Comprehensive List of Programming Algorithms

Basic Category

Linear Data Structures and Algorithms

• Arrays
• Linked List
• Stack
• Queues

Basic Algorithms

• Sorting
  • Merge Sort
  • Insertion Sort
  • Quick Sort
• Number of Inversions
• Matrix Multiplication
• Prime Sieving
• Modular Math
  • Multiplication and Division
  • Euclidean Algorithm for GCD
  • Modular Inverse
• Fast Exponentiation
• Fibonacci Number with Matrix Multiplication

Probability and Statistics

• Probability Distribution and Expected Value
• Mean
• Median
• Variance
• Bayes Theorem

Popular Algorithmic Techniques

• Divide and Conquer
  • Binary Search
  • Maximum Subarray
• Greedy Algorithms
  • Activity Selection
  • Huffman Encoding
• Dynamic Programming
  • Matrix Chain Multiplication
  • Knapsack
• Linear Programming
  • Variable Maximisation
  • Linear Time Sorting
• String Algorithms
  • Manacher
  • LCS (Longest Common Subsequence)
  • Edit Distance

Non-linear Data Structures

• Trees
  • Binary Tree
  • General Tree
  • Lowest Common Ancestor
• Binary Search Tree
  • Inorder Traversal
  • Level Order Traversal
  • Finding Kth Largest Element
  • Diameter
  • Depth
• Heaps
  • Array Implementation
  • Heapify
  • Heap Sort
• Union Find
• Hash Table
  • Linear Probing
  • Open Addressing
  • Collision Avoidance

Graphs

• Adjacency List
• Adjacency Matrix
• Weighted Edge Graphs
• Basic Traversal Algorithms
  • Breadth First Search
  • Depth First Search
• Shortest Path Finding Algorithms
  • Dijkstra
  • Floyd Warshall
  • Bellman Ford
• Minimum Spanning Tree
  • Kruskal's Algorithm
  • Prim's Algorithm

Advanced Category

Advanced Tree and Graph

• Balanced Trees
  • AVL Trees
  • Red-Black Trees
• Heavy Light Decomposition
• B+ Trees
• Quad Tree
• Advanced Graph Techniques
  • Min Cut
  • Max Flow
  • Maximum Matching (Hall's Marriage)
  • Hamiltonian Cycle
  • Edge Graphs / Line Graphs
  • Strongly Connected Components
  • Dominant Sub-Graph
  • Vertex Cover
  • Travelling Salesman (Approximation Algorithms)

Advanced String Algorithms

• Knuth-Morris-Pratt Algorithm
• Rabin-Karp Algorithm
• Tries and Compressed Tries
• Prefix Trees
• Suffix Trees
• Suffix Automation (Ukkonen's Algorithm)

Advanced Math

• Fast Fourier Transform
• Primality Testing
• Computational Geometry
  • Closest Point Pair
  • Voronoi Diagram
  • Convex Hull

General Advanced Topics

• Iterating Through All Combinations/Permutations
• Bit Manipulation

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Congratulations! If you have mastered all these algorithms and data structures, you're ready to join top-tier companies like Google, Amazon, Facebook, Twitter, Dropbox, and Uber. Acquiring knowledge of 70-80% of these topics prepares you for any international software/IT company. Even with familiarity of 50%, local companies are keen to hire you.

If you're beginning your journey, take some time to learn these fundamental concepts.

Happy Programming! Happy Learning!