📚 Algorithm Learning Journey 🚀

Welcome to my Algorithm Learning Journey, a comprehensive exploration into the essential algorithms that power modern computing. This repository is designed to help you learn, implement, and understand key algorithms, complete with explanations, code implementations, and practical applications.

🌟 What’s Inside?

This repository covers a broad spectrum of algorithms organized into several categories. Each section includes detailed implementations and explanations to facilitate learning.

📚 Table of Contents

1. Sorting Algorithms

• Bubble Sort: Simple but inefficient; used mainly for educational purposes.
• Merge Sort: A divide-and-conquer algorithm; stable and efficient.
• Quick Sort: Generally faster than merge sort but not stable.
• Insertion Sort: Efficient for small datasets; often used in hybrid algorithms.
• Heap Sort: Based on binary heap data structure; not stable but efficient.
• Counting Sort: Non-comparison sort; effective when input range is small.
• Radix Sort: Non-comparative integer sorting algorithm; works well with large datasets.

2. Searching Algorithms

• Binary Search: Efficient for finding elements in sorted arrays.
• Depth-First Search (DFS): Used for traversing or searching tree or graph data structures.
• Breadth-First Search (BFS): Finds the shortest path in unweighted graphs.
• Exponential Search: Useful for unbounded or infinite lists; combines binary search with exponential growth.

3. Dynamic Programming

• Fibonacci Sequence: Classic example for dynamic programming.
• Knapsack Problem: Important for resource allocation problems.
• Longest Common Subsequence (LCS): Used in comparison algorithms.
• Longest Increasing Subsequence (LIS): Useful in optimization problems.
• Matrix Chain Multiplication: Demonstrates dynamic programming optimization.
• Bellman-Ford Algorithm: Computes shortest paths in graphs with negative weights.

4. Greedy Algorithms

• Dijkstra’s Algorithm: Shortest path algorithm for non-negative edge weights.
• Prim’s Algorithm: Finds the minimum spanning tree in a graph.
• Kruskal’s Algorithm: Another minimum spanning tree algorithm.
• Huffman Coding: Used in data compression.

5. Graph Algorithms

• Topological Sorting: Scheduling and dependency resolution problems.
• Floyd-Warshall Algorithm: Computes shortest paths between all pairs of nodes.
• Union-Find (Disjoint Set): Handles connected components in graphs.
• A Search Algorithm*: Pathfinding and graph traversal.
• Tarjan’s Algorithm: Finds strongly connected components in a graph.

6. String Algorithms

• KMP (Knuth-Morris-Pratt): Efficient string-matching algorithm.
• Rabin-Karp Algorithm: Finds multiple patterns in strings.
• Z-Algorithm: Pattern matching in strings.
• Boyer-Moore Algorithm: Efficient string-matching algorithm used in practice.

7. Advanced Data Structures

• Segment Trees: For range queries on arrays.
• Trie: Tree structure for efficient information retrieval.
• Fenwick Tree (Binary Indexed Tree): Handles prefix sum queries efficiently.
• Suffix Array: Array of suffixes of a string; useful in string algorithms.

8. Computational Geometry

• Convex Hull: Smallest convex polygon containing all points.
• Line Sweep Algorithms: Solves problems like finding line intersections.
• Graham's Scan: Finds the convex hull of a set of points.

9. Miscellaneous

• Fisher-Yates Shuffle: Generates a random permutation efficiently.
• Reservoir Sampling: Deals with streaming data.
• Karatsuba Algorithm: Fast multiplication algorithm; useful for large number multiplications.

10. Backtracking

• N-Queens Problem: Classic problem to understand backtracking.
• Sudoku Solver: Another example of backtracking in action.

🤝 Acknowledgements

Thanks to GitHub for providing a platform to share this learning journey. and thanks to you for following me on this path