Chapter 1: Introduction to Algorithms
Defines what algorithms are, their importance in computer science, and fundamental concepts that form the foundation of algorithmic thinking.
Table of Contents
This collection is structured into 12 chapters, each covering fundamental algorithm concepts with detailed explanations, code examples, visual diagrams, and practice problems. Chapters can be read sequentially or used as a reference for specific topics. Updating daily.
Chapter 2: Complexity Analysis
Presents Big O notation, time and space complexity analysis, and methods for evaluating algorithm efficiency.
Chapter 3: Recursion & Divide-and-Conquer
Comprehensive guide to recursive thinking, divide-and-conquer strategies, memoization, and common recursive patterns with detailed examples and practice problems.
- Recursion Basics - Fundamentals, call stack, examples
- Divide and Conquer - Master theorem, merge sort, binary search
- Memoization - Optimization techniques and patterns
- Common Patterns - Tree traversal, backtracking, DP
- Recursion vs Iteration - When to use each approach
- Common Pitfalls - Debugging tips and best practices
- Practice Problems - LeetCode problems by difficulty
Chapter 4: Trees
Comprehensive guide to tree data structures, traversals, binary search trees, and advanced tree algorithms with detailed implementations and examples. Trees are a special case of graphs and provide the foundation for understanding graph algorithms.
- Tree Fundamentals - Terminology, properties, types
- Binary Trees - Types, operations, construction
- Tree Traversals - Inorder, preorder, postorder, BFS, Morris
- Binary Search Trees - Search, insert, delete, validation
- Advanced Trees - Trie, Segment Tree
- Tree Problems - Common patterns and solutions
- Practice Problems - LeetCode problems by difficulty
Chapter 5: Sorting Algorithms
Comprehensive guide to the 8 most popular sorting algorithms: Bubble Sort, Quick Sort, Selection Sort, Insertion Sort, Merge Sort, Heap Sort, Radix Sort, and Tim Sort with detailed implementations and comparisons.
- 1. Bubble Sort - Simple comparison-based sort
- 2. Quick Sort - Fast divide-and-conquer
- 3. Selection Sort - In-place selection
- 4. Insertion Sort - Efficient for small arrays
- 5. Merge Sort - Stable divide-and-conquer
- 6. Heap Sort - In-place O(n log n)
- 7. Radix Sort - Non-comparison based
- 8. Tim Sort - Hybrid stable sort
- Algorithm Comparison - Comprehensive table
- Selection Guide - When to use each algorithm
Chapter 6: Searching Algorithms
Fundamental searching algorithms for arrays and lists: Linear Search and Binary Search. For graph traversal and pathfinding algorithms, see Chapter 7: Graph Algorithms.
- 1. Linear Search - Sequential search for any data
- 2. Binary Search - Divide-and-conquer for sorted arrays
- Algorithm Comparison - When to use each
- Selection Guide - Best practices
Chapter 7: Graph Algorithms
Comprehensive guide to graph traversal, shortest paths, and pathfinding algorithms: DFS, BFS, Union-Find, Dijkstra's, Bellman-Ford, Floyd-Warshall, and A* with detailed implementations and visualizations.
- Graph Fundamentals - Terminology, representations
- 1. Depth-First Search (DFS) - Graph traversal
- 2. Breadth-First Search (BFS) - Level-order traversal
- 3. Union-Find - Disjoint set union
- 4. Dijkstra's Algorithm - Shortest path (non-negative weights)
- 5. Bellman-Ford Algorithm - Handles negative weights
- 6. Floyd-Warshall Algorithm - All-pairs shortest paths
- 7. A* Algorithm - Heuristic-based pathfinding
Chapter 8: Dynamic Programming
Comprehensive guide to dynamic programming techniques for solving optimization problems efficiently with detailed patterns, implementations, and practice problems.
- Introduction to DP - Core principles, when to use
- Memoization vs Tabulation - Top-down vs bottom-up approaches
- Common DP Patterns - 1D, 2D, Knapsack, LCS, Interval DP
- Classic DP Problems - Detailed solutions with code
- Optimization Techniques - Space optimization, state compression
- Identifying DP Problems - How to recognize DP
- Practice Problems - LeetCode problems by difficulty
Chapter 9: Greedy Algorithms
Describes greedy strategies for optimization problems and conditions when greedy approaches are optimal.
Chapter 10: String Algorithms
Covers string manipulation, pattern matching, and advanced string processing techniques.
Chapter 11: Encryption Algorithms
Comprehensive guide to the 5 most popular encryption algorithms: AES, RSA, DES, SHA, and MD5 with detailed implementations and security analysis.
- 1. AES - Advanced Encryption Standard
- 2. RSA - Public-key cryptography
- 3. DES - Legacy encryption standard
- 4. SHA - Secure Hash Algorithm
- 5. MD5 - Message Digest 5
- Algorithm Comparison - Security and use cases
- Selection Guide - When to use each algorithm
Chapter 12: Machine Learning Algorithms
Introduction to machine learning algorithms including supervised learning, unsupervised learning, and neural networks with implementations and applications.
- Supervised Learning - Linear/Logistic Regression, Decision Trees, KNN, SVM
- Unsupervised Learning - K-Means, PCA
- Neural Networks - Perceptron, MLP
- Evaluation Metrics - Classification and regression metrics
- Best Practices - Data preprocessing, validation
- Applications - Real-world use cases
Suggested Reading Order
This reading order follows a pedagogically sound progression, building concepts from fundamentals to advanced topics. Each chapter builds upon previous knowledge:
- Chapter 1: Introduction to Algorithms - Foundational concepts and terminology
- Chapter 2: Complexity Analysis - Essential for evaluating any algorithm
- Chapter 3: Recursion & Divide-and-Conquer - Core technique used throughout
- Chapter 4: Trees - Simpler than graphs; establishes recursive structures and traversal concepts
- Chapter 5: Sorting Algorithms - Prerequisite for binary search; builds on divide-and-conquer
- Chapter 6: Searching Algorithms - Linear and Binary Search (requires sorted data from Ch 5)
- Chapter 7: Graph Algorithms - Builds on trees; includes DFS, BFS, shortest paths
- Chapter 8: Dynamic Programming - Benefits from recursion, trees, and graph concepts
- Chapter 9: Greedy Algorithms - Often compared with DP; uses graph concepts
- Chapter 10: String Algorithms - Specialized domain; can leverage DP concepts
- Chapter 11: Encryption Algorithms - Specialized domain; independent of other chapters
- Chapter 12: Machine Learning Algorithms - Most specialized; requires optimization concepts
Key Dependencies:
- Chapter 2 (Complexity) is prerequisite for all subsequent chapters
- Chapter 3 (Recursion) is used in Chapters 4, 5, 6, 7, and 8
- Chapter 4 (Trees) should come before Chapter 7 (Graphs) - trees are simpler and trees are a special case of graphs
- Chapter 5 (Sorting) should come before Chapter 6 (Searching) - binary search requires sorted data
- Chapter 7 (Graphs) benefits from Chapter 4 (Trees) - many graph traversal concepts build on tree traversal
- Chapter 8 (DP) benefits from Chapters 3, 4, and 7 - many DP problems involve trees and graphs