There are many algorithms across different fields of computer science and mathematics. Below is a comprehensive list of commonly used algorithms, organized by category. This list covers areas like sorting, searching, graph theory, dynamic programming, machine learning, cryptography, and more.

Sorting Algorithms

• Bubble Sort
• Selection Sort
• Insertion Sort
• Merge Sort
• Quick Sort
• Heap Sort
• Counting Sort
• Radix Sort
• Bucket Sort
• Shell Sort

 Searching Algorithms

• Linear Search
• Binary Search
• Ternary Search
• Exponential Search
• Jump Search
• Fibonacci Search
• Interpolation Search

 Graph Algorithms

• Breadth-First Search (BFS)
• Depth-First Search (DFS)
• Dijkstra’s Algorithm (Shortest Path)
• Bellman-Ford Algorithm (Shortest Path with Negative Weights)
• Floyd-Warshall Algorithm (All-Pairs Shortest Path)
• A* (A-star) Algorithm
• Kruskal’s Algorithm (Minimum Spanning Tree)
• Prim’s Algorithm (Minimum Spanning Tree)
• Topological Sorting
• Tarjan’s Algorithm (Strongly Connected Components)
• Kosaraju's Algorithm (Strongly Connected Components)
• Johnson’s Algorithm (All-Pairs Shortest Path)

Dynamic Programming Algorithms

• Fibonacci Sequence (DP version)
• Knapsack Problem (0/1 and Fractional)
• Longest Common Subsequence (LCS)
• Longest Increasing Subsequence (LIS)
• Matrix Chain Multiplication
• Edit Distance (Levenshtein Distance)
• Coin Change Problem
• Rod Cutting Problem
• Subset Sum Problem
• Bellman-Ford Algorithm (as DP example for graphs)

Divide and Conquer Algorithms

• Binary Search
• Merge Sort
• Quick Sort
• Strassen’s Matrix Multiplication
• Closest Pair of Points Problem

 Greedy Algorithms

• Dijkstra’s Algorithm
• Kruskal’s Algorithm
• Prim’s Algorithm
• Huffman Coding
• Activity Selection Problem
• Fractional Knapsack Problem

 Backtracking Algorithms

• N-Queens Problem
• Sudoku Solver
• Graph Coloring Problem
• Hamiltonian Cycle
• Knight’s Tour Problem

String Matching Algorithms

• Naive Pattern Matching
• KMP Algorithm (Knuth-Morris-Pratt)
• Rabin-Karp Algorithm
• Z Algorithm
• Boyer-Moore Algorithm
• Aho-Corasick Algorithm

 Mathematical Algorithms

• Greatest Common Divisor (GCD) (Euclidean Algorithm)
• Sieve of Eratosthenes (Prime Generation)
• Modular Exponentiation
• Fast Fourier Transform (FFT)
• Matrix Exponentiation
• Extended Euclidean Algorithm
• Chinese Remainder Theorem
• Floyd’s Tortoise and Hare (Cycle Detection)

 Cryptographic Algorithms

• RSA Algorithm
• AES (Advanced Encryption Standard)
• DES (Data Encryption Standard)
• SHA (Secure Hash Algorithm)
• Elliptic Curve Cryptography (ECC)
• Diffie-Hellman Key Exchange
• MD5 Hashing Algorithm