GATE is the best approach for getting a good score in GATE. GATE Previous Year Question Paper PDF will help you in cracking GATE as it improves your approach towards the question pattern and helps in clearing fundamental concepts that give you confidence in cracking GATE.Master GATE 2025! Practice with official FREE GATE Previous Year Questions Papers (2024, 2023, 2022, 2021, 2020, 2019, and so on), including answer keys & quizzes. Sharpen your skills and dominate exam day! The GATE Rank Predictor 2025 is here to help you estimate your rank based on your response sheet! Enter your branch, slot, mobile number, and response sheet URL, and submit to get your predicted rank. GATE Previous Year Question Paper PDF with Answer KeysHere’s a year-wise list of GATE CSE and IT papers to streamline your preparation for GATE 2025. You can download these GATE CSE question papers spanning over 15 years, along with their official answer keys. We’ve also provided Quiz tests to help you practice key topics, improve speed, track your progress, and build confidence for the GATE exam 2025.YEAR Original PaperOfficial KeysQuizzes2024 [CS]2024 Set 1 Paper2024 Set 1 KeysGATE 2024 Quiz Set 12024 Set 2 Paper2024 Set 2 KeysGATE 2024 Quiz Set 22024 [DA]2024 Question Paper2024 KeysGATE DA 2024 Quiz20232023 Question Paper2023 KeysGATE 2023 Quiz20222022 Question Paper2022 KeysGATE 2022 Quiz20212021 Set 1 Paper2021 Set 1 KeysGATE 2021 Quiz Set 12021 Set 2 Paper2021 Set 2 KeysGATE 2021 Quiz Set 220202020 Paper2020 KeysGATE 2020 Quiz20192019 Paper2019 KeysGATE 2019 Quiz20182018 Paper2018 KeysGATE 2018 Quiz20172017 Set 1 Paper2017 Set 1 KeysGATE 2017 Quiz Set 12017 Set 2 Paper2017 Set 2 KeysGATE 2017 Quiz Set 220162016 Set 1 Paper2016 Set 1 KeysGATE 2016 Quiz Set 12016 Set 2 Paper2016 Set 2 KeysGATE 2016 Quiz Set 220152015 Set 1 Paper2015 Set 1 KeysGATE 2015 Quiz Set 12015 Set 2 Paper2015 Set 2 KeysGATE 2015 Quiz Set 22015 Set 3 Paper2015 Set 3 KeysGATE 2015 Quiz Set 320142014 Set 1 Paper2014 Set 1 KeysGATE 2014 Quiz Set 12014 Set 2 Paper2014 Set 2 KeysGATE 2014 Quiz Set 22014 Set 3 Paper2014 Set 3 KeysGATE 2014 Quiz Set 320132013 Paper2013 KeysGATE 2013 Quiz20122012 Paper2012 KeysGATE 2012 Quiz20112011 Paper2011 KeysGATE 2011 Quiz20102010 PaperGATE 2010 Quiz20092009 PaperGATE 2009 Quiz20082008 CS PaperGATE 2008 Quiz Set 12008 IT PaperGATE 2008 Quiz Set 220072007 CS PaperGATE 2007 Quiz Set 12007 IT PaperGATE 2007 Quiz Set 220062006 CS PaperGATE 2006 Quiz Set 12006 IT PaperGATE 2006 Quiz Set 220052005 CS PaperGATE 2005 Quiz Set 12005 IT PaperGATE 2005 Quiz Set 220042004 CS PaperGATE 2004 Quiz Set 12004 IT PaperGATE 2004 Quiz Set 220032003 PaperGATE 2003 Quiz20022002 PaperGATE 2002 Quiz20012001 PaperGATE 2001 Quiz20002000 PaperGATE 2000 Quiz19991999 PaperGATE 1999 Quiz19981998 PaperGATE 1998 Quiz19971997 PaperGATE 1997 Quiz19961996 PaperGATE 1996 Quiz19951995 PaperGATE 1995 Quiz19941994 PaperGATE 1994 Quiz19931993 PaperGATE 1993 Quiz19921992 PaperGATE 1992 Quiz19911991 PaperGATE 1991 QuizImportant LinksGATE CS NotesGATE Latest syllabusGATE CS PreparationFREE GATE CS 2025 All India Mock TestsConclusionWith 15+ years of GATE CSE and IT papers at your fingertips, along with answer keys and mock tests, you're well-equipped to excel in your preparation. Download the PDFs, attempt the mock tests, and track your progress to build confidence and improve your performance. Combining previous papers with a structured study plan will significantly enhance your chances of success in GATE CSE 2025!Previous Years GATE CSE and IT Papers Download Link - FAQsWhy should I practice previous years' GATE CSE and IT papers?Practicing previous years' papers helps you understand the exam pattern, the type of questions asked, and the difficulty level. It also helps you identify your strengths and areas where you need improvement.How many years of GATE papers should I practice?It's advisable to practice at least the last 10 years of GATE papers. This will give you a comprehensive understanding of the trends and question patterns over the years.How similar are the questions in previous years' papers to the actual GATE exam questions?While the exact questions rarely repeat, the concepts and types of questions often do. Practicing previous years' papers helps you get familiar with the format and the kind of thinking required to solve GATE questions.Is previous year paper enough for GATE?They are helpful but not enough on their own. You also need to cover the syllabus thoroughly with textbooks, practice mock tests, and work on time management.How to get previous year GATE question paper?You can download them for free from platforms like the GATE IIT portal or Geeksforgeek's along with answer keys.Can I crack GATE in 1 year?Yes, with consistent study, mock tests, and good time management, one year of preparation is enough.Do questions repeat in the GATE exam?Exact questions rarely repeat, but concepts and patterns do, making past papers highly useful. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’/GRE | List of words to enhance your vocabulary with root alphabet ‘E’/GRE | List of words to enhance your vocabulary with root alphabet ‘H’/ACID Properties in DBMS/File Organization in DBMS | Set 3/Last Minute Notes – DBMS/Commonly asked DBMS interview questions/Commonly asked DBMS Interview Questions | Set 2/Database Management System – GATE CSE Previous Year Questions/GATE CSE and IT Previous Years Papers PDF Download Link | https://www.geeksforgeeks.org/original-gate-previous-year-question-papers-cse-and-it-gq/ | Data Science & ML | GATE CSE and IT Previous Years Papers PDF Download Link | Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0553989373, 0.000516352942, -0.0176592711, 0.0191280097, 0.0302927084, 0.0354103409, 0.0134596005, 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06 Jan, 2025 | Theory of Computation – GATE CSE Previous Year Questions
06 Jan, 2025
In this article, we are mainly focusing on the Theory of Computation GATE Questions that have been asked in Previous Years, with their solutions. And, where an explanation is required, we have also provided the reason.
Topic-Wise Quizzes to Practice Previous Year’s Questions
Finite Automata and Regular Language
Push Down Automata and Context-Free language
Recursively Enumerable Language and Turing Machine
Undecidability
Below mentioned are the links to the Theory of Computation PYQ’s pages. On each page, you will get the questions asked in TOC along with the years asked.
GATE TOC Previous Year Questions
Automata Theory | Set 1, 2
Automata Theory | Set 3
Automata Theory | Set 4
Automata Theory | Set 5
Automata Theory | Set 6
GATE CSE Previous Year Question Papers
These previous year’s questions help you understand the question patterns followed by GATE that directly help a candidate in scoring good marks in GATE. Below is the links to year-wise GATE Previous Question Papers.
GATE CSE Previous Year Question Papers
These GATE CSE question papers span over 15 years, along with their official answer keys. We’ve also provided Quiz tests to help you practice key topics, improve speed, track your progress, and build confidence for the GATE exam 2025.
These previous year’s questions help you in understanding the question patterns followed by GATE that directly help a candidate in scoring good marks in GATE. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’/GRE | List of words to enhance your vocabulary with root alphabet ‘E’/GRE | List of words to enhance your vocabulary with root alphabet ‘H’/ACID Properties in DBMS/File Organization in DBMS | Set 3/Last Minute Notes – DBMS/Commonly asked DBMS interview questions/Commonly asked DBMS Interview Questions | Set 2/Database Management System – GATE CSE Previous Year Questions/GATE CSE and IT Previous Years Papers PDF Download Link/Theory of Computation – GATE CSE Previous Year Questions | https://www.geeksforgeeks.org/theory-of-computation-gate-questions/?ref=lbp | Data Science & ML | Theory of Computation – GATE CSE Previous Year Questions | Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Theory of Computation – GATE CSE Previous Year Questions, Basic Understanding of Bayesian Belief Networks, Differential Equations, Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Transformers in Machine Learning, Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0373687707, 0.00373265264, -0.0176222231, 0.0215691198, 0.0446590595, 0.0342064276, 0.00451116869, 0.0367169902, -0.0431865193, -0.0236330926, 0.00698853936, -0.0534943119, 0.00414605066, 0.00428183842, -0.00811708625, -0.0225226507, -0.00595051795, 0.0097827483, -0.0113397799, -0.050694067, -0.0409656353, -0.0173325427, -0.0299819205, 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13 Dec, 2022 | Automata Theory | Set 6
13 Dec, 2022
Following questions have been asked in GATE CS 2010 exam.
1) Let L={w ∈ (0 + 1)*|w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expression below represents L?
(A) (0*10*1)*
(B) 0*(10*10*)*
(C) 0*(10*1*)*0*
(D) 0*1(10*1)*10*
Answer (B)
Option (A) is incorrect because it cannot accept “110”
Option (C) is incorrect because it accept a string with single 1.
Option (D) is incorrect because it cannot accept 11101
2) Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?
(A) L2 – L1 is recursively enumerable.
(B) L1 – L3 is recursively enumerable
(C) L2 ∩ L1 is recursively enumerable
(D) L2 ∪ L1 is recursively enumerable
Answer (B)
3) Consider the languages L1={0i1j | i != j}, L2={0i1j | i = j}, L3 = {0i1j | i = 2j+1}, L4 = {0i1j | i != 2j}. Which one of the following statements is true?
(A) Only L2 is context free
(B) Only L2 and L3 are context free
(C) Only L1 and L2 are context free
(D) All are context free
Answer (D)
A Pushdown Automata can be built for all four languages.
4) Let w be any string of length n is {0,1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?
(A) n-1
(B) n
(C) n+1
(D) 2n-1
Answer (C)
We need minimum n+1 states to build NFA that accepts all substrings of a binary string. For example, following NFA accepts all substrings of “010” and it has 4 states.
Please see GATE Corner for all previous year paper/solutions/explanations, syllabus, important dates, notes, etc.
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13 Dec, 2022 | Data Structures and Algorithms | Set 21
13 Dec, 2022
Following questions have been asked in GATE CS 2008 exam.
1. The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,...,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?
(A) X[i, j] = X[i – 1, j] V X[i, j -ai]
(B) X[i, j] = X[i – 1, j] V X[i – 1, j – ai]
(C) X[i, j] = X[i – 1, j] V X[i, j – ai]
(D) X[i, j] = X[i – 1, j] V X[i -1, j – ai]
Answer (B)
X[I, j] (2 <= i <= n and ai <= j <= W), is true if any of the following is true
1) Sum of weights excluding ai is equal to j, i.e., if X[i-1, j] is true.
2) Sum of weights including ai is equal to j, i.e., if X[i-1, j-ai] is true so that we get (j – ai) + ai as j.
2. In question 1, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?
(A) X[1, W]
(B) X[n ,0]
(C) X[n, W]
(D) X[n -1, n]
Answer (C)
If we get the entry X[n, W] as true then there is a subset of {a1, a2, .. an} that has sum as W.
Reference: http://en.wikipedia.org/wiki/Subset_sum_problem
3. Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program is erroneous.
1. f(int Y[10], int x) {
2. int i, j, k;
3. i = 0; j = 9;
4. do {
5. k = (i + j) /2;
6. if( Y[k] < x) i = k; else j = k;
7. } while(Y[k] != x && i < j);
8. if(Y[k] == x) printf ("x is in the array ") ;
9. else printf (" x is not in the array ") ;
10. }
On which of the following contents of Y and x does the program fail?
(A) Y is [1 2 3 4 5 6 7 8 9 10] and x < 10
(B) Y is [1 3 5 7 9 11 13 15 17 19] and x < 1
(C) Y is [2 2 2 2 2 2 2 2 2 2] and x > 2
(D) Y is [2 4 6 8 10 12 14 16 18 20] and 2 < x < 20 and x is even
Answer (C)
The above program doesn’t work for the cases where element to be searched is the last element of Y[] or greater than the last element (or maximum element) in Y[]. For such cases, program goes in an infinite loop because i is assigned value as k in all iterations, and i never becomes equal to or greater than j. So while condition never becomes false.
4. In question 3, the correction needed in the program to make it work properly is
(A) Change line 6 to: if (Y[k] < x) i = k + 1; else j = k-1;
(B) Change line 6 to: if (Y[k] < x) i = k - 1; else j = k+1;
(C) Change line 6 to: if (Y[k] <= x) i = k; else j = k;
(D) Change line 7 to: } while ((Y[k] == x) && (i < j));
Answer (A)
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Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [0.0119845401, 0.0067257504, -0.0203278754, 0.0463140272, 0.0119583448, -0.00450893771, -0.0022446455, 0.0330066048, -0.0202623866, 0.0167914536, -0.00857909769, -0.0127704116, 0.0655416846, -0.00789145939, -0.0405771658, 0.00786526408, 0.00774738332, 0.0211530421, -0.0418083631, -0.0417559743, -0.0517365411, -0.00528171146, -0.0205243435, 0.0398698822, 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13 Dec, 2022 | Data Structures and Algorithms | Set 25
13 Dec, 2022
Following questions have been asked in GATE 2010 exam.
1 Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry Wij in the matrix W below is the weight of the edge {i, j}.
What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?
(A) 7
(B) 8
(C) 9
(D) 10
Answer (D)
To get the minimum spanning tree with vertex 0 as leaf, first remove 0th row and 0th column and then get the minimum spanning tree (MST) of the remaining graph. Once we have MST of the remaining graph, connect the MST to vertex 0 with the edge with minimum weight (we have two options as there are two 1s in 0th row).
2. In the graph given in question 1, what is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?
(A) 7
(B) 8
(C) 9
(D) 10
Answer (B)
Path: 1 -> 0 -> 4 -> 2
Weight: 1 + 4 + 3
3. The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1
(A) I and II
(B) III and IV
(C) IV only
(D) II and IV
Answer (D)
In sequence IV, we have a vertex with degree 8 which is not possible in a simple graph (no self loops and no multiple edges) with total vertex count as 8. Maximum possible degree in such a graph is 7.
In sequence II, four vertices are connected to 6 other vertices, but remaining 4 vertices have degrees as 3, 3, 2 and 2 which are not possible in a simple graph (no self loops and no multiple edges).
4. Consider a B+-tree in which the maximum number of keys in a node is 5. What is the minimum number of keys in any non-root node?
(A) 1
(B) 2
(C) 3
(D) 4
Answer (B)
Since the maximum number of keys is 5, maximum number of children a node can have is 6. By definition of B Tree, minimum children that a node can have would be 6/2 = 3. Therefore, minimum number of keys that a node can have becomes 2 (3-1).
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04 Dec, 2023 | Graph Data Structure Notes for GATE Exam [2024]
04 Dec, 2023
Graphs, a fundamental concept in computer science and mathematics, serve as powerful tools for modeling and solving a myriad of real-world problems. As aspirants gear up for the GATE Exam 2024, a comprehensive understanding of graph data structures becomes paramount. These notes aim to provide a concise and illuminating guide to graph data structures, unraveling the principles, representations, and algorithms associated with them, all of which are essential for mastering this topic in the GATE examination.
Table of Content
What is Graph?Components of a GraphBreadth First Search or BFS in GraphDepth First Search or DFS in GraphTypes of GraphsRepresentations of GraphBasic Properties of a GraphApplications of Graph Data StructureAdvantages of Graph:Disadvantages of GraphGate Previous Year Problems on Graph Data Structure
What is Graph?A Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(V, E).
Components of a GraphVertices: Vertices are the fundamental units of the graph. Sometimes, vertices are also known as vertex or nodes. Every node/vertex can be labeled or unlabelled.Edges: Edges are drawn or used to connect two nodes of the graph. It can be ordered pair of nodes in a directed graph. Edges can connect any two nodes in any possible way. There are no rules. Sometimes, edges are also known as arcs. Every edge can be labelled/unlabelled.Breadth First Search or BFS in GraphThe Breadth First Search (BFS) algorithm is used to search a graph data structure for a node that meets a set of criteria. It starts at the root of the graph and visits all nodes at the current depth level before moving on to the nodes at the next depth level.
BFS
Time Complexity: O(V+E), where V is the number of nodes and E is the number of edges.Auxiliary Space: O(V)
Depth First Search or DFS in GraphDepth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
DFS
Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.Auxiliary Space: O(V + E), since an extra visited array of size V is required, And stack size for iterative call to DFS function.
Types of Graphs1. Null GraphA graph is known as a null graph if there are no edges in the graph.
2. Trivial GraphGraph having only a single vertex, it is also the smallest graph possible.
3. Undirected GraphA graph in which edges do not have any direction. That is the nodes are unordered pairs in the definition of every edge.
4. Directed GraphA graph in which edge has direction. That is the nodes are ordered pairs in the definition of every edge.
5. Connected GraphThe graph in which from one node we can visit any other node in the graph is known as a connected graph.
6. Disconnected GraphThe graph in which at least one node is not reachable from a node is known as a disconnected graph.
7. Regular GraphThe graph in which the degree of every vertex is equal to K is called K regular graph.
8. Complete GraphThe graph in which from each node there is an edge to each other node.
9. Cycle GraphThe graph in which the graph is a cycle in itself, the degree of each vertex is 2.
10. Cyclic GraphA graph containing at least one cycle is known as a Cyclic graph.
11. Directed Acyclic GraphA Directed Graph that does not contain any cycle.
12. Bipartite GraphA graph in which vertex can be divided into two sets such that vertex in each set does not contain any edge between them.
13. Weighted Graph
A graph in which the edges are already specified with suitable weight is known as a weighted graph. Weighted graphs can be further classified as directed weighted graphs and undirected weighted graphs. Representations of GraphHere are the two most common ways to represent a graph :
Adjacency MatrixAdjacency ListAdjacency MatrixAn adjacency matrix is a way of representing a graph as a matrix of boolean (0’s and 1’s).
Let’s assume there are n vertices in the graph So, create a 2D matrix adjMat[n][n] having dimension n x n.
If there is an edge from vertex i to j, mark adjMat[i][j] as 1.If there is no edge from vertex i to j, mark adjMat[i][j] as 0.Representation of Directed Graph to Adjacency Matrix:The below figure shows a directed graph. Initially, the entire Matrix is initialized to 0. If there is an edge from source to destination, we insert 1 for that particular adjMat[destination].
Directed Graph to Adjacency Matrix
Adjacency ListAn array of Lists is used to store edges between two vertices. The size of array is equal to the number of vertices (i.e, n). Each index in this array represents a specific vertex in the graph. The entry at the index i of the array contains a linked list containing the vertices that are adjacent to vertex i.
Let’s assume there are n vertices in the graph So, create an array of list of size n as adjList[n].
adjList[0] will have all the nodes which are connected (neighbour) to vertex 0.adjList[1] will have all the nodes which are connected (neighbour) to vertex 1 and so on.Representation of Directed Graph to Adjacency list:The below directed graph has 3 vertices. So, an array of list will be created of size 3, where each indices represent the vertices. Now, vertex 0 has no neighbours. For vertex 1, it has two neighbour (i.e, 0 and 2) So, insert vertices 0 and 2 at indices 1 of array. Similarly, for vertex 2, insert its neighbours in array of list.
Directed Graph to Adjacency list
Basic Properties of a GraphA Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph.
The basic properties of a graph include:
Vertices (nodes): The points where edges meet in a graph are known as vertices or nodes. A vertex can represent a physical object, concept, or abstract entity.Edges: The connections between vertices are known as edges. They can be undirected (bidirectional) or directed (unidirectional).Weight: A weight can be assigned to an edge, representing the cost or distance between two vertices. A weighted graph is a graph where the edges have weights.Degree: The degree of a vertex is the number of edges that connect to it. In a directed graph, the in-degree of a vertex is the number of edges that point to it, and the out-degree is the number of edges that start from it.Path: A path is a sequence of vertices that are connected by edges. A simple path does not contain any repeated vertices or edges.Cycle: A cycle is a path that starts and ends at the same vertex. A simple cycle does not contain any repeated vertices or edges.Connectedness: A graph is said to be connected if there is a path between any two vertices. A disconnected graph is a graph that is not connected.Planarity: A graph is said to be planar if it can be drawn on a plane without any edges crossing each other.Bipartiteness: A graph is said to be bipartite if its vertices can be divided into two disjoint sets such that no two vertices in the same set are connected by an edge.Applications of Graph Data StructureIn Computer science graphs are used to represent the flow of computation.Google maps uses graphs for building transportation systems, where intersection of two(or more) roads are considered to be a vertex and the road connecting two vertices is considered to be an edge, thus their navigation system is based on the algorithm to calculate the shortest path between two vertices.In Facebook, users are considered to be the vertices and if they are friends then there is an edge running between them. Facebook’s Friend suggestion algorithm uses graph theory. Facebook is an example of undirected graph.In World Wide Web, web pages are considered to be the vertices. There is an edge from a page u to other page v if there is a link of page v on page u. This is an example of Directed graph. It was the basic idea behind Google Page Ranking Algorithm.In Operating System, we come across the Resource Allocation Graph where each process and resources are considered to be vertices. Edges are drawn from resources to the allocated process, or from requesting process to the requested resource. If this leads to any formation of a cycle then a deadlock will occur.In mapping system we use graph. It is useful to find out which is an excellent place from the location as well as your nearby location. In GPS we also use graphs.Facebook uses graphs. Using graphs suggests mutual friends. it shows a list of the f following pages, friends, and contact list.Microsoft Excel uses DAG means Directed Acyclic Graphs.In the Dijkstra algorithm, we use a graph. we find the smallest path between two or many nodes.Advantages of Graph:Representing complex data: Graphs are effective tools for representing complex data, especially when the relationships between the data points are not straightforward. They can help to uncover patterns, trends, and insights that may be difficult to see using other methods.Efficient data processing: Graphs can be processed efficiently using graph algorithms, which are specifically designed to work with graph data structures. This makes it possible to perform complex operations on large datasets quickly and effectively.Network analysis: Graphs are commonly used in network analysis to study relationships between individuals or organizations, as well as to identify important nodes and edges in a network. This is useful in a variety of fields, including social sciences, business, and marketing.Pathfinding: Graphs can be used to find the shortest path between two points, which is a common problem in computer science, logistics, and transportation planning.Visualization: Graphs are highly visual, making it easy to communicate complex data and relationships in a clear and concise way. This makes them useful for presentations, reports, and data analysis.Machine learning: Graphs can be used in machine learning to model complex relationships between variables, such as in recommendation systems or fraud detection.Disadvantages of GraphLimited representation: Graphs can only represent relationships between objects, and not their properties or attributes. This means that in order to fully understand the data, it may be necessary to supplement the graph with additional information.Difficulty in interpretation: Graphs can be difficult to interpret, especially if they are large or complex. This can make it challenging to extract meaningful insights from the data, and may require advanced analytical techniques or domain expertise.Scalability issues: As the number of nodes and edges in a graph increases, the processing time and memory required to analyze it also increases. This can make it difficult to work with large or complex graphs.Data quality issues: Graphs are only as good as the data they are based on, and if the data is incomplete, inconsistent, or inaccurate, the graph may not accurately reflect the relationships between objects.Lack of standardization: There are many different types of graphs, and each has its own strengths and weaknesses. This can make it difficult to compare graphs from different sources, or to choose the best type of graph for a given analysis.Privacy concerns: Graphs can reveal sensitive information about individuals or organizations, which can raise privacy concerns, especially in social network analysis or marketing.Gate Previous Year Problems on Graph Data Structure1. Consider the tree arcs of a BFS traversal from a source node W in an unweighted, connected, undirected graph. The tree T formed by the tree arcs is a data structure for computing. [GATE CSE 2014 Set 2]
(A) the shortest path between every pair of vertices.
(B) the shortest path from W to every vertex in the graph.
(C) the shortest paths from W to only those nodes that are leaves of T.
(D) the longest path in the graph.
Solution: Correct answer is (B)
2. Traversal of a graph is somewhat different from the tree because [GATE CSE 2006 Set 1]
(A) There can be a loop in a graph, so we must maintain a visited flag for every vertex
(B) DFS of a graph uses the stack, but the inorder traversal of a tree is recursive
(C) BFS of a graph uses a queue, but a time-efficient BFS of a tree is recursive.
(D) All of the above
Solution: Correct answer is (A)
Explanation: There can be a loop in a graph, and due to this, we must maintain a visited flag for every vertex.
3. What are the suitable Data Structures for the following algorithms? [GATE CSE 2013 Set 2]
1) Breadth-First Search
2) Depth First Search
3) Prim's Minimum Spanning Tree
4) Kruskal's Minimum Spanning Tree
(A)
1) Stack
2) Queue
3) Priority Queue
4) Union Find
(B)
1) Queue
2) Stack
3) Priority Queue
4) Union Find
(C)
1) Stack
2) Queue
3) Union Find
4) Priority Queue
(D)
1) Priority Queue
2) Queue
3) Stack
4) Union Find
Solution: (B)
Explanation: 1) Queue is used in Breadth-First Search
2) Stack is used in depth-first search-dfs
3) Priority Queue is used in Prim's Minimum Spanning Tree.
4) Union Find is used in Kruskal's Minimum Spanning Tree.
4. Let G be a weighted graph with edge weights greater than one and G' be the graph constructed by squaring the weights of edges in G. LetT and T' be the minimum spanning trees of G and G' respectively, with total weights t and t'. Which of the following statements is TRUE? [GATE CSE 2020 ]
(A) T' = T with total weight t' = t^2
(B) T' = T with total weight t' < t^2
(C) T' =t- T but total weight t' = t^2
(D) None of these
Solution: (D)
5. The Breadth-First Search algorithm has been implemented with the help of a queue. What is a possible order of visiting the nodes of the following graph is
(A) NQMPOR
(B) QMNPOR
(C) QMNPRO
(D) MNOPQR
.
Solution: (C)
Explanation: Option (A) is NQMPOR. It cannot be BFS because P is visited before O here.
Option (D) is MNOPQR. It cannot be a BFS because the traversal begins with M, but O has been visited before N and Q.
In BFS, every adjacent must be called before adjacent of adjacent.
(B) and (C) correspond to QMNP. Before N and P, M had been added to the queue (because M comes before NP in QMNP). R is placed in the line before N and P's neighbors because it is M's neighbor (which is O). As a result, R is visited first, followed by O.
6. Let G be an undirected graph. Consider a depth-first traversal of G, where T is the depth-first search tree that results. Let u be the first new (unvisited) vertex visited after u in the traversal, and v be its first new (unvisited) vertex visited after u. Which of the assertions below is always true? [GATE CSE 2014 ]
(A) In G, u,v must be an edge, while in T, u is a descendent of v.
(B) In G, u,v must be an edge, while in T, v is a descendent of u.
(C) If u,v in G is not an edge, then u in T is a leaf
(D) If u,v in G is not an edge, then u and v in T must have the same parent.
Solution: (C)
Explanation:
In DFS, if 'v' is visited
after 'u,' one of the following is true.
1) (u, v) is an edge.
u
/ \
v w
/ / \
x y z
2) A leaf node is 'u.'
w
/ \
x v
/ / \
u y z
In DFS, after we have visited a node, we first go back to all children who were not visited. If no children are left unvisited(u is a leaf), then control goes back to the parent, and the parent then visits the subsequent unvisited children.
7. Which of the two traversals (BFS and DFS) may be used to find if there is a path from s to t given two vertices in a graph s and t? [GATE CSE 2014 Set 2]
(A) Only BFS
(B) Only DFS
(C) Both BFS and DFS
(D) Neither BFS nor DFS
Solution: (C)
Explanation: Both traversals can be used to see if there is a path from s to t.
8. The statement written below is true or false? [GATE CSE 2021]
If a directed graph's DFS contains a back edge, any other directed graph's DFS will also have at least a single back edge.
(A) True
(B) False
Solution: (A)
Explanation: A cycle in the graph is called its back edge. So if we get a cycle, all DFS traversals would contain at least one back edge.
9. Which of the condition written below is sufficient to detect a cycle in a directed graph? [GATE CSE 2008]
(A) There is an edge from a currently visited node to an already seen node.
(B) There is an edge from the currently visited node to an ancestor of the currently visited node in the forest of DFS.
(C) Every node is seen two times in DFS.
(D) None of the above
Solution: (B)
Explanation: If there is an edge from the currently visited node to an ancestor of the currently visited node in the forest of DFS, it means a cycle is formed. As this is an apparent condition about cycle formation, so this condition is sufficient.
10. If the finishing time f[u] > f[v] of DFS for two vertices u and v in a graph G which is directed, and u and v are in the DFS tree same as each other in the DFS forest, then u is an ancestor of v in the depth-first tree. [GATE CSE 2014 Set 2]
(A) True
(B) False
Solution: (B)
Explanation: In a graph that contains three nodes, r u and v, with edges (r; u) and (r; v), and r is the starting point for the DFS, u and v are siblings in the DFS tree; neither as the ancestor of the other.
11. Is the statement written below true or false? [GATE CSE 2015]
A DFS of a directed graph generally produces the exact number of edges of a tree, i.e., not dependent on the order in which vertices are considered for DFS.
(A) True
(B) False
Solution: (B)
Explanation: Consider the following graph. If we start from 'a', then there is one tree edge. If we start from 'b,' there is no tree edge.
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04 Dec, 2023 | Binary Heap Notes for GATE Exam [2024]
04 Dec, 2023
In the GATE Exam, understanding binary heaps is like having a secret weapon. Questions might ask you to pick the right tool for a job, and heaps are often the superheroes of quick and efficient data organization.
Table of Content
Introduction to Heap:Types of heaps:Representation of Binary Heap:Operations on Binary Heaps:Advantages of Heap Data Structure:Disadvantages of Heap Data Structure:Previously Asked GATE Questions on Binary HeapIntroduction to Heap:Binary heap is a complete binary tree where the root of any subtree has a higher (or lower based on the type of heap) value than all the nodes in its subtree.
Types of heaps:There are 2 types of heaps:
Max-HeapMin-Heap1. Max-Heap:In a Max-Heap, the key at the root node must be the greatest among the keys present at all its children. The same property must be recursively true for all sub-trees in that Binary Tree.
2. Min-Heap:In a Min-Heap the key at the root node must be minimum among the keys present at all of it’s children. The same property must be recursively true for all sub-trees in that Binary Tree.
Representation of Binary Heap:A Binary Heap is a Complete Binary Tree. A binary heap is typically represented as an array.
The root element will be at Arr[0].The below table shows indices of other nodes for the ith node, i.e., Arr[i]:Arr[(i-1)/2]Returns the parent nodeArr[(2*i)+1]Returns the left child nodeArr[(2*i)+2]Returns the right child nodeBinary HeapOperations on Binary Heaps:The common operation involved using heaps are:
Heapify: Process to rearrange the heap in order to maintain heap-property.Insertion: Add a new item in the heap.Deletion: Delete an item from the heap.Find-max (or Find-min): find a maximum item of a max-heap, or a minimum item of a min-heap, respectively.1. Heapify:It is the process to rearrange the elements to maintain the property of heap data structure. It is done when a certain node creates an imbalance in the heap due to some operations on that node. It takes O(log N) to balance the tree.
2. Insertion:If we insert a new element into the heap since we are adding a new element into the heap so it will distort the properties of the heap so we need to perform the heapify operation so that it maintains the property of the heap. This operation also takes O(logN) time.
Example :
Assume initially heap(taking max-heap) is as follows
8 / \ 4 5 / \1 2
Now if we insert 10 into the heap 8 / \ 4 5 / \ /1 2 10
After heapify operation final heap will be look like this 10 / \ 4 8 / \ /1 2 5
3. Deletion:If we delete the element from the heap it always deletes the root element of the tree and replaces it with the last element of the tree. Since we delete the root element from the heap it will distort the properties of the heap so we need to perform heapify operations so that it maintains the property of the heap. It takes O(logN) time.
Example:
Assume initially heap(taking max-heap) is as follows 15 / \ 5 7 / \2 3
Now if we delete 15 into the heap it will be replaced by leaf node of the tree for temporary. 3 / \ 5 7 / 2
After heapify operation final heap will be look like this 7 / \ 5 3 / 2
4. Find-max (or Find-min):It finds the maximum element or minimum element for max-heap and min-heap respectively and as we know minimum and maximum elements will always be the root node itself for min-heap and max-heap respectively. It takes O(1) time.
Time Complexity of building a heap:Algorithm for building a Heap of an input array A:BUILD-HEAP(A)
heapsize := size(A);
for i := floor(heapsize/2) downto 1
do HEAPIFY(A, i);
end for
END
A quick look over the above algorithm suggests that the running time is O(n*log(n)) since each call to Heapify costs O(log(n)) and and Build-Heap makes O(n) such calls but this upper bound, though correct, is not asymptotically tight.
We can derive a tighter bound by observing that the running time of Heapify depends on the height of the tree ‘h’ (which is equal to log(n), where n is a number of nodes) and the heights of most sub-trees are small.. Line-3 of Build-Heap runs a loop from the index of the last internal node (heapsize/2) to the index of root(1) . Hence, Heapify takes a different time for each node, which is:
For finding the Time Complexity of building a heap, we must know the number of nodes having height h. For this we use the fact that, A heap of size n has at most nodes \left \lceil \frac{n}{2^{h+1}} \right \rceil
with height h.
To derive the time complexity, we express the total cost of Build-Heap as-
T(n) = \sum_{h = 0}^{lg(n)}\left \lceil \frac{n}{2^{h+1}} \right \rceil * O(h)= O(n * \sum_{h = 0}^{lg(n)}\frac{h}{2^{h}})= O(n * \sum_{h = 0}^{\infty}\frac{h}{2^{h}})
Step 2 uses the properties of the Big-Oh notation to ignore the ceiling function and the constant 2(2^{h+1} = 2.2^h)
. Similarly in Step three, the upper limit of the summation can be increased to infinity since we are using Big-Oh notation. Sum of infinite G.P. (x < 1)
\sum_{n = 0}^{\infty}{x}^{n} = \frac{1}{1-x}
On differentiating both sides and multiplying by x, we get
\sum_{n = 0}^{\infty}n{x}^{n} = \frac{x}{(1-x)^{2}}
Putting the result obtained in (3) back in our derivation (1), we get
= O(n * \frac{\frac{1}{2}}{(1 - \frac{1}{2})^2})= O(n * 2)= O(n)
Hence Proved that the Time complexity for Building a Binary Heap is O(n)
.
Advantages of Heap Data Structure:Efficient insertion and deletion: The heap data structure allows efficient insertion and deletion of elements. When a new element is added to the heap, it is placed at the bottom of the heap and moved up to its correct position using the heapify operation. Similarly, when an element is removed from the heap, it is replaced by the bottom element, and the heap is restructured using the heapify operation.Efficient priority queue: The heap data structure is commonly used to implement a priority queue, where the highest priority element is always at the top of the heap. The heap allows constant-time access to the highest priority element, making it an efficient data structure for implementing priority queues.Guaranteed access to the maximum or minimum element: In a max-heap, the top element is always the maximum element, and in a min-heap, the top element is always the minimum element. This provides guaranteed access to the maximum or minimum element in the heap, making it useful in algorithms that require access to the extreme values.Space efficiency: The heap data structure requires less memory compared to other data structures, such as linked lists or arrays, as it stores elements in a complete binary tree structure.Heap-sort algorithm: The heap data structure forms the basis for the heap-sort algorithm, which is an efficient sorting algorithm that has a worst-case time complexity of O(n log n).Disadvantages of Heap Data Structure:Lack of flexibility: The heap data structure is not very flexible, as it is designed to maintain a specific order of elements. This means that it may not be suitable for some applications that require more flexible data structures.Not ideal for searching: While the heap data structure allows efficient access to the top element, it is not ideal for searching for a specific element in the heap. Searching for an element in a heap requires traversing the entire tree, which has a time complexity of O(n).Not a stable data structure: The heap data structure is not a stable data structure, which means that the relative order of equal elements may not be preserved when the heap is constructed or modified.Memory management: The heap data structure requires dynamic memory allocation, which can be a challenge in some systems with limited memory. In addition, managing the memory allocated to the heap can be complex and error-prone.Complexity: While the heap data structure allows efficient insertion, deletion, and priority queue implementation, it has a worst-case time complexity of O(n log n), which may not be optimal for some applications that require faster algorithms.Previously Asked GATE Questions on Binary HeapQuestion 1: The elements 32, 15, 20, 30, 12, 25, 16 are inserted one by one in the given order into a Max Heap. The resultant Max Heap is.
Answer: (a)Question 2: In a heap with n elements with the smallest element at the root, the 7th smallest element can be found in time (GATE CS 2003)
a) Θ(n log n)b) Θ(n)c) Θ(log n)d) Θ(1)
Answer: (d)Explanation:The 7th smallest element must be in first 7 levels. Total number of nodes in any Binary Heap in first 7 levels is at most 1 + 2 + 4 + 8 + 16 + 32 + 64 which is a constant. Therefore we can always find 7th smallest element in Θ(1) time.
Question 3: The number of elements that can be sorted in Θ(logn) time using heap sort is
(a) Θ(1)(b) Θ(sqrt(logn))(c) Θ(Log n/(Log Log n))(d) Θ(Log n)
Answer: (c)Explanation: Time complexity of Heap Sort is Θ(mLogm) for m input elements. For m = Θ(Log n/(Log Log n)), the value of Θ(m * Logm) will be Θ( [Log n/(Log Log n)] * [Log (Log n/(Log Log n))] ) which will be Θ( [Log n/(Log Log n)] * [ Log Log n - Log Log Log n] ) which is Θ(Log n)
Question 4: A max-heap is a heap where the value of each parent is greater than or equal to the values of its children. Which of the following is a max-heap?
Answer: (B)A binary tree is max-heap if it is a complete binary tree (A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible) and it follows the max-heap property (value of each parent is greater than or equal to the values of its children).
A) is not a max-heap because it is not a complete binary treeB) is a max-heap because it is complete binary tree and follows max-heap property.C) is not a max-heap because 8 is a chile of 5 in this tree, so violates the max-heap property.D) is not a max-heap because 8 is a chile of 5 in this tree, so violates the max-heap property. There are many other nodes in this tree which violate max-heap property in this tree
Question 5: A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property.
Which one of the following is a valid sequence of elements in an array representing 3-ary max heap?(a) 1, 3, 5, 6, 8, 9(b) 9, 6, 3, 1, 8, 5(c) 9, 3, 6, 8, 5, 1(d) 9, 5, 6, 8, 3, 1
Answer: (d)
Question 6: Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3- ary max heap found in the above question, Which one of the following is the sequence of items in the array representing the resultant heap?
(a) 10, 7, 9, 8, 3, 1, 5, 2, 6, 4(b) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1(c) 10, 9, 4, 5, 7, 6, 8, 2, 1, 3(d) 10, 8, 6, 9, 7, 2, 3, 4, 1, 5
Answer: (a)
Question 7: Consider the process of inserting an element into a Max Heap, where the Max Heap is represented by an array. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of comparisons performed is:
(a) Θ(logn) (b) Θ(LogLogn ) (c) Θ(n) (d) Θ(nLogn)
Answer: (b)Explanation: The height of a Max Heap is Θ(logn). If we perform binary search for finding the correct position then we need to do Θ(LogLogn) comparisons.
Question 8: In a binary max heap containing n numbers, the smallest element can be found in time (GATE CS 2006)
(a) 0(n)(b) O(logn)(c) 0(loglogn)(d) 0(1)
Answer: (a)
In a max heap, the smallest element is always present at a leaf node. So we need to check for all leaf nodes for the minimum value. Worst case complexity will be O(n)
12 / \ / \ 8 7 / \ / \ / \ / \2 3 4 5Question 9: A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is:
(a) 10, 8, 7, 3, 2, 1, 5(b) 10, 8, 7, 2, 3, 1, 5(c) 10, 8, 7, 1, 2, 3, 5(d) 10, 8, 7, 5, 3, 2, 1
Answer: (a)
Question 10: Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4.
Array Index
1
2
3
4
5
6
7
8
9
Value
40
30
20
10
15
16
17
8
7
Now consider that a value 35 is inserted into this heap. After insertion, the new heap is
(a) 40, 30, 20, 10, 15, 16, 17, 8, 4, 35(b) 40, 35, 20, 10, 30, 16, 17, 8, 4, 15(c) 40, 30, 20, 10, 35, 16, 17, 8, 4, 15(d) 40, 35, 20, 10, 15, 16, 17, 8, 4, 30
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04 Dec, 2023 | Searching and Sorting Algorithm Notes for GATE Exam [2024]
04 Dec, 2023
As you gear up for the GATE Exam 2024, it's time to dive into the world of searching and sorting algorithms. Think of these algorithms as the super-smart tools that help computers find stuff quickly and organize data neatly. These notes are here to guide you through the ins and outs of these algorithms, breaking down how they work, when to use them, and why they're essential for acing the GATE exam.
Table of Content
Introduction to Searching Algorithm:Types of Searching Algorithm:Introduction to Sorting Algorithm:Types of Sorting Algorithm:Previously Asked Problems of Searching and Sorting on GATE:Introduction to Searching Algorithm:Searching Algorithms are designed to check for an element or retrieve an element from any data structure where it is stored. Searching algorithms are methods or procedures that are used to locate a specific item or element within a set of data. These algorithms are widely used in computer science and are essential for tasks such as searching for a specific record in a database, locating an element in a sorted list, and locating a file on a computer.
Types of Searching Algorithm:1. Linear Search:Linear Search is defined as a sequential search algorithm that starts at one end and goes through each element of a list until the desired element is found otherwise, the search continues till the end of the data set.
Key Points:Linear search, also known as sequential search, is a simple searching algorithm.It sequentially checks each element of the list until a match is found or the entire list has been searched.The Time Complexity of Linear search is O(n), where 'n' is the number of elements in the list.In the worst case, a linear search may have to scan the entire list.Linear search is efficient for small lists, but its efficiency decreases for larger lists.Linear search can be applied to any collection of elements that can be traversed sequentially, such as arrays or linked lists.Linear Search2. Binary Search:Binary Search is defined as a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log N).
Key Points:Binary search is a divide-and-conquer algorithm used for searching in sorted lists.It repeatedly divides the search interval in half until the target element is found or the interval is empty.The list must be sorted for binary search to work effectively.Time Complexity of Binary Search is O(log n), where 'n' is the number of elements in the list.Binary search is more efficient than linear search for large, sorted datasets.Binary search is highly efficient, especially for large datasets, as it reduces the search space exponentially with each step.Binary SearchLinear Search vs Binary Search:Linear Search
Binary Search
In linear search input data need not to be in sorted.In binary search input data need to be in sorted order.It is also called sequential search.It is also called half-interval search.The time complexity of linear search O(n). The time complexity of binary search O(log n).Multidimensional array can be used.Only single dimensional array is used.Linear search performs equality comparisonsBinary search performs ordering comparisonsIt is less complex.It is more complex.It is very slow process.It is very fast process.Introduction to Sorting Algorithm:A Sorting Algorithm is used to rearrange a given array or list of elements according to a comparison operator on the elements. The comparison operator is used to decide the new order of elements in the respective data structure.
Types of Sorting Algorithm:1. Selection Sort:Selection sort is a simple and efficient sorting algorithm that works by repeatedly selecting the smallest (or largest) element from the unsorted portion of the list and moving it to the sorted portion of the list.
The algorithm repeatedly selects the smallest (or largest) element from the unsorted portion of the list and swaps it with the first element of the unsorted part. This process is repeated for the remaining unsorted portion until the entire list is sorted.
Key Points:Selection sort is a comparison-based sorting algorithm.It divides the input list into a sorted and an unsorted region. In each iteration, it selects the smallest (or largest, depending on the order) element from the unsorted region and swaps it with the first unsorted element.Selection sort is an in-place sorting algorithm, meaning it doesn't require additional memory space for sorting.Selection sort is not stable. Stable sorting algorithms maintain the relative order of equal elements in the sorted output.The time complexity of selection sort is O(n2), where 'n' is the number of elements in the list.Selection sort is simple but less efficient than some other sorting algorithms like merge sort or quicksort, especially for large datasets.2. Bubble Sort:Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity is quite high.
Key Points:Bubble sort is a simple comparison-based sorting algorithm.It repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. This process is repeated until the list is sorted.Bubble sort is an in-place sorting algorithm, meaning it doesn't require additional memory space for sorting.Bubble sort is stable. Stable sorting algorithms maintain the relative order of equal elements in the sorted output.The time complexity of bubble sort is O(n2), where 'n' is the number of elements in the list.3. Insertion Sort:Insertion sort is a simple sorting algorithm that works similar to the way you sort playing cards in your hands. The array is virtually split into a sorted and an unsorted part. Values from the unsorted part are picked and placed at the correct position in the sorted part.
Key Points:Insertion sort is a simple comparison-based sorting algorithm.It builds the final sorted array one element at a time. It takes each element from the unsorted part of the array and inserts it into its correct position in the sorted part.Insertion sort is an in-place sorting algorithm, meaning it doesn't require additional memory space for sorting.Insertion sort is stable. Stable sorting algorithms maintain the relative order of equal elements in the sorted output.The time complexity of insertion sort is O(n2) in the worst case, where 'n' is the number of elements in the list.Insertion Sort4. Merge Sort:Merge sort is defined as a sorting algorithm that works by dividing an array into smaller subarrays, sorting each subarray, and then merging the sorted subarrays back together to form the final sorted array.
In simple terms, we can say that the process of merge sort is to divide the array into two halves, sort each half, and then merge the sorted halves back together. This process is repeated until the entire array is sorted.
Key Points:Merge sort is a divide-and-conquer algorithm used for sorting.It divides the unsorted list into 'n' sublists, each containing one element, and then repeatedly merges sublists to produce new sorted sublists until there is only one sublist remaining.Merge sort follows the divide-and-conquer strategy, breaking the problem into smaller subproblems, solving them independently, and then combining the solutions.Merge sort is stable. Stable sorting algorithms maintain the relative order of equal elements in the sorted output.The time complexity of merge sort is O(n log n), where 'n' is the number of elements in the list.Merge sort has a space complexity of O(n) as it requires additional space for merging.5. Quick Sort:QuickSort is a sorting algorithm based on the Divide and Conquer algorithm that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array.
Key Points:QuickSort follows the divide-and-conquer strategy, breaking the problem into smaller subproblems, solving them independently, and then combining the solutions.It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays according to whether they are less than or greater than the pivot. The process is then applied recursively to the sub-arrays.QuickSort is an in-place sorting algorithm, meaning it doesn't require additional memory space for sorting.The average and best-case time complexity of QuickSort is O(n log n), where 'n' is the number of elements in the list.The worst-case time complexity is O(n2), but this is rare and can be mitigated by using various strategies for pivot selection.QuickSort has a space complexity of O(log n) due to the recursive nature of the algorithm.6. Heap Sort:Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Key Points:Heap Sort is a comparison-based sorting algorithm that uses a binary heap data structure.It builds a binary heap from the input data and repeatedly extracts the maximum (for max-heap) or minimum (for min-heap) element from the heap and reconstructs the heap until the entire input is sorted.Heap Sort is an in-place sorting algorithm, meaning it doesn't require additional memory space for sorting, apart from a small constant amount.The time complexity of Heap Sort is O(n log n), where 'n' is the number of elements in the list.Heap Sort has a space complexity of O(1) because it uses a constant amount of extra space.7. Counting Sort:Counting Sort is a non-comparison-based sorting algorithm that works well when there is limited range of input values. It is particularly efficient when the range of input values is small compared to the number of elements to be sorted. The basic idea behind Counting Sort is to count the frequency of each distinct element in the input array and use that information to place the elements in their correct sorted positions.
Key Points:Counting Sort is an integer sorting algorithm.It works by counting the number of occurrences of each element and then using this information to reconstruct a sorted sequence.Counting Sort is stable. Stable sorting algorithms maintain the relative order of equal elements in the sorted output.The time complexity of Counting Sort is O(n + k), where 'n' is the number of elements in the list, and 'k' is the range of input values.Counting Sort has a space complexity of O(k), where 'k' is the range of input values. Additional space is required for the count array.Previously Asked Problems of Searching and Sorting on GATE:Question 1. [GATE-CS-2019]An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is ___.
Answer: 0.08
Question 2. [GATE-CS-2016] Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascending order, which of the following are TRUE?
I. Quicksort runs in Θ(n2) timeII. Bubble sort runs in Θ(n2) timeIII. Mergesort runs in Θ(n) timeIV. Insertion sort runs in Θ(n) time
(A) I and II only(B) I and III only(C) II and IV only(D) I and IV only
Answer: (D) I and IV only
Question 3. [GATE-CS-2015]Assume that a mergesort algorithm, in the worst case, takes 30 seconds for an input of size 64. Which of the following most closely approximates the maximum input size of a problem that can be solved in 6 minutes?
(A) 256(B) 512(C) 1024(D) 2048
Answer: (B) 512
Question 4. [GATE-CS-1996] The average number of key comparisons done in a successful sequential search in a list of length n is
(A) log n(B) (n-1)/2(C) n/2(D) (n+1)/2
Answer: (D) (n+1)/2
Question 5. [GATE-CS-2006]Which one of the following in place sorting algorithms needs the minimum number of swaps?
(A) Quick Sort(B) Insertion Sort(C) Selection Sort(D) Heap Sort
Answer: (C) Selection Sort
Question 6. [GATE-CS-1994]The recurrence relation that can arise in relation to the complexity of the binary search algorithm is:
(A) T(n) = 2T(n/2) + c, where c is constant.(B) T(n) = T(n/2) + c, where c is constant.(C) T(n) = T(n/2) + log n.(D) T(n) = T(n/2) + n.
Answer: (B) T(n) = T(n/2) + c, where c is constant.
Question 7. [GATE-CS-2013]Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes?
(A) O(1)(B) O(log n)(C) O(n)(D) O(n log n)
Answer: (C) O(n)
Question 8. [GATE-CS-2013] Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H, and wish to sum up all the numbers in T that lie between L and H. Suppose there are m such numbers in T. If the tightest upper bound on time to compute the sum is 0(na logbn + mc logdn), the value of a + 10b + 100c + 1000d is __.
Answer: 110
Question 9. [GATE-CS-2009]What is the number of swaps required to sort n elements using selection sort, in the worst case?
(A) O(n)(B) O(nlogn)(C) O(n2)(D) O(n2logn)
Answer: (A) O(n)
Question 10. [GATE-CS-2007]Which of the following sorting algorithms has the lowest worst-case complexity?
(A) Merge Sort(B) Bubble Sort(C) Quick Sort(D) Selection Sort
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06 Dec, 2023 | Recursion Notes for GATE Exam [2024]
06 Dec, 2023
This Recursion Notes for the GATE Exam provides a comprehensive guide to one of the fundamental concepts in computer science, recursion, specifically tailored for those preparing for the Graduate Aptitude Test in Engineering (GATE). Recursion is a powerful problem-solving technique where a function calls itself during its execution, and it plays a significant role in algorithm design and programming.
Table of Content
Introduction to RecursionNeed of RecursionTypes of RecursionDirect RecursionIndirect RecursionGate Previous Year Problems on RecursionIntroduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. Using a recursive algorithm, certain problems can be solved quite easily. Examples of such problems are Towers of Hanoi (TOH), Inorder/Preorder/Postorder Tree Traversals, DFS of Graph, etc. A recursive function solves a particular problem by calling a copy of itself and solving smaller subproblems of the original problems.
Need of RecursionRecursion is an amazing technique with the help of which we can reduce the length of our code and make it easier to read and write. It has certain advantages over the iteration technique which will be discussed later. A task that can be defined with its similar subtask, recursion is one of the best solutions for it. For example; The Factorial of a number.
Types of RecursionRecursion are mainly of two types depending on whether a function calls itself from within itself or more than one function call one another mutually. The first one is called direct recursion and another one is called indirect recursion. Thus, the two types of recursion are:
Direct RecursionDirect recursion occurs when a function directly calls itself within the same function. Direct Recursion can be further categorized into four types:
Tail Recursion If a recursive function calling itself and that recursive call is the last statement in the function then it’s known as Tail Recursion. After that call the recursive function performs nothing. The function has to process or perform any operation at the time of calling and it does nothing at returning time.
Tail Recursion
Time Complexity For Tail Recursion : O(n) Space Complexity For Tail Recursion : O(n)
Head RecursionIf a recursive function calling itself and that recursive call is the first statement in the function then it’s known as Head Recursion. There’s no statement, no operation before the call. The function doesn’t have to process or perform any operation at the time of calling and all operations are done at returning time.
Head Recursion
Time Complexity For Head Recursion: O(n) Space Complexity For Head Recursion: O(n)
Tree Recursion: To understand Tree Recursion let’s first understand Linear Recursion. If a recursive function calling itself for one time then it’s known as Linear Recursion. Otherwise if a recursive function calling itself for more than one time then it’s known as Tree Recursion.
Time Complexity For Tree Recursion: O(2^n) Space Complexity For Tree Recursion: O(n)
Nested Recursion: In this recursion, a recursive function will pass the parameter as a recursive call. That means “recursion inside recursion”. Let see the example to understand this recursion.
Indirect RecursionIn this recursion, there may be more than one functions and they are calling one another in a circular manner.
From the above diagram fun(A) is calling for fun(B), fun(B) is calling for fun(C) and fun(C) is calling for fun(A) and thus it makes a cycle.
Gate Previous Year Problems on RecursionQuestion 1: In the C language: [GATE 2002: 2 marks]
(A). At most one activation record exists between the current activation record and the activation record for the main.
(B). The number of activation records between the current activation record and the activation records from the main depends on the actual function calling sequence.
(C). The visibility of global variables depends on the actual function calling sequence
(D). Recursion requires the activation record for the recursive function to be saved in a different stack before the recursive function can be called.
Solution: Correct answer is (B)
Explanation:
A→Incorrect, There is no such restriction in the C language
B→ Correct
C→ Incorrect. In C, variables are statically scoped, not dynamically.
D→Incorrect. The activation records are stored on the same stack.
Question 2: Consider the following recursive C function that takes two arguments:
unsigned int foo (unsigned int n, unsigned int r) {
if (n > 0) return((n % r) + foo(n/r, r));
else return 0;
}
What is the return value of the function foo when it is called as foo (513, 2)? [GATE 2011: 2 marks]
(A). 9
(B). 8
(C). 5
(D). 2
Solution: Correct answer is (D)
Explanation
The function call foo(513, 2) will return 1 + foo(256, 2). All subsequent recursive function calls (including foo(256, 2)) will return 0 + foo(n/2, 2) except the last function call foo(1, 2) . The last call foo(1, 2) returns 1. So, the value returned by call foo(513, 2) is 1 + 0 + 0…. + 0 + 1.The function call foo(n, 2) returns the sum of bits (or count of set bits) in the number n.
Question 3: Choose the correct option to fill ? 1 and ? 2 so that the program below prints an input string in reverse order. Assume that the input string is terminated by a newline character.
void recerse (void) {
int c;
if (?1) reverse() ;
?2
}
main {
printf ("Enter Text" );
printf("\n");
reverse() ;
printf("\n") ;
}
What does f(173) print? [GATE 2008: 2 marks]
(A). ?1 is (getchar() != ’\n’)
?2 is getchar(c);
(B). ?1 is (c = getchar() ) != ’\n’)
?2 is getchar(c);
(C). ?1 is (c != ’\n’)
?2 is putchar(c);
(D). ?1 is ((c = getchar()) != ’\n’)
?2 is putchar(c);
Solution: Correct answer is (D)
Explanation:
As given in the question, the '=' operator has less priority than the '!=' operator in the c program. So (c=getchar()) has to be in brackets and after reversing the string, we use the function putchar(c) for printing the character.
So, option (D) is the correct answer.
Question 4: Consider the following recursive C function that takes two arguments.
unsigned int foo(unsigned int n, unsigned int r)
{
if(n>0) return((n%r)+foo(n/r,r));
else return 0;
}
What is the return value of the function foo when it is called as foo(345,10)? [GATE 2011: 2 marks]
(A). 345
(B). 12
(C). 5
(D). 3
Solution: Correct answer is (B)
Explanation:
The function call foo(345, 10) returns sum of decimal digits (because r is 10) in the number n.And Sum of digits for number (n) 345 is 3 + 4 + 5 = 12.
Question 5: Consider the following recursive C function:
int f(int n)
{
static int r = 0;
if(n <= 0) return 1;
if(n>3)
{
r = n;
return f(n-2)+2;
}
return f(n-1)+r;
}
What is the value of f(5)? [GATE 2008: 2 marks]
(A). 5
(B). 7
(C). 9
(D). 18
Solution: Correct answer is (D)
Explanation:
f(5) = f(3)+2
The line "r = n" takes the value of r to 5. Since r is static, its value is shared be all subsequence calls. Also, all subsequent calls don't change r because the statement "r = n" is in a if condition with n > 3.
f(3) = f(2)+5
f(2) = f(1)+5
f(1) = f(0)+5
f(0) = 1
So f(5) = 1+5+5+5+2 = 18
Question 6: Consider the following function written in the C programming language.
void foo(char *a){
if ( *a && *a != ' '){
foo(a+1);
putchar(*a);
}
}
The output of the above function on input “ABCD EFGH” is [GATE 2015: 2 marks]
(A). ABCD EFGH
(B). ABCD
(C). HGFE DCBA
(D). DCBA
Solution: Correct answer is (D)
Explanation:
The priority of != is greater than that of && in C program. The execution happens as: if ((*a) && (*a != ' '))
So, the if condition breaks either when ∗a=0 (not '0' but ASCII 0 or null character'\0'), or when ∗a=' '.
So, the recursive call goes like
'A' - 'B' - 'C' - 'D' -' ' (breaks) and then starts outputting
DCBA
Question 7: What will be the output of the following C program segment?Char inchar = 'A'; [GATE 2012: 2 marks]
Switch ( inchar ) {
case 'A' : printf ("Choice A\ n") ;
case 'B' :
case 'C' : printf (“Choice B”) ;
case 'D' :
case 'E' :
default : printf ( " No Choice" ) ; }
(A). No Choice
(B). Choice A
(C). Choise A Choise B No Choice
(D). Program gives no output as it is erroneous
Solution: Correct answer is (C)
Explanation:
Since there is no break statement in any case so all the cases will be executed and the answer will be an option(c).
Question 8: Which one of the following are essential features of an object-oriented programming language? [GATE 2005: 2 marks]i) Abstraction and encapsulation
ii) Strictly-typedness
iii) Type-safe property coupled with sub-type rule
iv) Polymorphism in the presence of inheritance
(A). (i) and (ii) only
(B). (i) and (iv) only
(C). (i), (ii) and (iv) only
(D). (i), (iii) and (iv) only
Solution: Correct answer is (B)
Explanation: Abstraction, Encapsulation, Polymorphism and Inheritance are the essential features of a OOP Language.
Question 9: An Abstract Data Type (ADT) is [GATE 2005: 2 marks]
(A). Same as an abstract class.
(B). A data type that cannot be instantiated
(C). A data type for which only the operations defined on it can be used, but none else
(D). All of the above
Solution: Correct answer is (C)
Explanation:
An abstract data type (ADT) supports only the operations which are defined.
An abstract class is one that may not have definitions of all the objects it has. Moreover, it can not be instantiated. To instantiate we have to create a subclass and then instantiate the class.
Question 10: Consider the following C function. [GATE 2003: 2 marks]
float f,(float x, int y) {
float p, s; int i;
for (s=1,p=1,i=1; i < y; i++) {
p *= x/i;
s+=p;
}
return s;
}
For large values of y, the return value of the function f best approximates
(A). x^y
(B). e^x
(C). ln(1 + x)
(D). x^x
Solution: Correct answer is (B)
Explanation:
i=1 then p=x & s=1+x
i=2 then p=x2/2 & s=1+x+x2/2
As y goes to infinity s tends to ex.
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11 Mar, 2024 | Divide and Conquer Notes for GATE Exam [2024]
11 Mar, 2024
Those preparing for the GATE (Graduate Aptitude Test in Engineering) exam in 2024 face many algorithmic challenges. Among the various algorithmic paradigms, "Divide and Conquer" stands out as a powerful approach to problem-solving. In this comprehensive guide for the GATE Exam, Divide and Conquer, and its applications will be explored through a range of important topics. These notes aim to provide a solid foundation for mastering these concepts in preparation for the upcoming GATE exam.
Table of Content
Introduction to Divide and ConquerApplication of Divide & Conquer in Binary SearchApplication of Divide & Conquer in Merge SortApplication of Divide & Conquer in Quick SortStandard Problems that uses Divide and Conquer AlgorithmAdvantages of Divide and Conquer AlgorithmDisadvantages of Divide and Conquer AlgorithmPreviously Asked GATE Questions on Divide and ConquerIntroduction to Divide and Conquer:Divide and Conquer is an algorithmic paradigm in which the problem is solved using the Divide, Conquer, and Combine strategy.
A typical Divide and Conquer algorithm solves a problem using following three steps:
Divide: This involves dividing the problem into smaller sub-problems.Conquer: Solve sub-problems by calling recursively until solved.Combine: Combine the sub-problems to get the final solution of the whole problem.Below are different algorithms which are based on Divide and Conquer:
Application of Divide & Conquer in Binary Search:Binary Search is a search algorithm that efficiently finds a target value within a sorted array. It repeatedly divides the search space in half until the target is found or the search space is empty.
Algorithm Steps:
Initialize low, high, and mid indices.Compare the target with the element at the mid index.If the target is found, return the index.If the target is smaller, update the high index to mid - 1.If the target is larger, update the low index to mid + 1.Repeat the process until the target is found or the search space is empty.Binary SearchApplication of Divide & Conquer in Merge Sort:Merge Sort is a divide-and-conquer sorting algorithm that recursively divides an array into two halves, sorts each half, and then merges them to produce a sorted array.
Algorithm Steps:
Divide the unsorted array into two halves.Recursively apply Merge Sort to each half.Merge the sorted halves to produce a sorted array.
Time Complexity:
Worst Case: O(n log n)Best Case: O(n log n)Average Case: O(n log n)Space Complexity: O(n), additional space for the temporary array used in the merge step.
Application of Divide & Conquer in Quick Sort:QuickSort is a sorting algorithm based on the Divide and Conquer algorithm that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array.
The key process in quickSort is a partition(). The target of partitions is to place the pivot (any element can be chosen to be a pivot) at its correct position in the sorted array and put all smaller elements to the left of the pivot, and all greater elements to the right of the pivot.Partition is done recursively on each side of the pivot after the pivot is placed in its correct position and this finally sorts the array.
Choice of Pivot:
There are many different choices for picking pivots.
Always pick the first element as a pivot.Always pick the last element as a pivotPick a random element as a pivot.Pick the middle as the pivot.Time Complexity:
Worst Case: O(n^2), occurs when the pivot selection consistently results in unbalanced partitions.Best Case: O(n log n), occurs when the pivot selection consistently results in balanced partitions.Average Case: O(n log n)Space Complexity: O(log n), for the recursive call stack.
Standard Problems that uses Divide and Conquer Algorithm:1. Merge Sort for Linked List:Merge Sort can be adapted for linked lists. It follows the same divide-and-conquer approach, dividing the linked list into two halves, recursively sorting each half, and then merging them.
Algorithm Steps:
If the list is empty or has one element, it is already sorted.Split the linked list into two halves.Recursively sort each half.Merge the sorted halves.2. How to make Merge Sort to perform O(n) comparisons in best case?Optimizing Merge Sort to perform O(n) comparisons in the best case involves detecting if the input is already sorted and skipping unnecessary merging steps.
Algorithm Steps:
Check if the input is already sorted.If sorted, skip merging and return the sorted array.Otherwise, proceed with the standard Merge Sort algorithm.3. Iterative Quick Sort:An iterative version of QuickSort uses a stack to eliminate the need for recursion. It follows the same steps as the recursive version but utilizes a stack data structure.
Algorithm Steps:
Create an empty stack and push the initial values onto it.Perform iterations until the stack is empty.Pop values from the stack, partition, and push the indices of the subarrays.4. Quick Sort on Singly Linked List:Adapting QuickSort for singly linked lists involves partitioning the list based on a pivot, similar to the array version.
Algorithm Steps:
Select a pivot from the list.Partition the list around the pivot.Recursively apply QuickSort to the partitions.5. Median of Two Sorted ArraysFinding the median of two sorted arrays involves merging the arrays and finding the middle element.
Algorithm Steps:
Merge the two sorted arrays.If the total length is odd, return the middle element.If the total length is even, return the average of the two middle elements.6. Count Inversions in an Array Using Merge SortCounting inversions in an array involves determining the number of pairs of indices (i, j) such that i < j and array[i] > array[j].
Algorithm Steps:
Apply Merge Sort while counting inversions during the merging step.Merge the two halves, counting inversions when elements from the second half are chosen.7. Closest Pair of PointsThe Closest Pair of Points problem involves finding the pair of points with the smallest Euclidean distance among a set of points.
Algorithm Steps:
Sort the points by their x-coordinates.Recursively find the closest pairs in the left and right halves.Check for a closer pair that spans the two halves.8. Strassen’s Matrix MultiplicationStrassen's Matrix Multiplication is a divide-and-conquer algorithm for multiplying matrices more efficiently than the standard method.
Algorithm Steps:
Split the input matrices into submatrices.Recursively compute seven products.Combine the products to form the result.9. Sort a Nearly Sorted (or K Sorted) ArraySorting a nearly sorted array involves efficiently sorting an array where each element is at most k positions away from its final sorted position.
Algorithm Steps:
Create a min-heap of size k + 1.Insert the first k + 1 elements into the heap.Extract the minimum and insert the next element from the array.10. Search in an Almost Sorted ArraySearching in an almost sorted array involves finding the position of an element in an array where each element is at most k positions away from its final sorted position.
Algorithm Steps:
Use a modified binary search to find the element.Compare the element with adjacent elements within the range of k.11. K-th Element of Two Sorted ArraysFinding the k-th element in two sorted arrays involves comparing the medians of the two arrays and eliminating half of the elements.
Algorithm Steps:
Compare the medians of the two arrays.Eliminate the half that cannot contain the k-th element.Repeat the process until the k-th element is found.12. K’th Smallest/Largest Element in Unsorted ArrayFinding the k-th smallest or largest element in an unsorted array involves using QuickSelect, a variation of QuickSort.
Algorithm Steps:
Choose a pivot and partition the array.Recursively apply QuickSelect to the relevant partition.Adjust the value of k based on the partitioning.Time Complexity of Divide and Conquer Algorithm:Advantages of Divide and Conquer Algorithm:It divides the entire problem into subproblems thus it can be solved parallelly ensuring multiprocessingEfficiently uses cache memory without occupying much space.Reduces time complexity of the problem.Disadvantages of Divide and Conquer Algorithm:It may crash the system if the recursion is performed rigorously.The process of dividing the problem into subproblems and then combining the solutions can require additional time and resources. Complexity: Dividing a problem into smaller subproblems can increase the complexity of the overall solution. When working with large data sets, the memory requirements for storing the intermediate results of the subproblems can become a limiting factor.Previously Asked GATE Questions on Divide and Conquer: Question 1: Which of the following algorithms is NOT a divide & conquer algorithm by nature?
(A) Euclidean algorithm to compute the greatest common divisor(B) Heap Sort(C) Cooley-Tukey fast Fourier transform(D) Quick Sort
Answer: (B)Explanation: See Divide and Conquer
Question 2: Consider the following C program
C
int main()
{
int x, y, m, n;
scanf("%d %d", &x, &y);
/* x > 0 and y > 0 */
m = x;
n = y;
while (m != n) {
if (m > n)
m = m - n;
else
n = n - m;
}
printf("%d", n);
}
What does the program compute?
(A) x + y using repeated subtraction(B) x mod y using repeated subtraction(C) the greatest common divisor of x and y(D) the least common multiple of x and y
Answer: (C)Explanation: This is an implementation of Euclid’s algorithm to find GCD
Question 3: Consider the polynomial p(x) = a0 + a1x + a2x^2 +a3x^3, where ai != 0, for all i. The minimum number of multiplications needed to evaluate p on an input x is:
(A) 3(B) 4(C) 6(D) 9
Answer: (A)Explanation: Multiplications can be minimized using following order for evaluation of the given expression. p(x) = a0 + x(a1 + x(a2 + a3x))
Question 4: Maximum Subarray Sum problem is to find the subarray with maximum sum. For example, given an array {12, -13, -5, 25, -20, 30, 10}, the maximum subarray sum is 45. The naive solution for this problem is to calculate sum of all subarrays starting with every element and return the maximum of all. We can solve this using Divide and Conquer, what will be the worst case time complexity using Divide and Conquer?
(A) O(n)(B) O(nLogn)(C) O(Logn)(D) O(n^2)
Answer: O(B)Explanation: See http://www.geeksforgeeks.org/divide-and-conquer-maximum-sum-subarray/
Question 5: Consider a situation where you don't have function to calculate power (pow() function in C) and you need to calculate x^n where x can be any number and n is a positive integer. What can be the best possible time complexity of your power function?
(A) O(n)(B) O(nLogn)(C) O(LogLogn)(D) O(Logn)
Answer: (D)Explanation: We can calculate power using divide and conquer in O(Logn) time.
Question 6: Consider the problem of searching an element x in an array 'arr[]' of size n. The problem can be solved in O(Logn) time if. 1) Array is sorted 2) Array is sorted and rotated by k. k is given to you and k <= n 3) Array is sorted and rotated by k. k is NOT given to you and k <= n 4) Array is not sorted
(A) 1 Only(B) 1 & 2 only(C) 1, 2 and 3 only(D) 1, 2, 3 and 4
Answer: (C)Explanation: See http://www.geeksforgeeks.org/search-an-element-in-a-sorted-and-pivoted-array/
Question 7: Consider the problem of computing min-max in an unsorted array where min and max are minimum and maximum elements of array. Algorithm A1 can compute min-max in a1 comparisons without divide and conquer. Algorithm A2 can compute min-max in a2 comparisons by scanning the array linearly. What could be the relation between a1 and a2 considering the worst case scenarios?
(A) a1 < a2(B) a1 > a2(C) a1 = a2(D) Depends on the input
Answer: (B)Explanation: When Divide and Conquer is used to find the minimum-maximum element in an array, Recurrence relation for the number of comparisons isT(n) = 2T(n/2) + 2 where 2 is for comparing the minimums as well the maximums of the left and right subarraysOn solving, T(n) = 1.5n - 2.While doing linear scan, it would take 2*(n-1) comparisons in the worst case to find both minimum as well maximum in one pass.
Question 8: Let P be an array containing n integers. Let t be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of n elements. Which one of the following choices is correct?
(A) t>2n−2 (B) t>3⌈n/2⌉ and t≤2n−2(C) t>n and t≤3⌈n/2⌉(D) t>⌈log2(n)⌉ and t≤n
Answer: (B)Explanation: It will take t≤2n−2 comparisons without divide and conquer technique. It will take t≤ 3⌈n/2⌉ - 2 with divide and conquer technique.
Question 9: A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?
(A) Θ(nlogn)(B) Θ(n)(C) Θ(logn)(D) Θ(1)
Answer: (D) Explanation: Pick any two elements from the root, and return minimum of these two. So, time is Θ(1).
Question 10: Consider the following array.
Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order?
(A) Selection sort(B) Mergesort(C) Insertion sort(D) Quicksort using the last element as pivot
Answer: (C)Explanation: Since, given array is almost sorted in ascending order, so Insertion sort will give its best case with time complexity of order O(n). | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic 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04 Dec, 2023 | Greedy Algorithm Notes for GATE Exam [2024]
04 Dec, 2023
In the dynamic landscape of algorithmic design, Greedy Algorithms stand out as powerful tools for solving optimization problems. Aspirants preparing for the GATE Exam 2024 are poised to encounter a range of questions that test their understanding of Greedy Algorithms. These notes aim to provide a concise and insightful overview, unraveling the principles and applications of Greedy Algorithms that are likely to be scrutinized in the upcoming GATE examination.Table of Content
Introduction to Greedy Algorithms:Activity Selection Problem:Job Sequencing ProblemHuffman CodingKruskal’s Minimum Spanning Tree AlgorithmDijkstra’s shortest path algorithmMCQ Questions for Greedy AlgorithmIntroduction to Greedy Algorithms:What is Greedy Algorithm?
Greedy is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. So the problems where choosing locally optimal also leads to global solution are the best fit for Greedy.
Characteristics of Greedy algorithm:
For a problem to be solved using the Greedy approach, it must follow a few major characteristics:
There is an ordered list of resources(profit, cost, value, etc.) Maximum of all the resources(max profit, max value, etc.) are taken. For example, in the fractional knapsack problem, the maximum value/weight is taken first according to available capacity. Examples of Greedy Algorithm :
Some Famous problems that exhibit Optimal substructure property and can be solved using Greedy approach are :
Job sequencing ProblemFractional Knapsack ProblemPrim’s algorithm to find Minimum Spanning TreeActivity Selection ProblemDijkstra’s shortest path algorithmAdvantages of the Greedy Approach:
The greedy approach is easy to implement and typically have less time complexity.Greedy algorithms can produce efficient solutions in many cases, especially when the problem has a substructure that exhibits the greedy choice property.Greedy algorithms are often faster than other optimization algorithms, such as dynamic programming or branch and bound, because they require less computation and memory.The greedy approach can be applied to a wide range of problems, including problems in computer science, operations research, economics, and other fields.The greedy approach can be used to solve problems in real-time, such as scheduling problems or resource allocation problems, because it does not require the solution to be computed in advance.Greedy algorithms can be used in conjunction with other optimization algorithms, such as local search or simulated annealing, to improve the quality of the solution.Disadvantages of the Greedy Approach:
The local optimal solution may not always be globally optimal.Greedy algorithms do not always guarantee to find the optimal solution, and may produce suboptimal solutions in some cases.The greedy approach relies heavily on the problem structure and the choice of criteria used to make the local optimal choice. If the criteria are not chosen carefully, the solution produced may be far from optimal.Greedy algorithms may require a lot of pre-processing to transform the problem into a form that can be solved by the greedy approach.Greedy algorithms may not be applicable to problems where the optimal solution depends on the order in which the inputs are processed.Some of the Important Greedy Algorithms are given below:
Activity Selection Problem:The activity selection problem is an optimization problem used to find the maximum number of activities a person can perform if they can only work on one activity at a time.
Problem Statement: You are given n activities with their start and finish times. Select the maximum number of activities that can be performed by a single person, assuming that a person can only work on a single activity at a time.
Approach:
The greedy choice is to always pick the next activity whose finish time is the least among the remaining activities and the start time is more than or equal to the finish time of the previously selected activity. We can sort the activities according to their finishing time so that we always consider the next activity as the minimum finishing time activity.
Here in this image we can see the selected activities.
Activity Selection Problem
Time Complexity: O(N * logN)Auxiliary Space: O(1)
Job Sequencing ProblemThe job sequencing problem states that We have a single processor operating system and a set of jobs that have to be completed with given deadline constraints. Our objective is to maximize the profit, given the condition that only one job can be completed at a given time.
Problem Statement : Given an array of jobs where every job has a deadline and associated profit if the job is finished before the deadline. It is also given that every job takes a single unit of time, so the minimum possible deadline for any job is 1. Task is to Maximize the total profit if only one job can be scheduled at a time.
Example:
Input: Five Jobs with following deadlines and profits
JobID Deadline Profit
a 2 100 b 1 19 c 2 27 d 1 25 e 3 15
Output: Following is maximum profit sequence of jobs: c, a, e
Approach: We can solve this problem using greedy approach .
We have to Greedily choose the jobs with maximum profit first, by sorting the jobs in decreasing order of their profit. This would help to maximize the total profit as choosing the job with maximum profit for every time slot will eventually maximize the total profit
Job Sequencing Problem
Huffman CodingHuffman coding is a lossless data compression algorithm. The idea is to assign variable-length codes to input characters and lengths of the assigned codes are based on the frequencies of corresponding characters.
The variable-length codes assigned to input characters are Prefix Codes, means the codes (bit sequences) are assigned in such a way that the code assigned to one character is not the prefix of code assigned to any other character. This is how Huffman Coding makes sure that there is no ambiguity when decoding the generated bitstream.
Let us understand prefix codes with a counter example. Let there be four characters a, b, c and d, and their corresponding variable length codes be 00, 01, 0 and 1. This coding leads to ambiguity because code assigned to c is the prefix of codes assigned to a and b. If the compressed bit stream is 0001, the de-compressed output may be “cccd” or “ccb” or “acd” or “ab”.
There are mainly two major parts in Huffman Coding:
Build a Huffman Tree from input characters.Traverse the Huffman Tree and assign codes to characters.Steps to build Huffman Tree:Input is an array of unique characters along with their frequency of occurrences and output is Huffman Tree.
Create a leaf node for each unique character and build a min heap of all leaf nodes (Min Heap is used as a priority queue. The value of frequency field is used to compare two nodes in min heap. Initially, the least frequent character is at root)Extract two nodes with the minimum frequency from the min heap. Create a new internal node with a frequency equal to the sum of the two nodes frequencies. Make the first extracted node as its left child and the other extracted node as its right child. Add this node to the min heap.Repeat steps#2 and #3 until the heap contains only one node. The remaining node is the root node and the tree is complete.Let us understand the algorithm with an example:character Frequency a 5 b 9 c 12 d 13 e 16 f 45After Creating Huffman Tree for these characters, our tree will look like below:
Huffman Tree
Huffman codes for below characters will look like this:
character code-word f 0 c 100 d 101 a 1100 b 1101 e 111Application of Huffman Coding:
Below are some of the applications of Huffman coding in the real life
Lossless Image CompressionUsing Structures in ImagesText CompressionAudio CompressionFractional Knapsack ProblemWe are given a set of items, each with a weight and a value, and we want to find the most valuable subset of items that we can fit into a knapsack with capacity W. The catch is that we can take fractional amounts of each item, so an item can be present in fractional form.
Problem Statement: Given the weights and profits of N items, in the form of {profit, weight} put these items in a knapsack of capacity W to get the maximum total profit in the knapsack. We are allowed to take fractional values in the knapsack.
Example:
Input: arr[] = {{60, 10}, {100, 20}, {120, 30}}, W = 50Output: 240 Explanation: By taking items of weight 10 and 20 kg and 2/3 fraction of 30 kg. Hence total price will be 60+100+(2/3)(120) = 240
Approach: An efficient solution is to use the Greedy approach.
The basic idea of the greedy approach is to calculate the ratio profit/weight for each item and sort the item on the basis of this ratio. Then take the item with the highest ratio and add them as much as we can (can be the whole element or a fraction of it).
This will always give the maximum profit because, in each step it adds an element such that this is the maximum possible profit for that much weight.
Time Complexity: O(N * logN)Auxiliary Space: O(N)
Optimal File Merge PatternsOptimal merge pattern is a pattern that relates to the merging of two or more sorted files in a single sorted file. here, we have two sorted files containing n and m records respectively then they could be merged together, to obtain one sorted file in time O(n+m).
Problem Statement: Given n number of sorted files, the task is to find the minimum computations done to reach the Optimal Merge Pattern. When two or more sorted files are to be merged altogether to form a single file, the minimum computations are done to reach this file are known as Optimal Merge Pattern.
If more than 2 files need to be merged then it can be done in pairs. For example, if need to merge 4 files A, B, C, D. First Merge A with B to get X1, merge X1 with C to get X2, merge X2 with D to get X3 as the output file.
If we have two files of sizes m and n, the total computation time will be m+n. Here, we use the greedy strategy by merging the two smallest size files among all the files present.
Example:
Input: n = 6, size = {2, 3, 4, 5, 6, 7} Output: 68 Explanation: Optimal way to combine these files
Approach:
Node represents a file with a given size also given nodes are greater than 2
Add all the nodes in a priority queue (Min Heap).{pq.poll = file size}Initialize count = 0 // variable to store file computations.Repeat while (size of priority Queue is greater than 1) int weight = pq.poll(); pq.pop;//pq denotes priority queue, remove 1st smallest and pop(remove) it outweight+=pq.poll() && pq.pop(); // add the second element and then pop(remove) it outcount +=weight;pq.add(weight) // add this combined cost to priority queue; count is the final answerTime Complexity: O(nlogn)Auxiliary Space: O(n)
Prim’s Algorithm for Minimum Spanning Tree (MST)It is a greedy algorithm that is used to find the MST from a graph. Prim's algorithm finds the subset of edges that includes every vertex of the graph such that the sum of the weights of the edges is minimized.
Prim's algorithm starts with the single node and explores all the adjacent nodes with all the connecting edges at each step. The edges with the minimal weights causing no cycles in the graph got selected.
How does Prim’s Algorithm Work? The working of Prim’s algorithm can be described by using the following steps:
Step 1: Determine an arbitrary vertex as the starting vertex of the MST.Step 2: Follow steps 3 to 5 till there are vertices that are not included in the MST (known as fringe vertex).Step 3: Find edges connecting any tree vertex with the fringe vertices.Step 4: Find the minimum among these edges.Step 5: Add the chosen edge to the MST if it does not form any cycle.Step 6: Return the MST and exit
Time Complexity: O(V2), If the input graph is represented using an adjacency list, then the time complexity of Prim’s algorithm can be reduced to O(E * logV) with the help of a binary heap. In this implementation, we are always considering the spanning tree to start from the root of the graphAuxiliary Space: O(V)
Kruskal’s Minimum Spanning Tree AlgorithmKruskal's algorithm is a well-known algorithm for finding the minimum spanning tree of a graph. It is a greedy algorithm that makes use of the fact that the edges of a minimum spanning tree must form a subset of the edges of any other spanning tree.
In Kruskal’s algorithm, sort all edges of the given graph in increasing order. Then it keeps on adding new edges and nodes in the MST if the newly added edge does not form a cycle. It picks the minimum weighted edge at first and the maximum weighted edge at last. Thus we can say that it makes a locally optimal choice in each step in order to find the optimal solution. Hence this is a Greedy Algorithm.
How to find MST using Kruskal’s algorithm?Below are the steps for finding MST using Kruskal’s algorithm:
Sort all the edges in non-decreasing order of their weight. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If the cycle is not formed, include this edge. Else, discard it. Repeat step#2 until there are (V-1) edges in the spanning tree.Note: In Step 2 we can use Union Find to detect cycles.
Time Complexity: O(E * logE) or O(E * logV) Auxiliary Space: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Dijkstra’s shortest path algorithmDijkstra’s algorithm is a popular algorithms for solving many single-source shortest path problems having non-negative edge weight in the graphs i.e., it is to find the shortest distance between two vertices on a graph. It was conceived by Dutch computer scientist Edsger W. Dijkstra in 1956.
The algorithm maintains a set of visited vertices and a set of unvisited vertices. It starts at the source vertex and iteratively selects the unvisited vertex with the smallest tentative distance from the source. It then visits the neighbours of this vertex and updates their tentative distances if a shorter path is found. This process continues until the destination vertex is reached, or all reachable vertices have been visited.
Need for Dijkstra’s Algorithm (Purpose and Use-Cases):The need for Dijkstra’s algorithm arises in many applications where finding the shortest path between two points is crucial.For example, It can be used in the routing protocols for computer networks and also used by map systems to find the shortest path between starting point and the Destination (as explained in How does Google Maps work?)
Can Dijkstra’s Algorithm work on both Directed and Undirected graphs? Yes, Dijkstra’s algorithm can work on both directed graphs and undirected graphs as this algorithm is designed to work on any type of graph as long as it meets the requirements of having non-negative edge weights and being connected.
In a directed graph, each edge has a direction, indicating the direction of travel between the vertices connected by the edge. In this case, the algorithm follows the direction of the edges when searching for the shortest path.In an undirected graph, the edges have no direction, and the algorithm can traverse both forward and backward along the edges when searching for the shortest path.Algorithm for Dijkstra’s Algorithm:Mark the source node with a current distance of 0 and the rest with infinity.Set the non-visited node with the smallest current distance as the current node.For each neighbour, N of the current node adds the current distance of the adjacent node with the weight of the edge connecting 0->1. If it is smaller than the current distance of Node, set it as the new current distance of N.Mark the current node 1 as visited.Go to step 2 if there are any nodes are unvisited.Previously Asked GATE Questions for Greedy AlgorithmQuestion 1: Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the following is the Huffman code for the letter a, b, c, d, e, f? GATE-2007
(A) 0, 10, 110, 1110, 11110, 11111(B) 11, 10, 011, 010, 001, 000(C) 11, 1, 01, 001, 0001, 0000(D) 110, 100, 010, 000, 001, 111
Correct Answer: (A)Explanation: We get the following Huffman Tree after applying Huffman Coding Algorithm. The idea is to keep the least probable characters as low as possible by picking them first.
The letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. 1 / \ / \ 1/2 a(1/2) / \ / \ 1/4 b(1/4) / \ / \ 1/8 c(1/8) / \ / \ 1/16 d(1/16) / \ e fQuestion 2: Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?
(A) 3(B) 2.1875(C) 2.25(D) 1.9375
Correct Answer: (D)Explanation: We get the following Huffman Tree after applying Huffman Coding Algorithm. The idea is to keep the least probable characters as low as possible by picking them first.
The letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. 1 / \ / \ 1/2 a(1/2) / \ / \ 1/4 b(1/4) / \ / \ 1/8 c(1/8) / \ / \ 1/16 d(1/16) / \ e fThe average length = (1*1/2 + 2*1/4 + 3*1/8 + 4*1/16 + 5*1/32 + 5*1/32) = 1.9375 Question 3: Consider the undirected graph below:
Using Prim's algorithm to construct a minimum spanning tree starting with node A, which one of the following sequences of edges represents a possible order in which the edges would be added to construct the minimum spanning tree?
(A) (E, G), (C, F), (F, G), (A, D), (A, B), (A, C)(B) (A, D), (A, B), (A, C), (C, F), (G, E), (F, G)(C) (A, B), (A, D), (D, F), (F, G), (G, E), (F, C)(D) (A, D), (A, B), (D, F), (F, C), (F, G), (G, E)
Correct Answer: (D)Explanation:A. False The idea behind Prim’s algorithm is to construct a spanning tree – means all vertices must be connected but here vertices are disconnected
B. False The idea behind Prim’s algorithm is to construct a spanning tree – means all vertices must be connected but here vertices are disconnected
C. False. Prim’s is a greedy algorithm and At every step, it considers all the edges that connect the two sets, and picks the minimum weight edge from these edges. In this option, since weight of AD<AB, so AD must be picked up first (which is not true as per the options).
D.TRUE.
Therefore, Answer is D
Question 4: Consider the weights and values of items listed below. Note that there is only one unit of each item.
The task is to pick a subset of these items such that their total weight is no more than 11 Kgs and their total value is maximized. Moreover, no item may be split. The total value of items picked by an optimal algorithm is denoted by Vopt. A greedy algorithm sorts the items by their value-to-weight ratios in descending order and packs them greedily, starting from the first item in the ordered list. The total value of items picked by the greedy algorithm is denoted by Vgreedy. The value of Vopt − Vgreedy is ______ .
(A) 16(B) 8(C) 44(D) 60
Correct Answer: (A)Explanation: First we will pick item_4 (Value weight ratio is highest). Second highest is item_1, but cannot be picked because of its weight. Now item_3 shall be picked. item_2 cannot be included because of its weight. Therefore, overall profit by Vgreedy = 20+24 = 44 Hence, Vopt - Vgreedy = 60-44 = 16 So, answer is 16.
Question 5: A text is made up of the characters a, b, c, d, e each occurring with the probability 0.11, 0.40, 0.16, 0.09 and 0.24 respectively. The optimal Huffman coding technique will have the average length of:
(A) 2.40(B) 2.16(C) 2.26(D) 2.15
Correct Answer: (B)Explanation: a = 0.11 b = 0.40 c = 0.16 d = 0.09 e = 0.24 we will draw a huffman tree.now huffman coding for character:
a = 1111 b = 0 c = 110 d = 1111 e = 10length for each character = no of bits * frequency of occurrence:a = 4 * 0.11 = 0.44b = 1 * 0.4 = 0.4c = 3 * 0.16 = 0.48d = 4 * 0.09 = 0.36 e = 2 * 0.24 = 0.48Now add these lenght for average length: 0.44 + 0.4 + 0.48 + 0.36 + 0.48 = 2.16Question 6: Which of the following is true about Huffman Coding.
(A) Huffman coding may become lossy in some cases(B) Huffman Codes may not be optimal lossless codes in some cases(C) In Huffman coding, no code is prefix of any other code.(D) All of the above
Correct Answer: (C)Explanation: Huffman coding is a lossless data compression algorithm. The codes assigned to input characters are Prefix Codes, means the codes are assigned in such a way that the code assigned to one character is not prefix of code assigned to any other character. This is how Huffman Coding makes sure that there is no ambiguity when decoding.
Question 7: Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?
(A) 7(B) 8(C) 9(D) 10
Correct Answer: (D)
Question 8: Kruskal’s algorithm for finding a minimum spanning tree of a weighted graph G with n vertices and m edges has the time complexity of:
(A) O(n2)(B) O(mn)(C) O(m2)(D) O(m log n)
Correct Answer: (D)
Question 9: In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by
(A) Dijkstra's algorithm starting from S(B) Warshall's algorithm(C) Performing a DFS starting from S(D) Performing a BFS starting from S
Correct Answer: (D)
Question 10: Let G = (V, E) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighted edge (u, v) ∈ V × V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph is
(A) Θ( |E|+|V| )(B) Θ( |E|*|V| )(C) Θ( |E| log(|V|) )(D) Θ( |V| )
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12 Dec, 2023 | Dynamic Programming (DP) Notes for GATE Exam [2024]
12 Dec, 2023
As the GATE Exam 2024 is coming up, having a good grasp of dynamic programming is really important for those looking to tackle tricky computational problems. These notes are here to help you understand the basic principles, strategies, and real-life uses of dynamic programming. They're like a handy guide to becoming a pro at dynamic programming, making it easier for you to ace the GATE exam. So, get ready to dive into the world of dynamic programming and make problem-solving a breeze!
Table of Content
What is Dynamic Programming?Overlapping Subproblems PropertyOptimal Substructure PropertyStandard problems on Dynamic ProgrammingPreviously Asked Problems of Dynamic Programming on GATEWhat is Dynamic Programming?Dynamic Programming is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using dynamic Programming. The idea is to simply store the results of subproblems so that we do not have to re-compute them when needed later. This simple optimization reduces time complexities from exponential to polynomial.
Dynamic Programming is an algorithmic paradigm that solves a given complex problem by breaking it into subproblems using recursion and storing the results of subproblems to avoid computing the same results again.
Following are the two main properties of a problem that suggest that the given problem can be solved using dynamic programming.
Overlapping Subproblems Optimal Substructure1. Overlapping Subproblems Property:Like Divide and Conquer, Dynamic Programming combines solutions to sub-problems. Dynamic Programming is mainly used when solutions to the same subproblems are needed again and again. In dynamic programming, computed solutions to subproblems are stored in a table so that these don’t have to be recomputed. So dynamic Programming is not useful when there are no common (overlapping) subproblems because there is no point in storing the solutions if they are not needed again. For example, Binary Search doesn’t have common subproblems. If we take the example of following a recursive program for Fibonacci Numbers, there are many subproblems that are solved again and again.
2. Optimal Substructure Property:A given problem is said to have Optimal Substructure Property if the optimal solution of the given problem can be obtained by using the optimal solution to its subproblems instead of trying every possible way to solve the subproblems.
Standard problems on Dynamic Programming:Longest Common Subsequence:A longest common subsequence (LCS) is defined as the longest subsequence which is common in all given input sequences.
Examples:
Input: S1 = “AGGTAB”, S2 = “GXTXAYB”Output: 4Explanation: The longest subsequence which is present in both strings is “GTAB”.
Matrix Chain Multiplication:Matrix chain multiplication is an optimization problem that needs the most efficient method of multiplying a given sequence of matrices. The problem is not to perform the multiplications, but rather to determine the order of the matrix multiplications involved. Dynamic programming could be used to solve the problem.
Example:
Input: arr[] = {40, 20, 30, 10, 30}Output: 26000Explanation:There are 4 matrices of dimensions 40×20, 20×30, 30×10, 10×30.Let the input 4 matrices be A, B, C and D.The minimum number of multiplications are obtained by putting parenthesis in following way (A(BC))D.The minimum is 20*30*10 + 40*20*10 + 40*10*30
Matrix Chain Multilpication0/1 Knapsack Problem:The 0/1 knapsack problem represents that either all or none of the items in a knapsack are completely filled. For example, consider two items weighing 2kg and 3kg, respectively. If we select the 2kg item, we cannot select a 1kg item from the 2kg item (item is not divisible); we must select the entire 2kg item. This is a 0/1 knapsack problem in which we either completely pick the item or pick that item. Dynamic programming is used to solve the 0/1 knapsack problem.
Example:
Input: N = 3, W = 4, profit[] = {1, 2, 3}, weight[] = {4, 5, 1}Output: 3Explanation: There are two items which have weight less than or equal to 4. If we select the item with weight 4, the possible profit is 1. And if we select the item with weight 1, the possible profit is 3. So the maximum possible profit is 3. Note that we cannot put both the items with weight 4 and 1 together as the capacity of the bag is 4.
Min Cost Path:Given a cost matrix cost[][] and a position (M, N) in cost[][], write a function that returns cost of minimum cost path to reach (M, N) from (0, 0). Each cell of the matrix represents a cost to traverse through that cell. The total cost of a path to reach (M, N) is the sum of all the costs on that path (including both source and destination). You can only traverse down, right and diagonally lower cells from a given cell, i.e., from a given cell (i, j), cells (i+1, j), (i, j+1), and (i+1, j+1) can be traversed.
Example:
Input:
Min Cost Path
The path with minimum cost is highlighted in the following figure. The path is (0, 0) –> (0, 1) –> (1, 2) –> (2, 2). The cost of the path is 8 (1 + 2 + 2 + 3).
Output:
Min Cost Path
Subset Sum Problem:The subset sum problem is a decision problem. In its most general form, there is a multiset of integers and a target sum, and the problem is to determine whether any subset of the integers sums exactly. It is well known that the problem is NP-hard. Furthermore, some restricted variants of it are NP-complete as well.
Example:
Input: set[] = {3, 34, 4, 12, 5, 2}, sum = 9Output: TrueExplanation: There is a subset (4, 5) with sum 9.
Bellman-Ford Algorithm:Bellman-Ford Algorithm is a single source shortest path algorithm that determines the shortest path between a given source vertex and every other vertex in a graph. This algorithm can be used on both weighted and unweighted graphs.
A Bellman-Ford algorithm is also guaranteed to find the shortest path in a graph, similar to Dijkstra’s algorithm. Although Bellman-Ford is slower than Dijkstra’s algorithm, it is capable of handling graphs with negative edge weights, which makes it more versatile. The shortest path cannot be found if there exists a negative cycle in the graph. If we continue to go around the negative cycle an infinite number of times, then the cost of the path will continue to decrease (even though the length of the path is increasing). As a result, Bellman-Ford is also capable of detecting negative cycles, which is an important feature.
Floyd Warshall Algorithm:The Floyd Warshall Algorithm is an all pair shortest path algorithm unlike Dijkstra and Bellman Ford which are single source shortest path algorithms. This algorithm works for both the directed and undirected weighted graphs. But, it does not work for the graphs with negative cycles (where the sum of the edges in a cycle is negative). It follows Dynamic Programming approach to check every possible path going via every possible node in order to calculate shortest distance between every pair of nodes.
Total number of non-decreasing numbers with n digits:A number is non-decreasing if every digit (except the first one) is greater than or equal to the previous digit. For example, 223, 4455567, 899, are non-decreasing numbers.So, given the number of digits n, you are required to find the count of total non-decreasing numbers with n digits.
Examples:
Input: n = 1Output: count = 10
Input: n = 2Output: count = 55
Smallest power of 2 greater than or equal to n:The problem is to find the smallest power of 2 that is greater than or equal to a positive integer 'n'. We must devise an algorithm to compute this value efficiently without using the power function. This can be useful in a variety of situations, including determining the appropriate size for data structures and optimizing algorithms.
Example:
Input: n = 5Output: 8
Input: n = 17Output: 32
Previously Asked Problems of Dynamic Programming on GATE:Q1. [GATE-CS-2016]The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy Paradigm(B) Divide-and-Conquer Paradigm(C) Dynamic Programming Paradigm(D) Neither Greedy nor Divide-and- Conquer nor Dynamic Programming Paradigm
Ans: (C) Dynamic Programming Paradigm
Q2. [GATE-CS-2015]
List-I
A. Prim’s algorithm for minimum spanning treeB. Floyd-Warshall algorithm for all pairs shortest pathsC. MergesortD. Hamiltonian circuit
List-II
1. Backtracking2. Greedy method3. Dynamic programming4. Divide and conquer
Codes:
A B C D(a) 3 2 4 1(b) 1 2 4 3(c) 2 3 4 1(d) 2 1 3 4
Options:
(A): a(B): b(C): c(D): d
Ans: (C)
Q3. [GATE-CS-2017] Kadane algorithm is generally used to find out.
(A) Maximum sum subsequence present in an array(B) Maximum sum subarray present in an array(C) Maximum product subsequence present in an array(D) Maximum product subarray present in an arrayAns: (B) Maximum sum subarray present in an array
Q4. [GATE-CS-2017] Which of the standard algorithms shown below is not based on Dynamic Programming?
(A) Prim's Minimum Spanning Tree(B) Bellman-Ford Algorithm for single-source shortest path(C) Floyd Warshall Algorithm for all-pairs shortest paths(D) 0-1 Knapsack problem
Ans: (A) Prim's Minimum Spanning Tree
Q5. [GATE-CS-2014] Consider two strings A = \”qpqrr\” and B = \”pqprqrp\”. Let x be the length of the longest common subsequence (not necessarily contiguous) between A and B and let y be the number of such longest common subsequences between A and B. Then x + 10y = ___.
(A) 33(B) 23(C) 43(D) 34
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base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [0.00559265539, 0.0123490579, -0.0287156366, 0.0383665822, 0.0449191406, 0.0142762819, 0.00216442067, 0.0294420514, -0.0526873358, 0.00288712955, 0.0134609174, -0.00947304629, 0.0520350449, -0.0191091672, -0.0375363901, 0.016411053, 0.010666443, 0.0116152298, -0.00637466367, -0.0448894911, -0.041746635, 0.00047809977, -0.0226078182, 0.0378625356, -0.00324107171, 0.0441186, 0.0141947456, -0.00841307361, -0.0392560698, 0.010273586, 0.0116448794, 0.00330222398, 0.0012906841, -0.050522916, -0.00298719713, -0.0216293819, -0.0121118613, -0.00600033766, -0.0324366614, -0.00304279, -0.0405013524, 0.00239605829, -0.00942115951, 0.00725303311, -0.000606890244, 0.0103625348, -0.0123490579, 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21 Apr, 2024 | Graph-Based Algorithms for GATE Exam [2024]
21 Apr, 2024
Ever wondered how computers figure out the best path in a maze or create efficient networks like a pro? That's where Graph-Based Algorithms come into play! Think of them as your digital navigation toolkit. As you prepare for GATE 2024, let these algorithms be your allies, unraveling the intricacies of graphs and leading you to success.
Table of Content
Depth First Search or DFS for a GraphDetect Cycle in a Directed GraphTopological SortingBellman–Ford AlgorithmFloyd Warshall AlgorithmShortest path with exactly k edges in a directed and weighted graphBiconnected graphArticulation Points (or Cut Vertices) in a GraphCheck if a graph is strongly connected (Kosaraju’s Theorem)Bridges in a graphTransitive closure of a graphPreviously Asked GATE Questions on Graph-Based AlgorithmsA Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(E, V).
In this comprehensive guide, we will explore key graph algorithms, providing detailed algorithm steps with its applications, which are relevance for the GATE Exam.
1. Breadth First Search or BFS for a Graph (BFS):BFS explores a graph level by level, visiting all neighbours of a node before moving on to the next level. It uses a queue data structure to maintain the order in which nodes are visited.
Algorithm Steps:
Enqueue the starting node into the queue.While the queue is not empty, dequeue a node and visit it.Enqueue all unvisited neighbors of the current node.Repeat steps 2-3 until the queue is empty.Applications:
Shortest path finding in unweighted graphs.Connectivity analysis in networks.Web crawling and indexing.2. Depth First Search or DFS for a Graph:DFS explores a graph by going as deep as possible along one branch before backtracking. It uses a stack (or recursion) to keep track of the visited nodes.
Algorithm Steps:
Start at the initial node and mark it as visited.Explore one adjacent node as deeply as possible before backtracking.Repeat step 2 until all paths are explored.Applications:
Topological sorting of directed acyclic graphs.Detecting cycles in a graph.Solving puzzles and games.3. Detect Cycle in a Directed Graph:Detecting cycles in a directed graph is a common problem with wide-ranging applications in various domains such as network analysis, scheduling, and resource allocation. The algorithmic approach involves traversing the graph using depth-first search (DFS) and identifying back edges. If a back edge is encountered during the traversal, it indicates the presence of a cycle.
Algorithm Steps:
Initialize arrays for visited vertices and recursion stack.Start DFS from each unvisited vertex.Mark the current vertex as visited and add it to the recursion stack.For each adjacent vertex:If the vertex is not visited, recursively call DFS.If the vertex is in the recursion stack, a cycle is detected.Remove the current vertex from the recursion stack upon backtracking.Applications:
Task scheduling in project management.Resource allocation in computer systems.4. Topological Sorting:Topological sorting is vital for scheduling tasks with dependencies, and it is often used in project management and task scheduling. The algorithm involves linearly ordering the vertices of a directed acyclic graph (DAG) in such a way that for every directed edge 'uv,' vertex 'u' comes before 'v' in the ordering.
Algorithm Steps:
Start DFS from any unvisited vertex.Mark the current vertex as visited.Recursively call DFS for each adjacent vertex.Add the current vertex to the topological order after recursion.The final order is the reverse of the order in which vertices are added.Applications:
Task scheduling with dependencies.Build systems to determine order of compilation.5. Bellman–Ford Algorithm:The Bellman–Ford algorithm is employed for finding the shortest paths from a single source vertex to all other vertices in a weighted graph, even if the graph contains negative weight edges. This algorithm is particularly useful in scenarios where Dijkstra's algorithm might fail due to negative weights.
Algorithm Steps:
Initialize distances from the source vertex to all others as infinity.Set the distance to the source as 0.Relax edges iteratively:For each edge (u, v), if distance[u] + weight(u, v) < distance[v], update distance[v].Repeat step 3 for V-1 times, where V is the number of vertices.Detect negative cycles by checking for further relaxation after V-1 iterations.Applications:
Single-source shortest path with negative weight edges.Network routing protocols.6. Floyd Warshall Algorithm:The Floyd Warshall algorithm is a dynamic programming approach to find the shortest paths between all pairs of vertices in a weighted graph. It works well for dense graphs and is capable of handling graphs with both positive and negative weights.
Algorithm Steps:
Initialize a matrix with direct edge weights.Update the matrix with shorter paths found through intermediate vertices:For each pair of vertices (i, j), if distance[i][k] + distance[k][j] < distance[i][j], update distance[i][j].Applications:
All-pairs shortest path in a weighted graph.Routing algorithms in computer networks.7. Shortest path with exactly k edges in a directed and weighted graph:This problem involves finding the shortest path with a specific number of edges in a directed and weighted graph. The solution often relies on dynamic programming techniques to calculate the shortest paths for varying numbers of edges.
Algorithm Steps:
Initialize a 3D array to store shortest paths for different numbers of edges.Use dynamic programming to fill the array:dp[i][j][e] represents the shortest path from i to j with exactly e edges.dp[i][j][e] = min(dp[i][j][e], dp[i][k][e-1] + dp[k][j][1]) for each vertex k.Applications:
Optimization problems involving specific edge constraints.8. Biconnected graph:A biconnected graph is a graph that remains connected even after the removal of any single vertex (and its incident edges). Biconnected graphs are crucial in designing robust network structures, and algorithms for identifying them are essential for network reliability.
Algorithm Steps:
Use DFS to traverse the graph, maintaining information about discovery time and low value for each vertex.For each edge (u, v), if v is not visited, recursively call DFS for v.Update the low value of u based on the low value of v.If the low value of v is greater than or equal to the discovery time of u, u is an articulation point.If u is the root of the DFS tree and has more than one child, it is an articulation point.Applications:
Designing robust network structures.Fault-tolerant systems.9. Articulation Points (or Cut Vertices) in a Graph:Articulation points are vertices whose removal would disconnect a graph. Detecting these points is essential in network design to ensure robustness and fault tolerance. Algorithms for finding articulation points often use depth-first search.
Algorithm Steps:
Use DFS to traverse the graph, maintaining information about discovery time and low value for each vertex.For each edge (u, v), if v is not visited, recursively call DFS for v.Update the low value of u based on the low value of v.If the low value of v is greater than or equal to the discovery time of u, u is an articulation point.Applications:
Network design for robustness.Fault detection in systems.10. Check if a graph is strongly connected (Kosaraju’s Theorem):Kosaraju’s Theorem provides an efficient algorithm for checking whether a directed graph is strongly connected, meaning there is a directed path from every vertex to every other vertex.
Algorithm Steps:
Perform DFS on the original graph, keeping track of finishing times.Transpose the graph (reverse all edges).Perform DFS on the transposed graph in decreasing order of finishing times.If all vertices are visited in the second DFS, the graph is strongly connected.Applications:
Web page ranking algorithms.Social network analysis.11. Bridges in a graph:Bridges, also known as cut edges, are edges whose removal increases the number of connected components in a graph. Detecting bridges is crucial for network design and ensuring connectivity.
Algorithm Steps:
Use DFS to traverse the graph, maintaining information about discovery time and low value for each vertex.For each edge (u, v), if v is not visited, recursively call DFS for v.Update the low value of u based on the low value of v.If the low value of v is greater than the discovery time of u, the edge (u, v) is a bridge.Applications:
Network design for reliability.Critical infrastructure analysis.12. Transitive closure of a graph:The transitive closure of a graph involves determining all pairs of vertices reachable from each other. Algorithms for transitive closure are vital in optimizing graph-related queries and analyses.
Algorithm Steps:
Initialize a matrix to represent the transitive closure.Perform a DFS from each vertex to mark reachable vertices.The matrix entry (i, j) is true if there is a path from i to j in the graph.Applications:
Query optimization in databases.Compiler optimizations.13. Minimum Spanning Tree (MST):A minimum spanning tree (MST) of a connected undirected graph is a subgraph that includes the all the vertices of graph with the minimum possible total edge weight. The MSTs have the various applications in the network design, circuit wiring and clustering algorithms.
Algorithm Steps:Start with the any vertex as the initial tree.At each step, add the minimum weight edge that connects a vertex in the tree to the vertex outside the tree.Repeat the process until all vertices are included in tree.Applications:Network design to minimize infrastructure costs.Circuit design to the minimize wire usage.Cluster analysis in the data mining and machine learning.Previously Asked GATE Questions on Graph-Based Algorithms:Question 1: Which of the following statements is/are TRUE for an undirected graph?P: Number of odd degree vertices is evenQ: Sum of degrees of all vertices is even
A) P OnlyB) Q OnlyC) Both P and QD) Neither P nor Q
Answer: (C)
Explanation: Q is true: Since the graph is undirected, every edge increases the sum of degrees by 2.P is true: If we consider sum of degrees and subtract all even degrees, we get an even number (because Q is true). So total number of odd degree vertices must be even.
Question 2: Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
(A) 1/8(B) 1(C) 7(D) 8
Answer: (C)
Explanation: A cycle of length 3 can be formed with 3 vertices. There can be total 8C3 ways to pick 3 vertices from 8. The probability that there is an edge between two vertices is 1/2. So expected number of unordered cycles of length 3 = (8C3)*(1/2)^3 = 7
Question 3: What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?
(A) Θ(n2)(B) Θ(n2 Logn)(C) Θ(n3)(D) Θ(n3 Logn)
Answer: (C)
Explanation: Time complexity of Bellman-Ford algorithm is Θ(VE) where V is number of vertices and E is number edges (See this). If the graph is complete, the value of E becomes Θ(V2). So overall time complexity becomes Θ(V3)
Question 4: Which of the following statements are TRUE?
(1) The problem of determining whether there exists a cycle in an undirected graph is in P.(2) The problem of determining whether there exists a cycle in an undirected graph is in NP.(3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.
(A) 1,2 and 3(B) 1 and 2 only(C) 2 and 3 only(D) 1 and 3 only
Answer: (A)
Explanation: 1 is true because cycle detection can be done in polynomial time using DFS (See this).2 is true because P is a subset of NP.3 is true because NP complete is also a subset of NP and NP means Non-deterministic Polynomial time solution exists. (See this)
Question 5: Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry Wij in the matrix W below is the weight of the edge {i, j}.What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?
(A) 7(B) 8(C) 9(D) 10
Answer: (D)
Explanation: To get the minimum spanning tree with vertex 0 as leaf, first remove 0th row and 0th column and then get the minimum spanning tree (MST) of the remaining graph. Once we have MST of the remaining graph, connect the MST to vertex 0 with the edge with minimum weight (we have two options as there are two 1s in 0th row).
Question 6: In the graph given in question 1, what is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?
(A) 7(B) 8(C) 9(D) 10
Answer: (B)
Explanation: Path: 1 -> 0 -> 4 -> 2Weight: 1 + 4 + 3
Question 7: The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1
(A) I and II(B) III and IV(C) IV only(D) II and IV
Answer: (D)
Explanation: In sequence IV, we have a vertex with degree 8 which is not possible in a simple graph (no self loops and no multiple edges) with total vertex count as 8. Maximum possible degree in such a graph is 7.
In sequence II, four vertices are connected to 6 other vertices, but remaining 4 vertices have degrees as 3, 3, 2 and 2 which are not possible in a simple graph (no self loops and no multiple edges).
Question 8: In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by
(A) Dijkstra’s algorithm starting from S. (B) Warshall’s algorithm (C) Performing a DFS starting from S. (D) Performing a BFS starting from S.
Answer: (D)
Explanation: * Time Complexity of the Dijkstra’s algorithm is O(|V|^2 + E) * Time Complexity of the Warshall’s algorithm is O(|V|^3) * DFS cannot be used for finding shortest paths * BFS can be used for unweighted graphs. Time Complexity for BFS is O(|E| + |V|)
Question 9: For a graph with E edges and V vertices what is the time complexity of Dijkstra algorithm using array as data structure for storing non-finalized vertices. Graph is undirected and represented as adjacency list?
(A) O(VE) (B) O(ElogV) (C) O(V^2 ) (D) O(E^2log V)
Answer: (C)
Explanation:Given data structure used is array so initialization of all nodes in array (setting infinity to all nodes which are not reachable), this operation takes O(V) At each step we have to delete minimum from the array. For one such operation it takes O(V), using selection sort first pass. We have V such steps. So total complexity due to deletion of minimum element at each step = V*O(V) = O(V^2) After a minimum is selected at each step we have to check its adjacent and perform decrease key to the neighbors of selected node. It takes total O(2E) to check adjacents for all steps. Also the decrease key of all the steps is E. O(1) = O(E) . Since the array is unsorted we don’t have to sort the array at each step. Total complexity = O(V) + O(V^2) + O(2E) + O(E) = O(V^2) Note: For a simple graph V^2 is always >= E
Question 10: To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:
(A) Queue(B) Stack(C) Heap(D) B-Tree
Answer: (A)
Explanation: The shortest path in an un-weighted graph means the smallest number of edges that must be traversed in order to reach the destination in the graph. This is the same problem as solving the weighted version where all the weights happen to be 1. If we use Queue (FIFO) instead of Priority Queue (Min Heap), we get the shortest path in linear time O(|V| + |E|). 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DBMS Interview Questions | Set 2/Database Management System – GATE CSE Previous Year Questions/GATE CSE and IT Previous Years Papers PDF Download Link/Theory of Computation – GATE CSE Previous Year Questions/Automata Theory | Set 6/Data Structures and Algorithms | Set 25/Graph Data Structure Notes for GATE Exam [2024]/Binary Heap Notes for GATE Exam [2024]/Searching and Sorting Algorithm Notes for GATE Exam [2024]/Recursion Notes for GATE Exam [2024]/Divide and Conquer Notes for GATE Exam [2024]/Greedy Algorithm Notes for GATE Exam [2024]/Dynamic Programming (DP) Notes for GATE Exam [2024]/Graph-Based Algorithms for GATE Exam [2024] | https://www.geeksforgeeks.org/graph-based-algorithms-for-gate-exam/?ref=next_article | Data Science & ML | Graph-Based Algorithms for GATE Exam [2024] | Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, 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in Scikit Learn, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0271586049, 0.0165944789, -0.0262489151, 0.0352724381, 0.0107988836, 0.00973513443, 0.0182964783, 0.0378254354, -0.027613448, 5.88615258e-05, 0.0127503118, 0.00875942, 0.0100652631, -0.0115471752, -0.0415815711, 0.0408186056, 0.0375319868, 0.0128823631, 0.018105736, -0.0554616563, -0.0437530838, 0.00306653068, -0.0422565, -0.00733253, -0.0120607093, 0.00691069849, 0.0172694102, -0.0110996673, -0.0524684861, 0.0272906553, 0.00218251883, 0.0282737073, 0.00718213758, -0.0281856731, -0.0221993346, 0.0139607843, 0.020453319, -0.0207614396, 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04 Dec, 2023 | Tips to Clear GATE CS Exam [2024]: Road to Success
04 Dec, 2023
The GATE (Graduate Aptitude Test in Engineering) Computer Science (CS) exam is a crucial gateway for those aspiring to pursue higher education or secure positions in the field of computer science. To ace this highly competitive examination, candidates need a well-thought-out strategy, dedication, and a comprehensive study plan. In this blog, we'll delve into various tips and strategies to help you prepare effectively and increase your chances of success in the GATE CS Exam.
Table of Content
1. Understand the Syllabus2. Create a Study Plan3. Refer to Standard Textbooks4. Solve Previous Year Papers5. Take Mock Tests6. Focus on Weak Areas7. Programming Practice8. Stay Updated with Current Trends9. Revision is Key10. Join Online Communities11. Time Management12. Health and Well-being13. Stay Positive14. Seek Guidance1. Understand the SyllabusOne of the first steps in preparing for the GATE CS exam is to thoroughly understand the syllabus. The official GATE CS syllabus outlines the topics and subjects you need to cover. Take the time to go through it carefully, and make sure you have a clear understanding of what is expected.
2. Create a Study PlanA well-structured study plan is essential for effective GATE preparation. Break down the syllabus into manageable sections and allocate specific time slots for each. Consider your strengths and weaknesses when planning, and be realistic about the time you can commit each day.
3. Refer to Standard TextbooksGATE CS demands a solid understanding of core concepts in computer science. Utilize standard textbooks recommended for GATE preparation. Books authored by renowned experts can provide in-depth knowledge and clear explanations of complex topics.
4. Solve Previous Year PapersPractice with previous year GATE CS question papers to understand the exam pattern and question format. This not only helps you gauge the difficulty level but also aids in time management during the actual exam. Analyze your performance to identify areas that need improvement.
5. Take Mock TestsRegularly take full-length mock tests to simulate exam conditions. This helps you get accustomed to the time constraints and pressure of the actual exam. Mock tests also highlight weak areas that require further attention.
6. Focus on Weak AreasIdentify your weaker subjects or topics early on and allocate more time to strengthen those areas. Consistent improvement across all subjects is crucial for achieving a well-balanced score.
7. Programming PracticeGATE CS involves programming, so regular coding practice is essential. Focus on data structures, algorithms, and programming languages like C, C++, or Java. Solve coding problems to enhance your problem-solving skills.
8. Stay Updated with Current TrendsComputer science is a rapidly evolving field. Stay updated with the latest developments, technologies, and trends. GATE questions may incorporate current industry practices, so keeping abreast of these updates is beneficial.
9. Revision is KeyRegularly revise the topics you've covered. Create concise notes summarizing important concepts and formulas. This aids in quick review closer to the exam date.
10. Join Online CommunitiesParticipate in online forums and communities where GATE aspirants share tips, discuss problems, and provide support. Engaging with peers can offer insights, motivation, and a sense of camaraderie during your preparation journey.
11. Time ManagementPractice effective time management during your preparation and in mock tests. Learn to allocate time strategically to each question during the exam. Prioritize questions based on your strengths and the marks they carry.
12. Health and Well-beingMaintain a healthy lifestyle. Get adequate sleep, engage in regular physical activity, and take breaks to stay focused and energized during your study sessions. A healthy mind and body contribute significantly to effective learning.
13. Stay PositiveMaintain a positive mindset throughout your preparation. Believe in your abilities, stay confident, and remain calm during the exam. A positive attitude can significantly impact your performance.
14. Seek GuidanceIf you face challenges in understanding certain topics, don't hesitate to seek guidance. Teachers, mentors, or online resources can provide valuable insights and clarification on complex concepts.
ConclusionPreparing for the GATE CS exam requires a holistic approach that combines effective study techniques, strategic planning, and a positive mindset. By following these comprehensive tips, you can enhance your preparation, boost your confidence, and increase your chances of success. Remember, success in the GATE CS exam is not just about hard work but also about smart and focused preparation. Consistency, dedication, and a well-organized study plan will significantly contribute to your success. Best of luck on your GATE CS journey! | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series 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2/Database Management System – GATE CSE Previous Year Questions/GATE CSE and IT Previous Years Papers PDF Download Link/Theory of Computation – GATE CSE Previous Year Questions/Automata Theory | Set 6/Data Structures and Algorithms | Set 25/Graph Data Structure Notes for GATE Exam [2024]/Binary Heap Notes for GATE Exam [2024]/Searching and Sorting Algorithm Notes for GATE Exam [2024]/Recursion Notes for GATE Exam [2024]/Divide and Conquer Notes for GATE Exam [2024]/Greedy Algorithm Notes for GATE Exam [2024]/Dynamic Programming (DP) Notes for GATE Exam [2024]/Graph-Based Algorithms for GATE Exam [2024]/Tips to Clear GATE CS Exam [2024]: Road to Success | https://www.geeksforgeeks.org/tips-to-clear-gate-cs-exam/?ref=next_article | Data Science & ML | Tips to Clear GATE CS Exam [2024]: Road to Success | Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Graph-Based Algorithms for GATE Exam [2024], Searching and Sorting Algorithm Notes for GATE Exam [2024], Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Theory of Computation – GATE CSE Previous Year Questions, Dynamic Programming (DP) Notes for GATE Exam [2024], Basic Understanding of Bayesian Belief Networks, Differential Equations, Automata Theory | Set 6, Graph Data Structure Notes for GATE Exam [2024], Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Recursion Notes for GATE Exam [2024], Transformers in Machine Learning, Divide and Conquer Notes for GATE Exam [2024], Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Data Structures and Algorithms | Set 25, Binary Heap Notes for GATE Exam [2024], Greedy Algorithm Notes for GATE Exam [2024], Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.00723588746, -0.00926090404, -0.0160582531, 0.0211530402, 0.0553590544, 0.00507544, -0.0125950873, 0.0400617942, -0.0116212741, -0.0244420804, -0.0164194033, -0.0118727889, 0.0271120071, -0.0175157487, -0.0314458, 0.0049529071, 0.0179284923, 0.00191054516, -0.0214368012, -0.0395458676, -0.0114213517, -0.0150908884, 0.00229587872, 0.016638672, -0.0435443074, 0.0203662496, 0.0381528623, 0.00997675397, -0.0294078849, -0.00490453886, 0.0174770541, 0.0261188447, -0.0139687452, -0.0438796617, 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11 Sep, 2023 | Data Structures and Algorithms | Set 1
11 Sep, 2023
Following questions have been asked in GATE CS exam
1. Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respectively, of a complete binary tree. Which of the following is always true? (GATE CS 2000) (a) LASTIN = LASTPOST (b) LASTIN = LASTPRE (c) LASTPRE = LASTPOST (d) None of the above
Answer (d)
It is given that the given tree is complete binary tree. For a complete binary tree, the last visited node will always be same for inorder and preorder traversal. None of the above is true even for a complete binary tree.
The option (a) is incorrect because the last node visited in Inorder traversal is right child and last node visited in Postorder traversal is root.
The option (c) is incorrect because the last node visited in Preorder traversal is right child and last node visited in Postorder traversal is root.
For option (b), see the following counter example. Thanks to Hunaif Muhammed for providing the correct explanation.
1
/ \
2 3
/ \ /
4 5 6
Inorder traversal is 4 2 5 1 6 3
Preorder traversal is 1 2 4 5 3 6
2. The most appropriate matching for the following pairs
X: depth first search 1: heap
Y: breadth-first search 2: queue
Z: sorting 3: stack
is (GATE CS 2000): (a) X—1 Y—2 Z-3 (b) X—3 Y—1 Z-2 (c) X—3 Y—2 Z-1 (d) X—2 Y—3 Z-1
Answer: (c) Stack is used for Depth first Search Queue is used for Breadth First Search Heap is used for sorting
3. Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree? (a) (1 2 (4 5 6 7)) (b) (1 (2 3 4) 5 6) 7) (c) (1 (2 3 4)(5 6 7)) (d) (1 (2 3 NULL) (4 5))
Answer (c)
4. Let s be a sorted array of n integers. Let t(n) denote the time taken for the most efficient algorithm to determined if there are two elements with sum less than 1000 in s. which of the following statements is true? (GATE CS 2000) a) t (n) is 0 (1) b) n < t (n) < n log2n c) n log2n < t (n) < nC2 d) t (n) = nC2
Answer (a) Let array be sorted in ascending order, if sum of first two elements is less than 1000 then there are two elements with sum less than 1000 otherwise not. For array sorted in descending order we need to check last two elements. For an array data structure, number of operations are fixed in both the cases and not dependent on n, complexity is O(1)
5. B+ trees are preferred to binary trees in databases because (GATE CS 2000) (a) Disk capacities are greater than memory capacities (b) Disk access is much slower than memory access (c) Disk data transfer rates are much less than memory data transfer rates (d) Disks are more reliable than memory
Answer (b) Disk access is slow and B+ Tree provide search in less number of disk hits. 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12 Apr, 2019 | Data Structures and Algorithms | Set 2
12 Apr, 2019
Following questions have been asked in GATE CS exam.
1. Consider the function f defined below.
struct item
{
int data;
struct item * next;
};
int f(struct item *p)
{
return (
(p == NULL) ||
(p->next == NULL) ||
(( P->data <= p->next->data) && f(p->next))
);
}
For a given linked list p, the function f returns 1 if and only if (GATE CS 2003)
a) the list is empty or has exactly one element
b) the elements in the list are sorted in non-decreasing order of data value
c) the elements in the list are sorted in non-increasing order of data value
d) not all elements in the list have the same data value.
Answer (b)
The function f() works as follows
1) If linked list is empty return 1
2) Else If linked list has only one element return 1
3) Else if node->data is smaller than equal to node->next->data and the same thing holds for rest of the list then return 1
4) Else return 0
2. Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely (GATE CS 2004)?
i) preorder and postorder
ii) inorder and postorder
iii) preorder and inorder
iv) level order and postorder
a) (i) only
b) (ii), (iii)
c) (iii) only
d) (iv) only
Answer (b)
Please see this post for the explanation.
3. The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)? (GATE CS 2004)
a) 2
b) 3
c) 4
d) 6
Answer(b)
Constructed binary search tree will be..
10
/ \
1 15
\ / \
3 12 16
\
5
4. A data structure is required for storing a set of integers such that each of the following operations can be done in (log n) time, where n is the number of elements in the set.
o Deletion of the smallest element
o Insertion of an element if it is not already present in the set
Which of the following data structures can be used for this purpose?
(a) A heap can be used but not a balanced binary search tree
(b) A balanced binary search tree can be used but not a heap
(c) Both balanced binary search tree and heap can be used
(d) Neither balanced binary search tree nor heap can be used
Answer(b)
A self-balancing balancing binary search tree containing n items allows the lookup, insertion, and removal of an item in O(log n) worst-case time. Since it’s a self-balancing BST, we can easily find out minimum element in O(logn) time which is always the leftmost element (See Find the node with the minimum value in a Binary Search Tree).
Since Heap is a balanced binary tree (or almost complete binary tree), insertion complexity for heap is O(logn). Also, complexity to get minimum in a min heap is O(logn) because removal of root node causes a call to heapify (after removing the first element from the array) to maintain the heap tree property. But a heap cannot be used for the above purpose as the question says – insert an element if it is not already present. For a heap, we cannot find out in O(logn) if an element is present or not. Thanks to the game for providing the correct solution.
5. A circularly linked list is used to represent a Queue. A single variable p is used to access the Queue. To which node should p point such that both the operations enQueue and deQueue can be performed in constant time? (GATE 2004)
a) rear node
b) front node
c) not possible with a single pointer
d) node next to the front
Answer(a)
The answer is not “(b) front node”, as we can not get rear from the front in O(1), but if p is rear we can implement both enQueue and deQueue in O(1) because from rear we can get front in O(1). Below are sample functions. Note that these functions are just sample and are not working. Code to handle base cases is missing.
/* p is pointer to address of rear (double pointer). This function adds new
node after rear and updates rear which is *p to point to new node */
void enQueue(struct node **p, struct node *new_node)
{
/* Missing code to handle base cases like *p is NULL */
new_node->next = (*p)->next;
(*p)->next = new_node;
(*p) = new_node /* new is now rear */
/* Note that p is again front and p->next is rear */
}
/* p is pointer to rear. This function removes the front element and
returns the new front */
struct node *deQueue(struct node *p)
{
/* Missing code to handle base cases like p is NULL,
p->next is NULL,... etc */
struct node *temp = p->next->next;
p->next = p->next->next;
return temp;
/* Note that p is again front and p->next is rear */
} | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation 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your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Graph-Based Algorithms for GATE Exam [2024], Searching and Sorting Algorithm Notes for GATE Exam [2024], Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Theory of Computation – GATE CSE Previous Year Questions, Dynamic Programming (DP) Notes for GATE Exam [2024], Basic Understanding of Bayesian Belief Networks, Differential Equations, Automata Theory | Set 6, Graph Data Structure Notes for GATE Exam [2024], Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Recursion Notes for GATE Exam [2024], Transformers in Machine Learning, Divide and Conquer Notes for GATE Exam [2024], Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Data Structures and Algorithms | Set 25, Binary Heap Notes for GATE Exam [2024], Greedy Algorithm Notes for GATE Exam [2024], Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Data Structures and Algorithms | Set 1, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0226756986, 0.00549956551, -0.018857412, 0.0207296051, -0.0040985, -0.000375477743, 0.0095641939, 0.0360397063, -0.0214563105, -0.0217642374, 4.85465207e-05, -0.00622011302, -0.0196826551, -0.00965041295, -0.0105803506, 0.0339458063, 0.00857882947, 0.0561657734, -0.00988443755, -0.0584321134, -0.0406216495, -0.0170468055, 0.00652188109, 0.00966273, -0.00925626699, 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03 Feb, 2023 | Data Structures and Algorithms | Set 3
03 Feb, 2023
Following questions have asked in GATE CS exam.
1. Suppose you are given an array s[1…n] and a procedure reverse (s,i,j) which reverses the order of elements in a between positions i and j (both inclusive). What does the following sequence
do, where 1 < k <= n:
reverse (s, 1, k);
reverse (s, k + 1, n);
reverse (s, 1, n);
(GATE CS 2000)
(a) Rotates s left by k positions
(b) Leaves s unchanged
(c) Reverses all elements of s
(d) None of the above
Answer: (a) Effect of the above 3 reversals for any k is equivalent to left rotation of the array of size n by k. Please see this post for details. If we rotate an array n times for k = 1 to n, we get the same array back.
2. The best data structure to check whether an arithmetic expression has balanced parentheses is a (GATE CS 2004)
a) queue
b) stack
c) tree
d) list
Answer(b) There are three types of parentheses [ ] { } (). Below is an arbitrary c code segment which has parentheses of all three types.
c
void func(int c, int a[])
{
return ((c +2) + arr[(c-2)]) ;
}
Stack is a straightforward choice for checking if left and right parentheses are balanced. Here is a algorithm to do the same.
c
/*Return 1 if expression has balanced parentheses */
bool areParenthesesBalanced(expression )
{
for each character in expression
{
if(character == ’(’ || character == ’{’ || character == ’[’)
push(stack, character);
if(character == ’)’ || character == ’}’ || character == ’]’)
{
if(isEmpty(stack))
return 0; /*We are seeing a right parenthesis
without a left pair*/
/* Pop the top element from stack, if it is not a pair
bracket of character then there is a mismatch.
This will happen for expressions like {(}) */
else if (! isMatchingPair(pop(stack), character) )
return 0;
}
}
if(isEmpty(stack))
return 1; /*balanced*/
else
return 0; /*not balanced*/
} /* End of function to check parentheses */
/* Returns 1 if character1 and character2 are matching left
and right parentheses */
bool isMatchingPair(character1, character2)
{
if(character1 == ‘(‘ && character2 == ‘)’)
return 1;
else If(character1 == ‘{‘ && character2 == ‘}’)
return 1;
else If(character1 == ‘[‘ && character2 == ‘]’)
return 1;
else
return 0;
}
3. Level order traversal of a rooted tree can be done by starting from the root and performing (GATE CS 2004)
a) preorder traversal
b) in-order traversal
c) depth first search
d) breadth first search
Answer(d) See this post for details
4. Given the following input (4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199) and the hash function x mod 10, which of the following statements are true? i. 9679, 1989, 4199 hash to the same value ii. 1471, 6171 has to the same value iii. All elements hash to the same value iv. Each element hashes to a different value (GATE CS 2004)
a) i only
b) ii only
c) i and ii only
d) iii or iv
Answer (c)
5. Postorder traversal of a given binary search tree, T produces the following sequence of keys 10, 9, 23, 22, 27, 25, 15, 50, 95, 60, 40, 29 Which one of the following sequences of keys can be the result of an in-order traversal of the tree T? (GATE CS 2005)
a) 9, 10, 15, 22, 23, 25, 27, 29, 40, 50, 60, 95
b) 9, 10, 15, 22, 40, 50, 60, 95, 23, 25, 27, 29
c) 29, 15, 9, 10, 25, 22, 23, 27, 40, 60, 50, 95
d) 95, 50, 60, 40, 27, 23, 22, 25, 10, 9, 15, 29
Answer (a) Inorder traversal of a BST always gives elements in increasing order. Among all four options, a) is the only increasing order sequence. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine 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Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Data Structures and Algorithms | Set 25, Binary Heap Notes for GATE Exam [2024], Data Structures and Algorithms | Set 3, Greedy Algorithm Notes for GATE Exam [2024], Division Property of Equality, Gaussian Discriminant Analysis, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Data Structures and Algorithms | Set 1, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder | GeeksforGeeks | [-0.0133393835, 0.0189660043, -0.0220534932, 0.0267502908, 0.0169871505, 0.00334378635, 0.0164030306, 0.0358577892, -0.0206706803, -0.0120519362, 0.0198719855, -0.0113784103, -0.0149248503, 0.00273284502, -0.0267502908, 0.021326324, 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15 Feb, 2021 | Data Structures and Algorithms | Set 4
15 Feb, 2021
Following questions have been asked in GATE CS exam. 1. Consider the following C program segment
c
struct CellNode
{
struct CelINode *leftchild;
int element;
struct CelINode *rightChild;
}
int Dosomething(struct CelINode *ptr)
{
int value = 0;
if (ptr != NULL)
{
if (ptr->leftChild != NULL)
value = 1 + DoSomething(ptr->leftChild);
if (ptr->rightChild != NULL)
value = max(value, 1 + DoSomething(ptr->rightChild));
}
return (value);
}
The value returned by the function DoSomething when a pointer to the root of a non-empty tree is passed as argument is (GATE CS 2004) a) The number of leaf nodes in the tree b) The number of nodes in the tree c) The number of internal nodes in the tree d) The height of the treeAnswer: (d) Explanation: DoSomething() returns max(height of left child + 1, height of left child + 1). So given that pointer to root of tree is passed to DoSomething(), it will return height of the tree. Note that this implementation follows the convention where height of a single node is 0.
2. Suppose we run Dijkstra’s single source shortest-path algorithm on the following edge weighted directed graph with vertex P as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized? (GATE CS 2004)a) P, Q, R, S, T, U b) P, Q, R, U, S, T c) P, Q, R, U, T, S d) P, Q, T, R, U, S
Answer (b)
3. Suppose each set is represented as a linked list with elements in arbitrary order. Which of the operations among union, intersection, membership, cardinality will be the slowest? (GATE CS 2004) a) union only b) intersection, membership c) membership, cardinality d) union, intersectionAnswer: (d) Cardinality and membership are definitely not the slowest one. For cardinality, just count the number of nodes in a list. For membership, just traverse the list and look for a matchFor getting intersection of L1 and L2, search for each element of L1 in L2 and print the elements we find in L2. There can be many ways for getting union of L1 and L2. One of them is as follows a) Print all the nodes of L1 and print only those which are not present in L2. b) Print nodes of L2.
4. The time complexity of the following C function is (assume n > 0 (GATE CS 2004)
c
int recursive (mt n)
{
if (n == 1)
return (1);
else
return (recursive (n-1) + recursive (n-1));
}
a) 0(n) b) 0(nlogn) c) 0(n^2) d) 0(2^n)Answer: (d) Explanation: Recursive expression for the above program will be.
T(n) = 2T(n-1) + c
T(1) = c1.
Let us solve it.
T(n) = 2(2T(n-2) + c) + c = 4T(n-2) + 3c
T(n) = 8T(n-3) + 6c + c = 8T(n-3) + 7c
T(n) = 16T(n-4) + 14c + c = 16T(n-4) + 15c
...................................................
...................................................
T(n) = (2^(n-1))T(1) + (2^(n-1) - 1)c
T(n) = O(2^n)
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27 Mar, 2017 | Data Structures and Algorithms | Set 6
27 Mar, 2017
Following questions have been asked in GATE CS exam.
1. The usual Θ(n^2) implementation of Insertion Sort to sort an array uses linear search to identify the position where an element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will (GATE CS 2003)
(a) remain Θ(n^2)
(b) become Θ(n(log n)^2)
(c) become Θ(n log n)
(d) become Θ(n)
Answer (a)
If we use binary search then there will be ⌈ Log2(n!) ⌉ comparisons in the worst case, which is Θ(n log n) ( If you want to know how ⌈ Log2(n!) ⌉ can be equal to Θ(n log n)), then see this for proof). But the algorithm as a whole will still have a running time of Θ(n^2) on average because of the series of swaps required for each insertion.
Reference:
http://en.wikipedia.org/wiki/Insertion_sort
2. The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of
a) n
b) n^2
c) nlogn
d) n(log^2)n
Answer (c)
The number of comparisons that a comparison sort algorithm requires increases in proportion to nlog(n), where n is the number of elements to sort. This bound is asymptotically tight:
Given a list of distinct numbers (we can assume this because this is a worst-case analysis), there are n factorial permutations exactly one of which is the list in sorted order. The sort algorithm must gain enough information from the comparisons to identify the correct permutations. If the algorithm always completes after at most f(n) steps, it cannot distinguish more than 2^f(n) cases because the keys are distinct and each comparison has only two possible outcomes. Therefore,
2^f(n) >= n!, or equivalently f(n) > Log2(n!).
References:
http://en.wikipedia.org/wiki/Comparison_sort
http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15451-s07/www/lecture_notes/lect0130.pdf
3. The problem 3-SAT and 2-SAT are
a) both in P
b) both NP complete
c) NP-complete and in P respectively
d) undecidable and NP-complete respectively
Answer (c)
The Boolean satisfiability problem (SAT) is a decision problem, whose instance is a Boolean expression written using only AND, OR, NOT, variables, and parentheses. The problem is: given the expression, is there some assignment of TRUE and FALSE values to the variables that will make the entire expression true? A formula of propositional logic is said to be satisfiable if logical values can be assigned to its variables in a way that makes the formula true.
3-SAT and 2-SAT are special cases of k-satisfiability (k-SAT) or simply satisfiability (SAT), when each clause contains exactly k = 3 and k = 2 literals respectively.
2-SAT is P while 3-SAT is NP Complete. (See this for explanation)
References:
http://en.wikipedia.org/wiki/Boolean_satisfiability_problem
4. Consider the following graph
Among the following sequences
I) a b e g h f
II) a b f e h g
III) a b f h g e
IV) a f g h b e
Which are depth first traversals of the above graph? (GATE CS 2003)
a) I, II and IV only
b) I and IV only
c) II, III and IV only
d) I, III and IV only
Answer (d)
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Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Data Structures and Algorithms | Set 6, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Data Structures and Algorithms | Set 1, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder, Data Structures and Algorithms | Set 4 | GeeksforGeeks | [-0.0175404754, 0.017845748, -0.0240784045, 0.0343432091, 0.0307308119, 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13 Dec, 2022 | Data Structures and Algorithms | Set 7
13 Dec, 2022
Following questions have been asked in GATE CS 2006 exam.
1. In a binary max heap containing n numbers, the smallest element can be found in time (GATE CS 2006)
(A) 0(n)
(B) O(logn)
(C) 0(loglogn)
(D) 0(1)
Answer (A)
In a max heap, the smallest element is always present at a leaf node. So we need to check for all leaf nodes for the minimum value. Worst case complexity will be O(n)
12
/ \
/ \
8 7
/ \ / \
/ \ / \
2 3 4 5
2. A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1 instead of 0. the root is stored at X[1]. For a node stored at X[i], the left child, if any, is stored in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on n vertices the minimum size of X should be. (GATE CS 2006)
(A) log2n
(B) n
(C) 2n + 1
(D) 2^n — 1
Answer (D)
For a right skewed binary tree, number of nodes will be 2^n – 1. For example, in below binary tree, node ‘A’ will be stored at index 1, ‘B’ at index 3, ‘C’ at index 7 and ‘D’ at index 15.
A
\
\
B
\
\
C
\
\
D
3. Which one of the following in place sorting algorithms needs the minimum number of swaps? (GATE CS 2006)
(A) Quick sort
(B) Insertion sort
(C) Selection sort
(D) Heap sort
Answer (C)
For selection sort, number of swaps required is minimum ( Θ(n) ).
4. An element in an array X is called a leader if it is greater than all elements to the right of it in X. The best algorithm to find all leaders in an array (GATE CS 2006)
(A) Solves it in linear time using a left to right pass of the array
(B) Solves it in linear time using a right to left pass of the array
(C) Solves it using divide and conquer in time 8(nlogn)
(D) Solves it in time 8(n2)
Answer (B)
Please see this post for explanation.
5. Consider a weighted complete graph G on the vertex set {v1, v2, ..vn} such that the weight of the edge (vi, vj) is 2|i-j|. The weight of a minimum spanning tree of G is: (GATE CS 2006)
(A) n — 1
(B) 2n — 2
(C) nC2
(D) 2
Answer (B)
Minimum spanning tree of such a graph is
v1
\
v2
\
v3
\
v4
.
.
.
vn
Weight of the minimum spanning tree
= 2|2 – 1| + 2|3 – 2| + 2|4 – 3| + 2|5 – 4| …. + 2| n – (n-1) |
= 2n – 2
Please see GATE Corner for all previous year paper/solutions/explanations, syllabus, important dates, notes, etc.
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13 Dec, 2022 | Data Structures and Algorithms | Set 8
13 Dec, 2022
Following questions have been asked in GATE CS exam.
1. Consider the following functions
Which of the following is true? (GATE CS 2000)
(a) h(n) is 0(f(n))
(b) h(n) is 0(g(n))
(c) g(n) is not 0(f(n))
(d) f(n) is 0(g(n))
Answer (d)
g(n) = 2√n Log n = n√n
f(n) and g(n) are of same asymptotic order and following statements are true.
f(n) = O(g(n))
g(n) = O(f(n)).
(a) and (b) are false because n! is of asymptotically higher order than n√n.
2. Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false? (GATE CS 2000)
(a) Every minimum spanning tree of G must contain emin
(b) If emax is in a minimum spanning tree, then its removal must disconnect G
(c) No minimum spanning tree contains emax
(d) G has a unique minimum spanning tree
Answer (c)
(a) and (b) are always true.
(c) is false because (b) is true.
(d) is true because all edge weights are distinct for G.
3. Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true? (GATE CS 2000)
(a) {u,v} must be an edge in G, and u is a descendant of v in T
(b) {u,v} must be an edge in G, and v is a descendant of u in T
(c) If {u,v} is not an edge in G then u is a leaf in T
(d) If {u,v} is not an edge in G then u and v must have the same parent in T
Answer (c)
See https://www.geeksforgeeks.org/data-structures-graph-question-20/ for explanation.
4. Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)
a) d(r, u) < d (r, v)
b) d(r, u) > d(r, v)
c) d(r, u) <= d (r, v)
d) None of the above
Answer (c)
d(r, u) and d(r, v) will be equal when u and v are at same level, otherwise d(r, u) will be less than d(r, v)
5. How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ? (GATE CS 2001)
a) n(n-l)/2
b) 2^n
c) n!
d) 2^(n(n-1)/2)
Answer (d)
In an undirected graph, there can be maximum n(n-1)/2 edges. We can choose to have (or not have) any of the n(n-1)/2 edges. So, total number of undirected graphs with n vertices is 2^(n(n-1)/2).
Please see GATE Corner for all previous year paper/solutions/explanations, syllabus, important dates, notes, etc.
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13 Dec, 2022 | Data Structures and Algorithms | Set 9
13 Dec, 2022
Follow questions have been asked in GATE CS exam.
1 In a heap with n elements with the smallest element at the root, the 7th smallest element can be found in time (GATE CS 2003)
a) Θ(n log n)
b) Θ(n)
c) Θ(log n)
d) Θ(1)
Answer(d)
The 7th smallest element must be in first 7 levels. Total number of nodes in any Binary Heap in first 7 levels is at most 1 + 2 + 4 + 8 + 16 + 32 + 64 which is a constant. Therefore we can always find 7th smallest element in Θ(1) time.
2. Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree? (GATE CS 2003)
a) 7 5 1 0 3 2 4 6 8 9
b) 0 2 4 3 1 6 5 9 8 7
c) 0 1 2 3 4 5 6 7 8 9
d) 9 8 6 4 2 3 0 1 5 7
Answer (c)
In-order traversal of a BST gives elements in increasing order. So answer c is correct without any doubt.
3. Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operation take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is (GATE CS 2003)
a) n(X+ Y)
b) 3Y + 2X
c) n(X + Y)-X
d) Y + 2X
Answer(c)
We can easily arrive at the result by taking few examples.
Please see GATE Corner for all previous year paper/solutions/explanations, syllabus, important dates, notes, etc.
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13 Dec, 2022 | Data Structures and Algorithms | Set 10
13 Dec, 2022
Following questions have been asked in GATE CS 2007 exam.
1. The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:
(A) 2^h -1
(B) 2^(h-1) – 1
(C) 2^(h+1) -1
(D) 2*(h+1)
Answer (C)
Maximum number of nodes will be there for a complete tree.
Number of nodes in a complete tree of height h = 1 + 2 + 2^2 + 2*3 + …. 2^h = 2^(h+1) – 1
2: The maximum number of binary trees that can be formed with three unlabelled nodes is:
(A) 1
(B) 5
(C) 4
(D) 3
Answer (B)
O
/ \
O O
(i)
O
/
O
/
O
(ii)
O
/
O
\
O
(iii)
O
\
O
\
O
(iv)
O
\
O
/
O
(v)
Note that nodes are unlabelled. If the nodes are labeled, we get more number of trees.
3. Which of the following sorting algorithms has the lowest worst-case complexity?
(A) Merge sort
(B) Bubble sort
(C) Quick sort
(D) Selection sort
Answer (A)
Worst case complexities for the above sorting algorithms are as follows:
Merge Sort — nLogn
Bubble Sort — n^2
Quick Sort — n^2
Selection Sort — n^2
4. The following postfix expression with single digit operands is evaluated using a stack:
8 2 3 ^ / 2 3 * + 5 1 * -
Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:
(A) 6, 1
(B) 5, 7
(C) 3, 2
(D) 1, 5
Answer (A)
The algorithm for evaluating any postfix expression is fairly straightforward:
1. While there are input tokens left
o Read the next token from input.
o If the token is a value
+ Push it onto the stack.
o Otherwise, the token is an operator
(operator here includes both operators, and functions).
* It is known a priori that the operator takes n arguments.
* If there are fewer than n values on the stack
(Error) The user has not input sufficient values in the expression.
* Else, Pop the top n values from the stack.
* Evaluate the operator, with the values as arguments.
* Push the returned results, if any, back onto the stack.
2. If there is only one value in the stack
o That value is the result of the calculation.
3. If there are more values in the stack
o (Error) The user input has too many values.
Source for algorithm: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_postfix_algorithm
Let us run the above algorithm for the given expression.
First three tokens are values, so they are simply pushed. After pushing 8, 2 and 3, the stack is as follows
8, 2, 3
When ^ is read, top two are popped and power(2^3) is calculated
8, 8
When / is read, top two are popped and division(8/8) is performed
1
Next two tokens are values, so they are simply pushed. After pushing 2 and 3, the stack is as follows
1, 2, 3
When * comes, top two are popped and multiplication is performed.
1, 6
5. The inorder and preorder traversal of a binary tree are d b e a f c g and a b d e c f g, respectively. The postorder traversal of the binary tree is:
(A) d e b f g c a
(B) e d b g f c a
(C) e d b f g c a
(D) d e f g b c a
Answer (A)
Below is the given tree.
a
/ \
/ \
b c
/ \ / \
/ \ / \
d e f g
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7/Data Structures and Algorithms | Set 8/Data Structures and Algorithms | Set 9/Data Structures and Algorithms | Set 10 | https://www.geeksforgeeks.org/data-structures-and-algorithms-set-10/?ref=next_article | Data Science & ML | Data Structures and Algorithms | Set 10 | Data Structures and Algorithms | Set 9, Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Graph-Based Algorithms for GATE Exam [2024], Searching and Sorting Algorithm Notes for GATE Exam [2024], Data Structures and Algorithms | Set 7, Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Theory of Computation – GATE CSE Previous Year Questions, Dynamic Programming (DP) Notes for GATE Exam [2024], Basic Understanding of Bayesian Belief Networks, Differential Equations, Automata Theory | Set 6, Graph Data Structure Notes for GATE Exam [2024], Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Recursion Notes for GATE Exam [2024], Transformers in Machine Learning, Divide and Conquer Notes for GATE Exam [2024], Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Data Structures and Algorithms | Set 25, Binary Heap Notes for GATE Exam [2024], Data Structures and Algorithms | Set 3, Data Structures and Algorithms | Set 8, Greedy Algorithm Notes for GATE Exam [2024], Division Property of Equality, Gaussian Discriminant Analysis, Data Structures and Algorithms | Set 10, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Data Structures and Algorithms | Set 6, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Data Structures and Algorithms | Set 1, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder, Data Structures and Algorithms | Set 4 | GeeksforGeeks | [-0.0296175629, -0.00269420259, -0.0147963371, 0.0243660454, 0.0179447588, 0.00844349433, 0.0216158424, 0.0313099958, -0.0284975711, 0.0119403573, 0.00463241059, -0.034022864, -0.0120896902, 0.0196994133, -0.0274522454, 0.0509471856, 0.010310147, 0.030488668, -0.0215785094, -0.0595835671, -0.0286220144, -0.0273029134, 0.00305508892, 0.019910967, -0.00804527476, 0.014074564, 0.00821327325, -0.0305384453, -0.0376068391, 0.00229287217, -0.0127927959, 0.0362130702, -0.01034748, -0.0424103588, -0.0317331031, 0.0252620392, -5.76523598e-05, 0.0169616546, -0.0438290164, 0.0163767692, -0.0288460124, 0.0415890329, 0.00605106726, 0.000839993882, -0.0141616752, 0.00894749071, 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13 Dec, 2022 | Data Structures and Algorithms | Set 11
13 Dec, 2022
Following questions have been asked in GATE CS 2007 exam.
1. Consider a hash table of size seven, with starting index zero, and a hash function (3x + 4)mod7. Assuming the hash table is initially empty, which of the following is the contents of the table when the sequence 1, 3, 8, 10 is inserted into the table using closed hashing? Note that ‘_’ denotes an empty location in the table. (A) 8, _, _, _, _, _, 10 (B) 1, 8, 10, _, _, _, 3 (C) 1, _, _, _, _, _,3 (D) 1, 10, 8, _, _, _, 3Answer (B) Please see http://lcm.csa.iisc.ernet.in/dsa/node38.html for closed hashing and probing.Let us put values 1, 3, 8, 10 in the hash of size 7.Initially, hash table is empty
- - - - - - -
0 1 2 3 4 5 6
The value of function (3x + 4)mod 7 for 1 is 0, so let us put the value at 0
1 - - - - - -
0 1 2 3 4 5 6
The value of function (3x + 4)mod 7 for 3 is 6, so let us put the value at 6
1 - - - - - 3
0 1 2 3 4 5 6
The value of function (3x + 4)mod 7 for 8 is 0, but 0 is already occupied, let us put the value(8) at next available space(1)
1 8 - - - - 3
0 1 2 3 4 5 6
The value of function (3x + 4)mod 7 for 10 is 6, but 6 is already occupied, let us put the value(10) at next available space(2)
1 8 10 - - - 3
0 1 2 3 4 5 6
2. In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by (A) Dijkstra’s algorithm starting from S. (B) Warshall’s algorithm (C) Performing a DFS starting from S. (D) Performing a BFS starting from S.Answer(D)
* Time Complexity of the Dijkstra’s algorithm is O(|V|^2 + E)
* Time Complexity of the Warshall’s algorithm is O(|V|^3)
* DFS cannot be used for finding shortest paths
* BFS can be used for unweighted graphs. Time Complexity for BFS is O(|E| + |V|)
3. A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n? (A) 3 (B) 4 (C) 5 (D) 6Answer (C) For an n-ary tree where each node has n children or no children, following relation holds
L = (n-1)*I + 1
Where L is the number of leaf nodes and I is the number of internal nodes.Let us find out the value of n for the given data.
L = 41 , I = 10
41 = 10*(n-1) + 1
(n-1) = 4
n = 5
4. In the following C function, let n >= m.
c
int gcd(n,m)
{
if (n%m ==0) return m;
n = n%m;
return gcd(m,n);
}
How many recursive calls are made by this function? (A) Θ(logn)? (B) Ω(n) (C) Θ(loglogn) (D) Θ(sqrt(n))Answer (A) Above code is implementation of the Euclidean algorithm for finding Greatest Common Divisor (GCD). Please see http://mathworld.wolfram.com/EuclideanAlgorithm.html for time complexity.5. What is the time complexity of the following recursive function:
c
int DoSomething (int n)
{
if (n <= 2)
return 1;
else
return (DoSomething (floor(sqrt(n))) + n);
}
(A) Θ(n) (B) Θ(nlogn) (C) Θ(logn) (D) Θ(loglogn)Answer (D) Recursive relation for the DoSomething() is
T(n) = T(√n) + C1 if n > 2
We have ignored the floor() part as it doesn’t matter here if it’s a floor or ceiling.
Let n = 2^m, T(n) = T(2^m)
Let T(2^m) = S(m)
From the above two, T(n) = S(m)
S(m) = S(m/2) + C1 /* This is simply binary search recursion*/
S(m) = O(logm)
= O(loglogn) /* Since n = 2^m */
Now, let us go back to the original recursive function T(n)
T(n) = S(m)
= O(LogLogn)
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13 Dec, 2022 | Data Structures and Algorithms | Set 12
13 Dec, 2022
Following questions have been asked in GATE CS 2007 exam.
1. Consider the following C program segment where CellNode represents a node in a binary tree:
C
struct CellNode
{
struct CellNOde *leftChild;
int element;
struct CellNode *rightChild;
};
int GetValue(struct CellNode *ptr)
{
int value = 0;
if (ptr != NULL)
{
if ((ptr->leftChild == NULL) &&
(ptr->rightChild == NULL))
value = 1;
else
value = value + GetValue(ptr->leftChild)
+ GetValue(ptr->rightChild);
}
return(value);
}
The value returned by GetValue() when a pointer to the root of a binary tree is passed as its argument is: (A) the number of nodes in the tree (B) the number of internal nodes in the tree (C) the number of leaf nodes in the tree (D) the height of the treeAnswer (C) For explanation, please see our post https://www.geeksforgeeks.org/?p=2755 for counting leaf nodes.
2. Consider the process of inserting an element into a Max Heap, where the Max Heap is represented by an array. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of comparisons performed is: (A) Θ(logn) (B) Θ(LogLogn ) (C) Θ(n) (D) Θ(nLogn)Answer (B) The height of a Max Heap is Θ(logn). If we perform binary search for finding the correct position then we need to do Θ(LogLogn) comparisons.
3. Let w be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight w . Which of the following is FALSE? (A) There is a minimum spanning tree containing e. (B) If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T, all edges have the same weight. (C) Every minimum spanning tree has an edge of weight w . (D) e is present in every minimum spanning tree.Answer (D) (A), (B) and (C) are correct. (D) is incorrect as there may be many edges of weight w in the graph and e may not be picked up in some of the minimum spanning trees.
4. An array of n numbers is given, where n is an even number. The maximum, as well as the minimum of these n numbers, needs to be determined. Which of the following is TRUE about the number of comparisons needed? (A) At least 2n – c comparisons, for some constant c, are needed. (B) At most 1.5n – 2 comparisons are needed. (C) At least nLog2n comparisons are needed. (D) None of the above.Answer (B)Please see the post https://www.geeksforgeeks.org/?p=4583 for details.
5. Consider the following C code segment:
C
int IsPrime(n)
{
int i,n;
for(i=2;i<=sqrt(n);i++)
if(n%i == 0)
{printf(“Not Prime\n”); return 0;}
return 1;
}
Let T(n) denotes the number of times the for loop is executed by the program on input n. Which of the following is TRUE? (A) T(n) = O(sqrt(n)) and T(n) = Ω(sqrt(n)) (B) T(n) = O(sqrt(n)) and T(n) = Ω(1) (C) T(n) = O(n) and T(n) = Ω(sqrt(n)) (D) None of the aboveAnswer (B) Big O notation describes the upper bound and Big Omega notation describes the lower bound for an algorithm.The for loop in the question is run maximum sqrt(n) times and minimum 1 time. Therefore, T(n) = O(sqrt(n)) and T(n) = Ω(1)Please see GATE Corner for all previous year paper/solutions/explanations, syllabus, important dates, notes, etc.Please write comments if you find any of the answers/explanations incorrect, or you want to share more information about the topics discussed above. | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP 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05 Jul, 2018 | Data Structures and Algorithms | Set 13
05 Jul, 2018
Following questions have been asked in GATE CS 2002 exam
1. The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:
a) n/2
b) (n-1)/3
c) (n-1)/2
d) (2n+1)/3
Answer(d)
Let L be the number of leaf nodes and I be the number of internal nodes, then following relation holds for above given tree (For details, please see question 3 of https://www.geeksforgeeks.org/data-structures-and-algorithms-set-11/)
L = (3-1)I + 1 = 2I + 1
Total number of nodes(n) is sum of leaf nodes and internal nodes
n = L + I
After solving above two, we get L = (2n+1)/3
2. The running time of the following algorithm
Procedure A(n)
If n <= 2 return(1) else return A();
is best described by
a) O(n)
b) O(log n)
c) O(1og log n)
d) O(1)
Answer(c)
For explanation, please see question 5 of https://www.geeksforgeeks.org/data-structures-and-algorithms-set-11/
3. A weight-balanced tree is a binary tree in which for each node. The number of nodes in the left sub tree is at least half and at most twice the number of nodes in the right sub tree. The maximum possible height (number of nodes on the path from the root to the farthest leaf) of such a tree on n nodes is best described by which of the following?
a) log2 n
b) log4/3 n
c) log3 n
d) log3/2 n
Answer(d)
Let the maximum possible height of a tree with n nodes is represented by H(n).
The maximum possible value of H(n) can be approximately written using the following recursion:
H(n) = H(2n/3) + 1
The solution of above recurrence is log3/2 n. We can simply get it by drawing a recursion tree.
4. Consider the following algorithm for searching for a given number x in an unsorted – array A[1..n] having n distinct values:
1) Choose an i uniformly at random from 1..n;
2) If A[i] = x then Stop else Goto 1;
Assuming that x is present in A, what is the expected number of comparisons made by the algorithm before it terminates?
a) n
b) n-l
c) 2n
d) n/2
Answer(a)
If you remember the coin and dice questions, you can just guess the answer for the above.
Below is proof of the answer.
Let expected number of comparisons be E. Value of E is sum of following expression for all the possible cases.
number_of_comparisons_for_a_case * probability_for_the_case
Case 1
If A[i] is found in the first attempt
number of comparisons = 1
probability of the case = 1/n
Case 2
If A[i] is found in the second attempt
number of comparisons = 2
probability of the case = (n-1)/n*1/n
Case 3
If A[i] is found in the third attempt
number of comparisons = 2
probability of the case = (n-1)/n*(n-1)/n*1/n
There are actually infinite such cases. So, we have following infinite series for E.
E = 1/n + [(n-1)/n]*[1/n]*2 + [(n-1)/n]*[(n-1)/n]*[1/n]*3 + …. (1)
After multiplying equation (1) with (n-1)/n, we get
E (n-1)/n = [(n-1)/n]*[1/n] + [(n-1)/n]*[(n-1)/n]*[1/n]*2 +
[(n-1)/n]*[(n-1)/n]*[(n-1)/n]*[1/n]*3 ……….(2)
Subtracting (2) from (1), we get
E/n = 1/n + (n-1)/n*1/n + (n-1)/n*(n-1)/n*1/n + …………
The expression on the right side is a GP with infinite elements. Let us apply the sum formula (a/(1-r))
E/n = [1/n]/[1-(n-1)/n] = 1
E = n
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05 Jul, 2018 | Data Structures and Algorithms | Set 14
05 Jul, 2018
Following questions have been asked in GATE CS 2008 exam.
1. We have a binary heap on n elements and wish to insert n more elements (not necessarily one after another) into this heap. The total time required for this is
(A) Θ(logn)
(B) Θ(n)
(C) Θ(nlogn)
(D) Θ(n2)
The worst case time complexity for insertion in a binary heap is O(Logn) (Refer Wiki). So inserting n elements in a heap of size n should take Θ(nlogn) time.
But choice (B) seems to be more appropriate answer. One of the solution of O(n) complexity can be to take the ‘n’ elements of the heap and other ‘n’ elements together and construct heap in O(2n) = O(n). Thanks to pankaj for suggesting this solution.
2. The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is
(A) MNOPQR
(B) NQMPOR
(C) QMNPRO
(D) QMNPOR
Answer (C)
3. Consider the following functions:
f(n) = 2^n
g(n) = n!
h(n) = n^logn
Which of the following statements about the asymptotic behaviour of f(n), g(n), and h(n) is true?
(A) f(n) = O(g(n)); g(n) = O(h(n))
(B) f(n) = Ω(g(n)); g(n) = O(h(n))
(C) g(n) = O(f(n)); h(n) = O(f(n))
(D) h(n) = O(f(n)); g(n) = Ω(f(n))
Answer (D)
According to order of growth: h(n) < f(n) < g(n) (g(n) is asymptotically greater than f(n) and f(n) is asymptotically greater than h(n) )
We can easily see above order by taking logs of the given 3 functions
lognlogn < n < log(n!) (logs of the given f(n), g(n) and h(n)).
Note that log(n!) = Θ(nlogn)
4. The minimum number of comparisons required to determine if an integer appears more than n/2 times in a sorted array of n integers is
(A) Θ(n)
(B) Θ(logn)
(C) Θ(log*n)
(D) Θ(n)
Answer (B)
Please see the post Check for Majority Element in a sorted array for details.
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27 Mar, 2017 | Data Structures and Algorithms | Set 15
27 Mar, 2017
Following questions have been asked in GATE CS 2008 exam.
1. The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity.
(A) Θ(n)
(B) Θ(m)
(C) Θ(m + n)
(D) Θ(mn)
Answer (C)
Connected components can be found in O(m + n) using Tarjan’s algorithm. Once we have connected components, we can count them.
2. Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Then
(A) T(n) <= 2T(n/5) + n
(B) T(n) <= T(n/5) + T(4n/5) + n
(C) T(n) <= 2T(4n/5) + n
(D) T(n) <= 2T(n/2) + n
Answer (B)
For the case where n/5 elements are in one subset, T(n/5) comparisons are needed for the first subset with n/5 elements, T(4n/5) is for the rest 4n/5 elements, and n is for finding the pivot.
If there are more than n/5 elements in one set then other set will have less than 4n/5 elements and time complexity will be less than T(n/5) + T(4n/5) + n because recursion tree will be more balanced.
3 Dijkstra’s single source shortest path algorithm when run from vertex a in the below graph, computes the correct shortest path distance to
(A) only vertex a
(B) only vertices a, e, f, g, h
(C) only vertices a, b, c, d
(D) all the vertices
Answer (D)
Dijkstra’s single source shortest path is not guaranteed to work for graphs with negative weight edges, but it works for the given graph.
Let us see…
Let us run the 1st pass
b 1
b is minimum, so shortest distance to b is 1.
After 1st pass, distances are
c 3, e -2.
e is minimum, so shortest distance to e is -2
After 2nd pass, distances are
c 3, f 0.
f is minimum, so shortest distance to f is 0
After 3rd pass, distances are
c 3, g 3.
Both are same, let us take g. so shortest distance to g is 3.
After 4th pass, distances are
c 3, h 5
c is minimum, so shortest distance to c is 3
After 5th pass, distances are
h -2
h is minimum, so shortest distance to h is -2
4. The following C function takes a single-linked list of integers as a parameter and rearranges the elements of the list. The function is called with the list containing the integers 1, 2, 3, 4, 5, 6, 7 in the given order. What will be the contents of the list after the function completes execution?
struct node
{
int value;
struct node *next;
};
void rearrange(struct node *list)
{
struct node *p, * q;
int temp;
if ((!list) || !list->next)
return;
p = list;
q = list->next;
while(q)
{
temp = p->value;
p->value = q->value;
q->value = temp;
p = q->next;
q = p?p->next:0;
}
}
(A) 1,2,3,4,5,6,7
(B) 2,1,4,3,6,5,7
(C) 1,3,2,5,4,7,6
(D) 2,3,4,5,6,7,1
Answer (B)
The function rearrange() exchanges data of every node with its next node. It starts exchanging data from the first node itself.
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27 Mar, 2017 | Data Structures and Algorithms | Set 16
27 Mar, 2017
Following questions have been asked in GATE CS 2009 exam.
1. Consider a binary max-heap implemented using an array. Which one of the following array represents a binary max-heap?
(A) 25,12,16,13,10,8,14
(B) 25,14,13,16,10,8,12
(C) 25,14,16,13,10,8,12
(D) 25,14,12,13,10,8,16
Answer (C)
A tree is max-heap if data at every node in the tree is greater than or equal to it’s children’ s data.
In array representation of heap tree, a node at index i has its left child at index 2i + 1 and right child at index 2i + 2.
25
/ \
/ \
14 16
/ \ / \
/ \ / \
13 10 8 12
2. What is the content of the array after two delete operations on the correct answer to the previous question?
(A) 14,13,12,10,8
(B) 14,12,13,8,10
(C) 14,13,8,12,10
(D) 14,13,12,8,10
Answer(D)
For Heap trees, deletion of a node includes following two operations.
1) Replace the root with last element on the last level.
2) Starting from root, heapify the complete tree from top to bottom..
Let us delete the two nodes one by one:
1) Deletion of 25:
Replace 25 with 12
12
/ \
/ \
14 16
/ \ /
/ \ /
13 10 8
Since heap property is violated for root (16 is greater than 12), make 16 as root of the tree.
16
/ \
/ \
14 12
/ \ /
/ \ /
13 10 8
2) Deletion of 16:
Replace 16 with 8
8
/ \
/ \
14 12
/ \
/ \
13 10
Heapify from root to bottom.
14
/ \
/ \
8 12
/ \
/ \
13 10
14
/ \
/ \
13 12
/ \
/ \
8 10
3. In quick sort, for sorting n elements, the (n/4)th smallest element is selected as pivot using an O(n) time algorithm. What is the worst case time complexity of the quick sort?
(A) Θ(n)
(B) Θ(n Log n)
(C) Θ(n^2)
(D) Θ(n2 log n)
Answer(B)
The recursion expression becomes:
T(n) = T(n/4) + T(3n/4) + cn
After solving the above recursion, we get Θ(nLogn).
4. What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0.
(A) 2
(B) 3
(C) 4
(D) 5
Answer(B)
AVL trees are binary trees with the following restrictions.
1) the height difference of the children is at most 1.
2) both children are AVL trees
a
/ \
/ \
b c
/ \ /
/ \ /
d e g
/
/
h
References:
http://en.wikipedia.org/wiki/AVL_tree
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27 Mar, 2017 | Data Structures and Algorithms | Set 17
27 Mar, 2017
Following questions have been asked in GATE CS 2006 exam.
1. An implementation of a queue Q, using two stacks S1 and S2, is given below:
void insert(Q, x) {
push (S1, x);
}
void delete(Q){
if(stack-empty(S2)) then
if(stack-empty(S1)) then {
print(“Q is empty”);
return;
}
else while (!(stack-empty(S1))){
x=pop(S1);
push(S2,x);
}
x=pop(S2);
}
Let n insert and m (<=n) delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?
(A) n+m <= x < 2n and 2m <= y <= n+m
(B) n+m <= x < 2n and 2m<= y <= 2n
(C) 2m <= x < 2n and 2m <= y <= n+m
(D) 2m <= x <2n and 2m <= y <= 2n
Answer(A)
The order in which insert and delete operations are performed matters here.
The best case: Insert and delete operations are performed alternatively. In every delete operation, 2 pop and 1 push operations are performed. So, total m+ n push (n push for insert() and m push for delete()) operations and 2m pop operations are performed.
The worst case: First n elements are inserted and then m elements are deleted. In first delete operation, n + 1 pop operations and n push operation are performed. Other than first, in all delete operations, 1 pop operation is performed. So, total m + n pop operations and 2n push operations are performed (n push for insert() and m push for delete())
2. Consider the following graph:
Which one of the following cannot be the sequence of edges added, in that order, to a minimum spanning tree using Kruskal’s algorithm?
(A) (a—b),(d—f),(b—f),(d—c),(d—e)
(B) (a—b),(d—f),(d—c),(b—f),(d—e)
(C) (d—f),(a—b),(d—c),(b—f),(d—e)
(D) (d—f),(a—b),(b—f),(d—e),(d—c)
Answer (D)
The edge (d-e) cannot be considered before (d-c) in Kruskal’s minimum spanning tree algorithm because Kruskal’s algorithm picks the edge with minimum weight from the current set of edges at each step.
3. The median of n elements can be found in O(n)time. Which one of the following is correct about the complexity of quick sort, in which median is selected as pivot?
(A) Θ(n)
(B) Θ(nlogn)
(C) Θ(n^2)
(D) Θ(n^3)
Answer (B)
If median is always used as pivot, then recursion remains T(n) = 2T(n/2) + cn for all the cases where cn is combined time for median finding and partition. So, worst case time complexity of this quick sort becomes Θ(nlogn). In practical implementations, however, this variant is considerably slower on average (see http://en.wikipedia.org/wiki/Quicksort#Selection-based_pivoting)
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Algorithms | Set 6, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Data Structures and Algorithms | Set 1, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Data Structures and Algorithms | Set 12, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Data Structures and Algorithms | Set 14, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder, Data Structures and Algorithms | Set 13, Data Structures and Algorithms | Set 4 | GeeksforGeeks | [-0.0425575152, -0.0146694472, -0.0211795568, 0.0399534702, 0.0244532116, -0.00330775557, 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27 Mar, 2017 | Data Structures and Algorithms | Set 18
27 Mar, 2017
Following questions have been asked in GATE CS 2006 exam.
1. Consider the polynomial p(x) = a0 + a1x + a2x^2 +a3x^3, where ai != 0, for all i. The minimum number of multiplications needed to evaluate p on an input x is:
(A) 3
(B) 4
(C) 6
(D) 9
Answer (A)
Multiplications can be minimized using following order for evaluation of the given expression.
p(x) = a0 + x(a1 + x(a2 + a3x))
2. To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:
(A) Queue
(B) Stack
(C) Heap
(D) B-Tree
Answer(A)
The shortest path in an un-weighted graph means the smallest number of edges that must be traversed in order to reach the destination in the graph. This is the same problem as solving the weighted version where all the weights happen to be 1. If we use Queue (FIFO) instead of Priority Queue (Min Heap), we get the shortest path in linear time O(|V| + |E|). Basically we do BFS traversal of the graph to get the shortest paths.
3. A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property.
Which one of the following is a valid sequence of elements in an array representing 3-ary max heap?
(A) 1, 3, 5, 6, 8, 9
(B) 9, 6, 3, 1, 8, 5
(C) 9, 3, 6, 8, 5, 1
(D) 9, 5, 6, 8, 3, 1
Answer (D)
9
/ | \
/ | \
5 6 8
/ |
/ |
3 1
4. Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3- ary max heap found in the above question, Which one of the following is the sequence of items in the array representing the resultant heap?
(A) 10, 7, 9, 8, 3, 1, 5, 2, 6, 4
(B) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
(C) 10, 9, 4, 5, 7, 6, 8, 2, 1, 3
(D) 10, 8, 6, 9, 7, 2, 3, 4, 1, 5
Answer(A)
After insertion of 7
9
/ | \
/ | \
7 6 8
/ | \
/ | \
3 1 5
After insertion of 2
9
/ | \
/ | \
7 6 8
/ | \ /
/ | \ /
3 1 5 2
After insertion of 10
10
/ | \
/ | \
7 9 8
/ | \ / |
/ | \ / |
3 1 5 2 6
After insertion of 4
10
/ | \
/ | \
7 9 8
/ | \ / | \
/ | \ / | \
3 1 5 2 6 4
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27 Mar, 2017 | Data Structures and Algorithms | Set 19
27 Mar, 2017
Following questions have been asked in GATE CS 2009 exam.
1. Let X be a problem that belongs to the class NP. Then which one of the following is TRUE?
(A) There is no polynomial time algorithm for X.
(B) If X can be solved deterministically in polynomial time, then P = NP.
(C) If X is NP-hard, then it is NP-complete.
(D) X may be undecidable.
Answer (C)
(A) is incorrect because set NP includes both P(Polynomial time solvable) and NP-Complete .
(B) is incorrect because X may belong to P (same reason as (A))
(C) is correct because NP-Complete set is intersection of NP and NP-Hard sets.
(D) is incorrect because all NP problems are decidable in finite set of operations.
2. What is the number of swaps required to sort n elements using selection sort, in the worst case?
(A) Θ(n)
(B) Θ(n log n)
(C) Θ(n2 )
(D) Θ(nn2 log n)
Answer (A)
Here is Selection Sort algorithm for sorting in ascending order.
1. Find the minimum value in the list
2. Swap it with the value in the first position
3. Repeat the steps above for the remainder of the list (starting at
the second position and advancing each time)
As we can see from the algorithm, selection sort performs swap only after finding the appropriate position of the current picked element. So there are O(n) swaps performed in selection sort.
Because swaps require writing to the array, selection sort is preferable if writing to memory is significantly more expensive than reading. This is generally the case if the items are huge but the keys are small. Another example where writing times are crucial is an array stored in EEPROM or Flash. There is no other algorithm with less data movement.
References:
http://en.wikipedia.org/wiki/Selection_sort
3. The running time of an algorithm is represented by the following recurrence relation:
if n <= 3 then T(n) = n
else T(n) = T(n/3) + cn
Which one of the following represents the time complexity of the algorithm?
(A) Θ(n)
(B) Θ(n log n)
(C) Θ(n2)
(D) Θ(n2 log n)
Answer(A)
T(n) = cn + T(n/3)
= cn + cn/3 + T(n/9)
= cn + cn/3 + cn/9 + T(n/27)
Taking the sum of infinite GP series. The value of T(n) will
be less than this sum.
T(n) <= cn(1/(1-1/3))
<= 3cn/2
or we can say
cn <= T(n) <= 3cn/2
Therefore T(n) = Θ(n)
This can also be solved using Master Theorem for solving recurrences. The given expression lies in Case 3 of the theorem.
4. The keys 12, 18, 13, 2, 3, 23, 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h(k) = k mod 10 and linear probing. What is the resultant hash table?
Answer (C)
To get the idea of open addressing concept, you can go through below lines from Wikipedia
.
Open addressing, or closed hashing, is a method of collision resolution in hash tables. With this method a hash collision is resolved by probing, or searching through alternate locations in the array (the probe sequence) until either the target record is found, or an unused array slot is found, which indicates that there is no such key in the table. Well known probe sequences include:
linear probing in which the interval between probes is fixed--often at 1.
quadratic probing in which the interval between probes increases linearly (hence, the indices are described by a quadratic function).
double hashing in which the interval between probes is fixed for each record but is computed by another hash function.
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21 Dec, 2023 | Check for Majority Element in a sorted array
21 Dec, 2023
Given an array arr of N elements, A majority element in an array arr of size N is an element that appears more than N/2 times in the array. The task is to write a function say isMajority() that takes an array (arr[] ), array’s size (n) and a number to be searched (x) as parameters and returns true if x is a majority element (present more than n/2 times).
Examples:
Input: arr[] = {1, 2, 3, 3, 3, 3, 10}, x = 3Output: True (x appears more than n/2 times in the given array)Input: arr[] = {1, 1, 2, 4, 4, 4, 6, 6}, x = 4Output: False (x doesn't appear more than n/2 times in the given array)Input: arr[] = {1, 1, 1, 2, 2}, x = 1Output: True (x appears more than n/2 times in the given array)
Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.
METHOD 1 (Using Linear Search): Linearly search for the first occurrence of the element, once you find it (let at index i), check the element at index i + n/2. If the element is present at i+n/2 then return 1 else return 0.
C++
/* C++ Program to check for majority element in a sorted array */
#include<bits/stdc++.h>
using namespace std;
bool isMajority(int arr[], int n, int x)
{
int i;
/* get last index according to n (even or odd) */
int last_index = n % 2 ? (n / 2 + 1): (n / 2);
/* search for first occurrence of x in arr[]*/
for (i = 0; i < last_index; i++)
{
/* check if x is present and is present more than n/2
times */
if (arr[i] == x && arr[i + n / 2] == x)
return 1;
}
return 0;
}
/* Driver code */
int main()
{
int arr[] ={1, 2, 3, 4, 4, 4, 4};
int n = sizeof(arr)/sizeof(arr[0]);
int x = 4;
if (isMajority(arr, n, x))
cout << x <<" appears more than "<<
n/2 << " times in arr[]"<< endl;
else
cout <<x <<" does not appear more than" << n/2 <<" times in arr[]" << endl;
return 0;
}
// This code is contributed by shivanisinghss2110
C
/* C Program to check for majority element in a sorted array */
# include <stdio.h>
# include <stdbool.h>
bool isMajority(int arr[], int n, int x)
{
int i;
/* get last index according to n (even or odd) */
int last_index = n%2? (n/2+1): (n/2);
/* search for first occurrence of x in arr[]*/
for (i = 0; i < last_index; i++)
{
/* check if x is present and is present more than n/2
times */
if (arr[i] == x && arr[i+n/2] == x)
return 1;
}
return 0;
}
/* Driver program to check above function */
int main()
{
int arr[] ={1, 2, 3, 4, 4, 4, 4};
int n = sizeof(arr)/sizeof(arr[0]);
int x = 4;
if (isMajority(arr, n, x))
printf("%d appears more than %d times in arr[]",
x, n/2);
else
printf("%d does not appear more than %d times in arr[]",
x, n/2);
return 0;
}
Java
/* Program to check for majority element in a sorted array */
import java.io.*;
class Majority {
static boolean isMajority(int arr[], int n, int x)
{
int i, last_index = 0;
/* get last index according to n (even or odd) */
last_index = (n%2==0)? n/2: n/2+1;
/* search for first occurrence of x in arr[]*/
for (i = 0; i < last_index; i++)
{
/* check if x is present and is present more
than n/2 times */
if (arr[i] == x && arr[i+n/2] == x)
return true;
}
return false;
}
/* Driver function to check for above functions*/
public static void main (String[] args) {
int arr[] = {1, 2, 3, 4, 4, 4, 4};
int n = arr.length;
int x = 4;
if (isMajority(arr, n, x)==true)
System.out.println(x+" appears more than "+
n/2+" times in arr[]");
else
System.out.println(x+" does not appear more than "+
n/2+" times in arr[]");
}
}
/*This article is contributed by Devesh Agrawal*/
Python3
'''Python3 Program to check for majority element in a sorted array'''
def isMajority(arr, n, x):
# get last index according to n (even or odd) */
last_index = (n//2 + 1) if n % 2 != 0 else (n//2)
# search for first occurrence of x in arr[]*/
for i in range(last_index):
# check if x is present and is present more than n / 2 times */
if arr[i] == x and arr[i + n//2] == x:
return 1
# Driver program to check above function */
arr = [1, 2, 3, 4, 4, 4, 4]
n = len(arr)
x = 4
if (isMajority(arr, n, x)):
print ("% d appears more than % d times in arr[]"
%(x, n//2))
else:
print ("% d does not appear more than % d times in arr[]"
%(x, n//2))
# This code is contributed by shreyanshi_arun.
C#
// C# Program to check for majority
// element in a sorted array
using System;
class GFG {
static bool isMajority(int[] arr,
int n, int x)
{
int i, last_index = 0;
// Get last index according to
// n (even or odd)
last_index = (n % 2 == 0) ? n / 2 :
n / 2 + 1;
// Search for first occurrence
// of x in arr[]
for (i = 0; i < last_index; i++) {
// Check if x is present and
// is present more than n/2 times
if (arr[i] == x && arr[i + n / 2] == x)
return true;
}
return false;
}
// Driver code
public static void Main()
{
int[] arr = { 1, 2, 3, 4, 4, 4, 4 };
int n = arr.Length;
int x = 4;
if (isMajority(arr, n, x) == true)
Console.Write(x + " appears more than " +
n / 2 + " times in arr[]");
else
Console.Write(x + " does not appear more than " +
n / 2 + " times in arr[]");
}
}
// This code is contributed by Sam007
Javascript
<script>
// Javascript Program to check for majority
// element in a sorted array
function isMajority(arr, n, x)
{
let i, last_index = 0;
// Get last index according to
// n (even or odd)
last_index = (n % 2 == 0) ?
parseInt(n / 2, 10) : parseInt(n / 2, 10) + 1;
// Search for first occurrence
// of x in arr[]
for (i = 0; i < last_index; i++) {
// Check if x is present and
// is present more than n/2 times
if (arr[i] == x && arr[i +
parseInt(n / 2, 10)] == x)
return true;
}
return false;
}
let arr = [ 1, 2, 3, 4, 4, 4, 4 ];
let n = arr.length;
let x = 4;
if (isMajority(arr, n, x) == true)
document.write(x + " appears more than " +
parseInt(n / 2, 10) + " times in arr[]");
else
document.write(x + " does not appear more than " +
parseInt(n / 2, 10) + " times in arr[]");
</script>
PHP
<?php
// PHP Program to check for
// majority element in a
// sorted array
// function returns majority
// element in a sorted array
function isMajority($arr, $n, $x)
{
$i;
// get last index according
// to n (even or odd)
$last_index = $n % 2? ($n / 2 + 1): ($n / 2);
// search for first occurrence
// of x in arr[]
for ($i = 0; $i < $last_index; $i++)
{
// check if x is present and
// is present more than n/2
// times
if ($arr[$i] == $x && $arr[$i + $n / 2] == $x)
return 1;
}
return 0;
}
// Driver Code
$arr = array(1, 2, 3, 4, 4, 4, 4);
$n = sizeof($arr);
$x = 4;
if (isMajority($arr, $n, $x))
echo $x, " appears more than "
, floor($n / 2), " times in arr[]";
else
echo $x, "does not appear more than "
, floor($n / 2), "times in arr[]";
// This code is contributed by Ajit
?>
Output
4 appears more than 3 times in arr[]
Time Complexity: O(n)Auxiliary Space: O(1)
METHOD 2 (Using Binary Search): Use binary search methodology to find the first occurrence of the given number. The criteria for binary search is important here.
C++
// C++ program to check for majority
// element in a sorted array
#include<bits/stdc++.h>
using namespace std;
// If x is present in arr[low...high]
// then returns the index of first
// occurrence of x, otherwise returns -1
int _binarySearch(int arr[], int low,
int high, int x);
// This function returns true if the x
// is present more than n/2 times in
// arr[] of size n
bool isMajority(int arr[], int n, int x)
{
// Find the index of first occurrence
// of x in arr[]
int i = _binarySearch(arr, 0, n - 1, x);
// If element is not present at all,
// return false
if (i == -1)
return false;
// Check if the element is present
// more than n/2 times
if (((i + n / 2) <= (n - 1)) &&
arr[i + n / 2] == x)
return true;
else
return false;
}
// If x is present in arr[low...high] then
// returns the index of first occurrence
// of x, otherwise returns -1
int _binarySearch(int arr[], int low,
int high, int x)
{
if (high >= low)
{
int mid = (low + high)/2; /*low + (high - low)/2;*/
/* Check if arr[mid] is the first occurrence of x.
arr[mid] is first occurrence if x is one of
the following is true:
(i) mid == 0 and arr[mid] == x
(ii) arr[mid-1] < x and arr[mid] == x
*/
if ((mid == 0 || x > arr[mid - 1]) &&
(arr[mid] == x) )
return mid;
else if (x > arr[mid])
return _binarySearch(arr, (mid + 1),
high, x);
else
return _binarySearch(arr, low,
(mid - 1), x);
}
return -1;
}
// Driver code
int main()
{
int arr[] = { 1, 2, 3, 3, 3, 3, 10 };
int n = sizeof(arr) / sizeof(arr[0]);
int x = 3;
if (isMajority(arr, n, x))
cout << x << " appears more than "
<< n / 2 << " times in arr[]"
<< endl;
else
cout << x << " does not appear more than"
<< n / 2 << " times in arr[]" << endl;
return 0;
}
// This code is contributed by shivanisinghss2110
C
/* C Program to check for majority element in a sorted array */
# include <stdio.h>
# include <stdbool.h>
/* If x is present in arr[low...high] then returns the index of
first occurrence of x, otherwise returns -1 */
int _binarySearch(int arr[], int low, int high, int x);
/* This function returns true if the x is present more than n/2
times in arr[] of size n */
bool isMajority(int arr[], int n, int x)
{
/* Find the index of first occurrence of x in arr[] */
int i = _binarySearch(arr, 0, n-1, x);
/* If element is not present at all, return false*/
if (i == -1)
return false;
/* check if the element is present more than n/2 times */
if (((i + n/2) <= (n -1)) && arr[i + n/2] == x)
return true;
else
return false;
}
/* If x is present in arr[low...high] then returns the index of
first occurrence of x, otherwise returns -1 */
int _binarySearch(int arr[], int low, int high, int x)
{
if (high >= low)
{
int mid = (low + high)/2; /*low + (high - low)/2;*/
/* Check if arr[mid] is the first occurrence of x.
arr[mid] is first occurrence if x is one of the following
is true:
(i) mid == 0 and arr[mid] == x
(ii) arr[mid-1] < x and arr[mid] == x
*/
if ( (mid == 0 || x > arr[mid-1]) && (arr[mid] == x) )
return mid;
else if (x > arr[mid])
return _binarySearch(arr, (mid + 1), high, x);
else
return _binarySearch(arr, low, (mid -1), x);
}
return -1;
}
/* Driver program to check above functions */
int main()
{
int arr[] = {1, 2, 3, 3, 3, 3, 10};
int n = sizeof(arr)/sizeof(arr[0]);
int x = 3;
if (isMajority(arr, n, x))
printf("%d appears more than %d times in arr[]",
x, n/2);
else
printf("%d does not appear more than %d times in arr[]",
x, n/2);
return 0;
}
Java
/* Java Program to check for majority element in a sorted array */
import java.io.*;
class Majority {
/* If x is present in arr[low...high] then returns the index of
first occurrence of x, otherwise returns -1 */
static int _binarySearch(int arr[], int low, int high, int x)
{
if (high >= low)
{
int mid = (low + high)/2; /*low + (high - low)/2;*/
/* Check if arr[mid] is the first occurrence of x.
arr[mid] is first occurrence if x is one of the following
is true:
(i) mid == 0 and arr[mid] == x
(ii) arr[mid-1] < x and arr[mid] == x
*/
if ( (mid == 0 || x > arr[mid-1]) && (arr[mid] == x) )
return mid;
else if (x > arr[mid])
return _binarySearch(arr, (mid + 1), high, x);
else
return _binarySearch(arr, low, (mid -1), x);
}
return -1;
}
/* This function returns true if the x is present more than n/2
times in arr[] of size n */
static boolean isMajority(int arr[], int n, int x)
{
/* Find the index of first occurrence of x in arr[] */
int i = _binarySearch(arr, 0, n-1, x);
/* If element is not present at all, return false*/
if (i == -1)
return false;
/* check if the element is present more than n/2 times */
if (((i + n/2) <= (n -1)) && arr[i + n/2] == x)
return true;
else
return false;
}
/*Driver function to check for above functions*/
public static void main (String[] args) {
int arr[] = {1, 2, 3, 3, 3, 3, 10};
int n = arr.length;
int x = 3;
if (isMajority(arr, n, x)==true)
System.out.println(x + " appears more than "+
n/2 + " times in arr[]");
else
System.out.println(x + " does not appear more than " +
n/2 + " times in arr[]");
}
}
/*This code is contributed by Devesh Agrawal*/
Python3
'''Python3 Program to check for majority element in a sorted array'''
# This function returns true if the x is present more than n / 2
# times in arr[] of size n */
def isMajority(arr, n, x):
# Find the index of first occurrence of x in arr[] */
i = _binarySearch(arr, 0, n-1, x)
# If element is not present at all, return false*/
if i == -1:
return False
# check if the element is present more than n / 2 times */
if ((i + n//2) <= (n -1)) and arr[i + n//2] == x:
return True
else:
return False
# If x is present in arr[low...high] then returns the index of
# first occurrence of x, otherwise returns -1 */
def _binarySearch(arr, low, high, x):
if high >= low:
mid = (low + high)//2 # low + (high - low)//2;
''' Check if arr[mid] is the first occurrence of x.
arr[mid] is first occurrence if x is one of the following
is true:
(i) mid == 0 and arr[mid] == x
(ii) arr[mid-1] < x and arr[mid] == x'''
if (mid == 0 or x > arr[mid-1]) and (arr[mid] == x):
return mid
elif x > arr[mid]:
return _binarySearch(arr, (mid + 1), high, x)
else:
return _binarySearch(arr, low, (mid -1), x)
return -1
# Driver program to check above functions */
arr = [1, 2, 3, 3, 3, 3, 10]
n = len(arr)
x = 3
if (isMajority(arr, n, x)):
print ("% d appears more than % d times in arr[]"
% (x, n//2))
else:
print ("% d does not appear more than % d times in arr[]"
% (x, n//2))
# This code is contributed by shreyanshi_arun.
C#
// C# Program to check for majority
// element in a sorted array */
using System;
class GFG {
// If x is present in arr[low...high]
// then returns the index of first
// occurrence of x, otherwise returns -1
static int _binarySearch(int[] arr, int low,
int high, int x)
{
if (high >= low) {
int mid = (low + high) / 2;
//low + (high - low)/2;
// Check if arr[mid] is the first
// occurrence of x. arr[mid] is
// first occurrence if x is one of
// the following is true:
// (i) mid == 0 and arr[mid] == x
// (ii) arr[mid-1] < x and arr[mid] == x
if ((mid == 0 || x > arr[mid - 1]) &&
(arr[mid] == x))
return mid;
else if (x > arr[mid])
return _binarySearch(arr, (mid + 1),
high, x);
else
return _binarySearch(arr, low,
(mid - 1), x);
}
return -1;
}
// This function returns true if the x is
// present more than n/2 times in arr[]
// of size n
static bool isMajority(int[] arr, int n, int x)
{
// Find the index of first occurrence
// of x in arr[]
int i = _binarySearch(arr, 0, n - 1, x);
// If element is not present at all,
// return false
if (i == -1)
return false;
// check if the element is present
// more than n/2 times
if (((i + n / 2) <= (n - 1)) &&
arr[i + n / 2] == x)
return true;
else
return false;
}
//Driver code
public static void Main()
{
int[] arr = { 1, 2, 3, 3, 3, 3, 10 };
int n = arr.Length;
int x = 3;
if (isMajority(arr, n, x) == true)
Console.Write(x + " appears more than " +
n / 2 + " times in arr[]");
else
Console.Write(x + " does not appear more than " +
n / 2 + " times in arr[]");
}
}
// This code is contributed by Sam007
Javascript
<script>
// Javascript Program to check for majority
// element in a sorted array */
// If x is present in arr[low...high]
// then returns the index of first
// occurrence of x, otherwise returns -1
function _binarySearch(arr, low, high, x)
{
if (high >= low) {
let mid = parseInt((low + high) / 2, 10);
//low + (high - low)/2;
// Check if arr[mid] is the first
// occurrence of x. arr[mid] is
// first occurrence if x is one of
// the following is true:
// (i) mid == 0 and arr[mid] == x
// (ii) arr[mid-1] < x and arr[mid] == x
if ((mid == 0 || x > arr[mid - 1]) && (arr[mid] == x))
return mid;
else if (x > arr[mid])
return _binarySearch(arr, (mid + 1), high, x);
else
return _binarySearch(arr, low, (mid - 1), x);
}
return -1;
}
// This function returns true if the x is
// present more than n/2 times in arr[]
// of size n
function isMajority(arr, n, x)
{
// Find the index of first occurrence
// of x in arr[]
let i = _binarySearch(arr, 0, n - 1, x);
// If element is not present at all,
// return false
if (i == -1)
return false;
// check if the element is present
// more than n/2 times
if (((i + parseInt(n / 2, 10)) <= (n - 1)) && arr[i + parseInt(n / 2, 10)] == x)
return true;
else
return false;
}
let arr = [ 1, 2, 3, 3, 3, 3, 10 ];
let n = arr.length;
let x = 3;
if (isMajority(arr, n, x) == true)
document.write(x + " appears more than " + parseInt(n / 2, 10) + " times in arr[]");
else
document.write(x + " does not appear more than " + parseInt(n / 2, 10) + " times in arr[]");
</script>
Output
3 appears more than 3 times in arr[]
Time Complexity: O(log n)Auxiliary Space: O(1)
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2/Database Management System – GATE CSE Previous Year Questions/GATE CSE and IT Previous Years Papers PDF Download Link/Theory of Computation – GATE CSE Previous Year Questions/Automata Theory | Set 6/Data Structures and Algorithms | Set 25/Graph Data Structure Notes for GATE Exam [2024]/Binary Heap Notes for GATE Exam [2024]/Searching and Sorting Algorithm Notes for GATE Exam [2024]/Recursion Notes for GATE Exam [2024]/Divide and Conquer Notes for GATE Exam [2024]/Greedy Algorithm Notes for GATE Exam [2024]/Dynamic Programming (DP) Notes for GATE Exam [2024]/Graph-Based Algorithms for GATE Exam [2024]/Tips to Clear GATE CS Exam [2024]: Road to Success/Data Structures and Algorithms | Set 1/Data Structures and Algorithms | Set 2/Data Structures and Algorithms | Set 3/Data Structures and Algorithms | Set 4/Data Structures and Algorithms | Set 6/Data Structures and Algorithms | Set 7/Data Structures and Algorithms | Set 8/Data Structures and Algorithms | Set 9/Data Structures and Algorithms | Set 10/Data Structures and Algorithms | Set 11/Data Structures and Algorithms | Set 12/Data Structures and Algorithms | Set 13/Data Structures and Algorithms | Set 14/Check for Majority Element in a sorted array | https://www.geeksforgeeks.org/check-for-majority-element-in-a-sorted-array/ | Data Science & ML | Check for Majority Element in a sorted array | Data Structures and Algorithms | Set 9, Artificial Intelligence – Boon or Bane, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Graph-Based Algorithms for GATE Exam [2024], Searching and Sorting Algorithm Notes for GATE Exam [2024], Data Structures and Algorithms | Set 7, Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Theory of 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to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Data Structures and Algorithms | Set 14, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Check for Majority Element in a sorted array, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder, Data Structures and Algorithms | Set 13, Data Structures and Algorithms | Set 4 | GeeksforGeeks | [0.00269197579, -0.00992066413, -0.0156992693, 0.0237951111, 0.0209854636, -0.00336361211, -0.0216516685, 0.0248957984, -0.011477557, 0.0321226753, -0.0326440521, -0.00209456356, 0.0529777929, -0.00425792, -0.0118541075, 0.00667291367, -0.00568446796, 0.013077897, -0.0135051375, -0.0561350286, -0.0377709381, 0.00573153701, -0.0369019732, 0.0444040224, 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09 Dec, 2024 | Allocate Minimum Pages
09 Dec, 2024
Try it on GfG Practice
Given an array arr[] and an integer k, where arr[i] denotes the number of pages of a book and k denotes total number of students. All the books need to be allocated to k students in contiguous manner, with each student getting at least one book.
The task is to minimize the maximum number of pages allocated to a student. If it is not possible to allocate books to all students, return -1.
Examples:
Input: arr[] = [12, 34, 67, 90], k = 2Output: 113Explanation: Books can be distributed in following ways:
[12] and [34, 67, 90] – The maximum pages assigned to a student is 34 + 67 + 90 = 191.[12, 34] and [67, 90] – The maximum pages assigned to a student is 67 + 90 = 157.[12, 34, 67] and [90] – The maximum pages assigned to a student is 12 + 34 + 67 = 113.The third combination has the minimum pages assigned to a student which is 113.
Input: arr[] = [15, 17, 20], k = 5Output: -1Explanation: Since there are more students than total books, it’s impossible to allocate a book to each student.
Input: arr[] = [22, 23, 67], k = 1Output: 112Explanation: Since there is only 1 student, all books are assigned to that student. So, maximum pages assigned to a student is 22 + 23 + 67 = 112.
Table of Content
[Naive Approach] By Iterating Over All Possible Page Limits[Expected Approach] Using Binary Search[Naive Approach] By Iterating Over All Possible Page LimitsThe idea is to iterate over all possible page limits, or maximum pages that can be allocated to a student.
The minimum possible page limit is the highest page count among all books, as the book with the most pages must be assigned to some student. The maximum possible page limit is the sum of pages of all books, It is in the case when all books are given to a single student.To find the number of students that will be allocated books for a page limit, we start assigning books to the first student until the page limit is reached, then we move to the next student and so on. As soon as we find the first page limit with which we can allocate books to all k students, we will return it.
C++
// C++ program to find the minimum page limit by iterating
// over all possible page limits
#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
bool check(vector<int> &arr, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < arr.size(); i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
int findPages(vector<int> &arr, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.size())
return -1;
// Minimum and maximum possible page limits
int minPageLimit = *max_element(arr.begin(), arr.end());
int maxPageLimit = accumulate(arr.begin(), arr.end(), 0);
// Iterating over all possible page limits
for(int i = minPageLimit; i <= maxPageLimit; i++) {
// Return the first page limit with we can
// allocate books to all k students
if(check(arr, k, i))
return i;
}
return -1;
}
int main() {
vector<int> arr = {12, 34, 67, 90};
int k = 2;
cout << findPages(arr, k);
return 0;
}
C
// C program to find the minimum page limit by iterating
// over all possible page limits
#include <stdio.h>
#include <stdbool.h>
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
bool check(int arr[], int n, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < n; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
int findPages(int arr[], int n, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > n)
return -1;
// Minimum and maximum possible page limits
int minPageLimit = arr[0];
int maxPageLimit = 0;
for(int i = 0; i < n; i++) {
if(arr[i] > minPageLimit) minPageLimit = arr[i];
maxPageLimit += arr[i];
}
// Iterating over all possible page limits
for(int i = minPageLimit; i <= maxPageLimit; i++) {
// Return the first page limit with we can
// allocate books to all k students
if(check(arr, n, k, i))
return i;
}
return -1;
}
int main() {
int arr[] = {12, 34, 67, 90};
int k = 2;
int n = sizeof(arr) / sizeof(arr[0]);
printf("%d\n", findPages(arr, n, k));
return 0;
}
Java
// Java program to find the minimum page limit by iterating
// over all possible page limits
import java.util.Arrays;
class GfG {
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
static boolean check(int[] arr, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < arr.length; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
static int findPages(int[] arr, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.length)
return -1;
// Minimum and maximum possible page limits
int minPageLimit = Arrays.stream(arr).max().getAsInt();
int maxPageLimit = Arrays.stream(arr).sum();
// Iterating over all possible page limits
for(int i = minPageLimit; i <= maxPageLimit; i++) {
// Return the first page limit with we can
// allocate books to all k students
if(check(arr, k, i))
return i;
}
return -1;
}
public static void main(String[] args) {
int[] arr = {12, 34, 67, 90};
int k = 2;
System.out.println(findPages(arr, k));
}
}
Python
# Python program to find the minimum page limit by iterating
# over all possible page limits
# Function to check if books can be allocated to
# all k students without exceeding 'pageLimit'
def check(arr, k, pageLimit):
# Starting from the first student
cnt = 1
pageSum = 0
for pages in arr:
# If adding the current book exceeds the page
# limit, assign the book to the next student
if pageSum + pages > pageLimit:
cnt += 1
pageSum = pages
else:
pageSum += pages
# If books can assigned to less than k students then
# it can be assigned to exactly k students as well
return cnt <= k
def findPages(arr, k):
# If number of students are more than total books
# then allocation is not possible
if k > len(arr):
return -1
# Minimum and maximum possible page limits
minPageLimit = max(arr)
maxPageLimit = sum(arr)
# Iterating over all possible page limits
for i in range(minPageLimit, maxPageLimit + 1):
# Return the first page limit with we can
# allocate books to all k students
if check(arr, k, i):
return i
return -1
if __name__ == "__main__":
arr = [12, 34, 67, 90]
k = 2
print(findPages(arr, k))
C#
// C# program to find the minimum page limit by iterating
// over all possible page limits
using System;
using System.Linq;
class GfG {
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
static bool check(int[] arr, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < arr.Length; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
static int findPages(int[] arr, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.Length)
return -1;
// Minimum and maximum possible page limits
int minPageLimit = arr.Max();
int maxPageLimit = arr.Sum();
// Iterating over all possible page limits
for(int i = minPageLimit; i <= maxPageLimit; i++) {
// Return the first page limit with we can
// allocate books to all k students
if(check(arr, k, i))
return i;
}
return -1;
}
static void Main() {
int[] arr = {12, 34, 67, 90};
int k = 2;
Console.WriteLine(findPages(arr, k));
}
}
JavaScript
// JavaScript program to find the minimum page limit by iterating
// over all possible page limits
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
function check(arr, k, pageLimit) {
// Starting from the first student
let cnt = 1;
let pageSum = 0;
for(let i = 0; i < arr.length; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
function findPages(arr, k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.length)
return -1;
// Minimum and maximum possible page limits
const minPageLimit = Math.max(...arr);
const maxPageLimit = arr.reduce((a, b) => a + b, 0);
// Iterating over all possible page limits
for(let i = minPageLimit; i <= maxPageLimit; i++) {
// Return the first page limit with we can
// allocate books to all k students
if(check(arr, k, i))
return i;
}
return -1;
}
// Driver Code
const arr = [12, 34, 67, 90];
const k = 2;
console.log(findPages(arr, k));
Output113Time Complexity: O(n*(Sum(arr) – MAX)), where n is the total number of books, sum(arr) is the total number of pages in all the books and MAX is maximum number of pages in any book.Auxiliary Space: O(1)
[Expected Approach] Using Binary SearchThe maximum number of pages(page limit) that a student can be allocated has a monotonic property:
If, at a page limit p, books cannot be allocated to all k students, then we need to reduce the page limit to ensure more students receive books.If, at a page limit p, we can allocate books to more than k students, then we need to increase the page limit so that fewer students are allocated books.Therefore, we can apply binary search to minimize the maximum pages a student can be allocated. To check the number of students that can be allotted books for any page limit, we start assigning books to the first student until the page limit is reached, then move to the next student.
C++
// C++ program to find the minimum page limit by iterating
// over all possible page limits
#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
bool check(vector<int> &arr, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < arr.size(); i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
int findPages(vector<int> &arr, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.size())
return -1;
// Search space for Binary Search
int lo = *max_element(arr.begin(), arr.end());
int hi = accumulate(arr.begin(), arr.end(), 0);
int res = -1;
while(lo <= hi) {
int mid = lo + (hi - lo)/2;
if(check(arr, k, mid)){
res = mid;
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
return res;
}
int main() {
vector<int> arr = {12, 34, 67, 90};
int k = 2;
cout << findPages(arr, k);
return 0;
}
C
// C program to find the minimum page limit by iterating
// over all possible page limits
#include <stdio.h>
#include <stdbool.h>
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
bool check(int arr[], int n, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < n; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
int findPages(int arr[], int n, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > n)
return -1;
// Maximum element of the array is minimum page limit
int lo = arr[0];
for(int i = 1; i < n; i++)
if(arr[i] > lo) lo = arr[i];
// Summation of all element is maximum page limit
int hi = 0;
for(int i = 0; i < n; i++)
hi += arr[i];
int res = -1;
while(lo <= hi) {
int mid = lo + (hi - lo)/2;
if(check(arr, n, k, mid)){
res = mid;
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
return res;
}
int main() {
int arr[] = {12, 34, 67, 90};
int k = 2;
int n = sizeof(arr) / sizeof(arr[0]);
printf("%d\n", findPages(arr, n, k));
return 0;
}
Java
// Java program to find the minimum page limit by iterating
// over all possible page limits
import java.util.Arrays;
class GfG {
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
static boolean check(int[] arr, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < arr.length; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
static int findPages(int[] arr, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.length)
return -1;
// Search space for Binary Search
int lo = Arrays.stream(arr).max().getAsInt();
int hi = Arrays.stream(arr).sum();
int res = -1;
while(lo <= hi) {
int mid = lo + (hi - lo) / 2;
if(check(arr, k, mid)){
res = mid;
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
return res;
}
public static void main(String[] args) {
int[] arr = {12, 34, 67, 90};
int k = 2;
System.out.println(findPages(arr, k));
}
}
Python
# Python program to find the minimum page limit by iterating
# over all possible page limits
# Function to check if books can be allocated to
# all k students without exceeding 'pageLimit'
def check(arr, k, pageLimit):
# Starting from the first student
cnt = 1
pageSum = 0
for pages in arr:
# If adding the current book exceeds the page
# limit, assign the book to the next student
if pageSum + pages > pageLimit:
cnt += 1
pageSum = pages
else:
pageSum += pages
# If books can assigned to less than k students then
# it can be assigned to exactly k students as well
return cnt <= k
def findPages(arr, k):
# If number of students are more than total books
# then allocation is not possible
if k > len(arr):
return -1
# Search space for Binary Search
lo = max(arr)
hi = sum(arr)
res = -1
while lo <= hi:
mid = lo + (hi - lo) // 2
if check(arr, k, mid):
res = mid
hi = mid - 1
else:
lo = mid + 1
return res
if __name__ == "__main__":
arr = [12, 34, 67, 90]
k = 2
print(findPages(arr, k))
C#
// C# program to find the minimum page limit by iterating
// over all possible page limits
using System;
using System.Linq;
class GfG {
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
static bool check(int[] arr, int k, int pageLimit) {
// Starting from the first student
int cnt = 1;
int pageSum = 0;
for(int i = 0; i < arr.Length; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
static int findPages(int[] arr, int k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.Length)
return -1;
// Search space for Binary Search
int lo = arr.Max();
int hi = arr.Sum();
int res = -1;
while(lo <= hi) {
int mid = lo + (hi - lo) / 2;
if(check(arr, k, mid)){
res = mid;
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
return res;
}
static void Main() {
int[] arr = {12, 34, 67, 90};
int k = 2;
Console.WriteLine(findPages(arr, k));
}
}
JavaScript
// JavaScript program to find the minimum page limit by iterating
// over all possible page limits
// Function to check if books can be allocated to
// all k students without exceeding 'pageLimit'
function check(arr, k, pageLimit) {
// Starting from the first student
let cnt = 1;
let pageSum = 0;
for(let i = 0; i < arr.length; i++) {
// If adding the current book exceeds the page
// limit, assign the book to the next student
if(pageSum + arr[i] > pageLimit) {
cnt++;
pageSum = arr[i];
}
else {
pageSum += arr[i];
}
}
// If books can assigned to less than k students then
// it can be assigned to exactly k students as well
return (cnt <= k);
}
function findPages(arr, k) {
// If number of students are more than total books
// then allocation is not possible
if(k > arr.length)
return -1;
// Search space for Binary Search
let lo = Math.max(...arr);
let hi = arr.reduce((a, b) => a + b, 0);
let res = -1;
while(lo <= hi) {
let mid = lo + Math.floor((hi - lo) / 2);
if(check(arr, k, mid)){
res = mid;
hi = mid - 1;
}
else {
lo = mid + 1;
}
}
return res;
}
// Driver Code
const arr = [12, 34, 67, 90];
const k = 2;
console.log(findPages(arr, k));
Output113Time Complexity: O(n*log(Sum(arr) – MAX)), where n is the total number of books, sum(arr) is the total number of pages in all the books and MAX is maximum number of pages in any book.Auxiliary Space: O(1) | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’/GRE | List of words to enhance your vocabulary with root alphabet ‘E’/GRE | List of words to enhance your vocabulary with root alphabet ‘H’/ACID Properties in DBMS/File Organization in DBMS | Set 3/Last Minute Notes – DBMS/Commonly asked DBMS interview questions/Commonly asked DBMS Interview Questions | Set 2/Database Management System – GATE CSE Previous Year Questions/GATE CSE and IT Previous Years Papers PDF Download Link/Theory of Computation – GATE CSE Previous Year Questions/Automata Theory | Set 6/Data Structures and Algorithms | Set 25/Graph Data Structure Notes for GATE Exam [2024]/Binary Heap Notes for GATE Exam [2024]/Searching and Sorting Algorithm Notes for GATE Exam [2024]/Recursion Notes for GATE Exam [2024]/Divide and Conquer Notes for GATE Exam [2024]/Greedy Algorithm Notes for GATE Exam [2024]/Dynamic Programming (DP) Notes for GATE Exam [2024]/Graph-Based Algorithms for GATE Exam [2024]/Tips to Clear GATE CS Exam [2024]: Road to Success/Data Structures and Algorithms | Set 1/Data Structures and Algorithms | Set 2/Data Structures and Algorithms | Set 3/Data Structures and Algorithms | Set 4/Data Structures and Algorithms | Set 6/Data Structures and Algorithms | Set 7/Data Structures and Algorithms | Set 8/Data Structures and Algorithms | Set 9/Data Structures and Algorithms | Set 10/Data Structures and Algorithms | Set 11/Data Structures and Algorithms | Set 12/Data Structures and Algorithms | Set 13/Data Structures and Algorithms | Set 14/Check for Majority Element in a sorted array/Allocate Minimum Pages | https://www.geeksforgeeks.org/allocate-minimum-number-pages/?ref=lbp | Data Science & ML | Allocate Minimum Pages | Data Structures and Algorithms | Set 9, Artificial Intelligence – Boon or Bane, Allocate Minimum Pages, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Graph-Based Algorithms for GATE Exam [2024], Searching and Sorting Algorithm Notes for GATE Exam [2024], Data Structures and Algorithms | Set 7, Hidden Markov Model in Machine learning, Last Minute Notes – DBMS, ACID Properties in DBMS, Updated 300+ GRE Vocabulary List of Words With Usage and Definition, Practice Questions on Divisibility Rules, Theory of Computation – GATE CSE Previous Year Questions, Dynamic Programming (DP) Notes for GATE Exam [2024], Data Structures and Algorithms | Set 11, Basic Understanding of Bayesian Belief Networks, Differential Equations, Automata Theory | Set 6, Graph Data Structure Notes for GATE Exam [2024], Artificial Intelligence Examples, ML | Naive Bayes Scratch Implementation using Python, Recursion Notes for GATE Exam [2024], Transformers in Machine Learning, Divide and Conquer Notes for GATE Exam [2024], Ordinary Least Squares (OLS) using statsmodels, Commonly asked DBMS interview questions, Latest GRE Verbal Reasoning Topics and Format 2024, GRE | List of words to enhance your vocabulary with root alphabet ‘E’, Stacking in Machine Learning, AI ML DS - How To Get Started?, Camera Calibration with Python – OpenCV, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Quadratic Discriminant Analysis, Logarithmic Differentiation, Properties of Logarithms, GCD Practice Questions Medium Level, NumPy Introduction, GRE | List of words to enhance your vocabulary with root alphabet ‘H’, GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities, Data Structures and Algorithms | Set 25, Binary Heap Notes for GATE Exam [2024], Data Structures and Algorithms | Set 3, Data Structures and Algorithms | Set 8, Greedy Algorithm Notes for GATE Exam [2024], Division Property of Equality, Gaussian Discriminant Analysis, Data Structures and Algorithms | Set 10, Applying Multinomial Naive Bayes to NLP Problems, Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts, Does Artificial Intelligence Require Coding?, Data Structures and Algorithms | Set 6, Database Management System – GATE CSE Previous Year Questions, Divisibility Rule of 17, Data Structures and Algorithms | Set 1, Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn, Data Structures and Algorithms | Set 12, Tips to Clear GATE CS Exam [2024]: Road to Success, Components of Time Series Data, Data Science & ML, GATE CSE and IT Previous Years Papers PDF Download Link, Change of base rule for Logarithm, How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?, Data Structures and Algorithms | Set 2, Data Structures and Algorithms | Set 14, Agents in Artificial Intelligence, Score High on GRE: How to Get Good Score in GRE, Check for Majority Element in a sorted array, Commonly asked DBMS Interview Questions | Set 2, Difference Between Encoder and Decoder, Data Structures and Algorithms | Set 13, Data Structures and Algorithms | Set 4 | GeeksforGeeks | [-0.00606960198, -0.0125776771, -0.0196338426, 0.0212902967, -0.00847714301, -0.024927998, 0.0179124307, 0.0378710702, -0.0294751246, 0.0375787541, 0.00666641258, -0.0208193436, 0.0137063386, 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19 Oct, 2023 | Find a String in given Array of Strings using Binary Search
19 Oct, 2023
Given a sorted array of Strings arr and a String x, find an index of x if it is present in the array, using Binary Search
Examples:
Input: arr[] = {“contribute”, “geeks”, “ide”, “practice”}, x = “ide”Output: 2Explanation: The String x is present at index 2.
Input : arr[] = {“contribute”, “geeks”, “ide”, “practice”}, x = “zz”Output : -1Explanation: The String “zz” is not present.
Approach to Find a String in a given Array of Strings:
The idea is to apply Binary Search on the given Array of Strings.
Illustrations:
Suppose the array of string is arr[] = {“contribute”, “geeks”, “ide”, “practice”}, and the key string to find is x = “ide”.
Now the above approach will be performed like this:
1st iteration:
Low = 0, High = 4, Hence Mid = 2
Element at index 2 = “ide”, which is equal to the key string x
Therefore, x is found.
Below are the steps on how to Find a String in a given Array of Strings using Binary Search:
Find the Middle element of the Array of the String, and compare it with the String x.
If the key is found, return the index of the middle.
Else check if the mid string is smaller or larger than the key string x.
If it is smaller, reduce the search space to the lower half
If it is larger, reduce the search space to greater than half
Repeat the above steps till the key string x is found, or no more search space is left to search.
Below is the implementation of the above approach:
C++
// C++ program to implement
// Binary Search for strings
#include <bits/stdc++.h>
using namespace std;
// Returns index of x if it is present
// in arr[], else return -1
int binarySearch(string arr[], string x, int n)
{
int l = 0;
int r = n - 1;
// Loop to implement Binary Search
while (l <= r) {
// Calculatiing mid
int m = l + (r - l) / 2;
// Some random value assigned
// as 0 belongs to index
int res = -1000;
if (x == (arr[m]))
res = 0;
// Check if x is present at mid
if (res == 0)
return m;
// If x greater, ignore left half
if (x > (arr[m]))
l = m + 1;
// If x is smaller, ignore right half
else
r = m - 1;
}
return -1;
}
// Driver code
int main()
{
string arr[]
= { "contribute", "geeks", "ide", "practice" };
string x = "ide";
int n = 4;
int result = binarySearch(arr, x, n);
if (result == -1)
cout << ("Element not present");
else
cout << ("Element found at index ") << result;
}
// This code is contributed by
// Shashank_Sharma
Java
// Java program to implement Binary Search for strings
class GFG {
// Returns index of x if it is present in arr[],
// else return -1
static int binarySearch(String[] arr, String x)
{
int l = 0, r = arr.length - 1;
// Loop to implement Binary Search
while (l <= r) {
// Calculatiing mid
int m = l + (r - l) / 2;
int res = x.compareTo(arr[m]);
// Check if x is present at mid
if (res == 0)
return m;
// If x greater, ignore left half
if (res > 0)
l = m + 1;
// If x is smaller, ignore right half
else
r = m - 1;
}
return -1;
}
// Driver method to test above
public static void main(String[] args)
{
String[] arr
= { "contribute", "geeks", "ide", "practice" };
String x = "ide";
int result = binarySearch(arr, x);
if (result == -1)
System.out.println("Element not present");
else
System.out.println("Element found at "
+ "index " + result);
}
}
Python3
# Python3 program to implement Binary
# Search for strings
# Returns index of x if it is present
# in arr[], else return -1
def binarySearch(arr, x):
l = 0
r = len(arr)
# Loop to implement Binary Search
while (l <= r):
# Calculatiing mid
m = l + ((r - l) // 2)
res = (x == arr[m])
# Check if x is present at mid
if (res == 0):
return m - 1
# If x greater, ignore left half
if (res > 0):
l = m + 1
# If x is smaller, ignore right half
else:
r = m - 1
return -1
# Driver Code
if __name__ == "__main__":
arr = ["contribute", "geeks",
"ide", "practice"]
x = "ide"
result = binarySearch(arr, x)
if (result == -1):
print("Element not present")
else:
print("Element found at index",
result)
# This code is contributed by ita_c
C#
// C# program to implement Binary Search for strings
using System;
class GFG {
// Returns index of x if it is present in arr[],
// else return -1
static int binarySearch(String[] arr, String x)
{
int l = 0, r = arr.Length - 1;
// Loop to implement Binary Search
while (l <= r) {
// Calculatiing mid
int m = l + (r - l) / 2;
int res = x.CompareTo(arr[m]);
// Check if x is present at mid
if (res == 0)
return m;
// If x greater, ignore left half
if (res > 0)
l = m + 1;
// If x is smaller, ignore right half
else
r = m - 1;
}
return -1;
}
// Driver method to test above
public static void Main(String[] args)
{
String[] arr
= { "contribute", "geeks", "ide", "practice" };
String x = "ide";
int result = binarySearch(arr, x);
if (result == -1)
Console.WriteLine("Element not present");
else
Console.WriteLine("Element found at "
+ "index " + result);
}
// This code is contributed by Ryuga
}
PHP
<?php
// PHP program to implement Binary
// Search for strings
// Returns index of x if it is present
// in arr[], else return -1
function binarySearch($arr, $x)
{
$l = 0;
$r = count($arr);
// Loop to implement Binary Search
while ($l <= $r)
{
// Calculatiing mid
$m = $l + (int)(($r - $l) / 2);
$res = strcmp($x, $arr[$m]);
// Check if x is present at mid
if ($res == 0)
return $m;
// If x greater, ignore left half
if ($res > 0)
$l = $m + 1;
// If x is smaller, ignore right half
else
$r = $m - 1;
}
return -1;
}
// Driver Code
$arr = array("contribute", "geeks",
"ide", "practice");
$x = "ide";
$result = binarySearch($arr, $x);
if ($result == -1)
print("Element not present");
else
print("Element found at index " .
$result);
// This code is contributed by mits
?>
Javascript
// Javascript program to implement Binary Search for strings
// Returns index of x if it is present in arr[],
// else return -1
function binarySearch(arr, x) {
let l = 0,
r = arr.length - 1;
// Loop to implement Binary Search
while (l <= r) {
// Calculatiing mid
let m = l + Math.floor((r - l) / 2);
let res = x.localeCompare(arr[m]);
// Check if x is present at mid
if (res == 0)
return m;
// If x greater, ignore left half
if (res > 0)
l = m + 1;
// If x is smaller, ignore right half
else
r = m - 1;
}
return -1;
}
// Driver method to test above
let arr = ["contribute", "geeks", "ide", "practice"];
let x = "ide";
let result = binarySearch(arr, x);
if (result == -1)
console.log("Element not present");
else
console.log("Element found at " +
"index " + result);
// This code is contributed by rag2127
Output
Element found at index 2
Time Complexity: O(log(n) * len), where n = no. of string in arr & len = max length of the string for comparing two strings we need O(len) timeAuxiliary Space: O(1) | Data Science & ML/AI ML DS - How To Get Started?/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/Transformers in Machine Learning/Difference Between Encoder and Decoder/Camera Calibration with Python – OpenCV/NumPy Introduction/How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?/Ordinary Least Squares (OLS) using statsmodels/Stacking in Machine Learning/ML | Naive Bayes Scratch Implementation using Python/Applying Multinomial Naive Bayes to NLP Problems/Gaussian Process Classification (GPC) on the XOR Dataset in Scikit Learn/Gaussian Discriminant Analysis/Quadratic Discriminant Analysis/Basic Understanding of Bayesian Belief Networks/Hidden Markov Model in Machine learning/Components of Time Series Data/Pearson Correlation Coefficient/Differential Equations/Logarithmic Differentiation/Change of base rule for Logarithm/Properties of Logarithms/Division Property of Equality/Divisibility Rule of 23/Divisibility Rule of 17/Practice Questions on Divisibility Rules/GCD Practice Questions Medium Level/Top 10 Tips for GRE Quantitative Exam: Learn Maths Tricks and Shortcuts/GRE Accepting Universities in USA in 2024: GRE Score Required for US Universities/Score High on GRE: How to Get Good Score in GRE/Latest GRE Verbal Reasoning Topics and Format 2024/Updated 300+ GRE Vocabulary List of Words With Usage and Definition/GRE | List of words to enhance your vocabulary with alphabet ‘B’/GRE | List of words to enhance your vocabulary with root alphabet ‘E’/GRE | List of words to enhance your vocabulary with root alphabet ‘H’/ACID Properties in DBMS/File Organization in DBMS 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Algorithms | Set 7/Data Structures and Algorithms | Set 8/Data Structures and Algorithms | Set 9/Data Structures and Algorithms | Set 10/Data Structures and Algorithms | Set 11/Data Structures and Algorithms | Set 12/Data Structures and Algorithms | Set 13/Data Structures and Algorithms | Set 14/Check for Majority Element in a sorted array/Allocate Minimum Pages/Find a String in given Array of Strings using Binary Search | https://www.geeksforgeeks.org/binary-search-a-string/?ref=lbp | Data Science & ML | Find a String in given Array of Strings using Binary Search | Data Structures and Algorithms | Set 9, Artificial Intelligence – Boon or Bane, Allocate Minimum Pages, File Organization in DBMS | Set 3, Pearson Correlation Coefficient, GRE | List of words to enhance your vocabulary with alphabet ‘B’, AI ML DS - Projects, Divisibility Rule of 23, Graph-Based Algorithms for GATE Exam [2024], Searching and Sorting Algorithm Notes for GATE Exam [2024], Data Structures and Algorithms | Set 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