Mastering Algorithms - Algorithms Collection

Algorithms Collection

This collection contains 12 comprehensive topics, each covering fundamental algorithm concepts with detailed explanations, code examples, visual diagrams, and practice problems. Topics can be explored sequentially or used as a reference for specific algorithms. Updating daily.

Introduction to Algorithms

Defines what algorithms are, their importance in computer science, and fundamental concepts that form the foundation of algorithmic thinking.

Complexity Analysis

Presents Big O notation, time and space complexity analysis, and methods for evaluating algorithm efficiency.

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

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

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

Searching Algorithms

Fundamental searching algorithms for arrays and lists: Linear Search and Binary Search. For graph traversal and pathfinding algorithms, see 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

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

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

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

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