How many algorithms are there in programming?

The number of algorithms in programming is virtually limitless because algorithms are not fixed; they are creative solutions to problems. However, we can group them into common categories that represent the foundational techniques and applications most frequently used in programming. Let’s break it down.

Algorithms by Categories

1. Sorting Algorithms

These arrange data in a specific order (ascending, descending, etc.).

• Common Examples: Bubble Sort, Quick Sort, Merge Sort, Heap Sort, Radix Sort, Counting Sort.
• Purpose: Optimizing data processing, searching, or visualization.

2. Searching Algorithms

These find specific elements or information in data.

• Common Examples: Linear Search, Binary Search, Depth-First Search (DFS), Breadth-First Search (BFS).
• Purpose: Quickly locate data or traverse structures like graphs.

3. Graph Algorithms

These solve problems involving graphs (nodes and edges).

• Common Examples: Dijkstra’s Algorithm, A*, Floyd-Warshall, Kruskal’s Algorithm, Prim’s Algorithm.
• Purpose: Shortest path finding, network optimization, cycle detection.

4. Dynamic Programming Algorithms

These solve problems by breaking them into overlapping subproblems and storing results.

• Common Examples: Fibonacci Sequence, Knapsack Problem, Longest Common Subsequence (LCS), Matrix Chain Multiplication.
• Purpose: Optimization and solving complex recursive problems efficiently.

5. Greedy Algorithms

These make the best local choice at each step, hoping for a global optimum.

• Common Examples: Huffman Coding, Activity Selection, Kruskal’s Algorithm, Prim’s Algorithm.
• Purpose: Resource allocation, optimization, scheduling.

6. Divide and Conquer Algorithms

These split a problem into smaller subproblems, solve them recursively, and combine the results.

• Common Examples: Merge Sort, Quick Sort, Binary Search, Closest Pair of Points.
• Purpose: Efficient problem-solving and optimization.

7. Backtracking Algorithms

These explore all possibilities and backtrack when a solution fails.

• Common Examples: N-Queens Problem, Sudoku Solver, Permutations and Combinations, Subset Sum Problem.
• Purpose: Solving constraint-based problems.

8. String Algorithms

These manipulate or analyze strings of text.

• Common Examples: KMP (Knuth-Morris-Pratt), Rabin-Karp, Longest Palindromic Substring, Suffix Tree/Array.
• Purpose: Pattern matching, text processing.

9. Mathematical Algorithms

These solve problems involving numbers or mathematical operations.

• Common Examples: Euclidean Algorithm (GCD), Sieve of Eratosthenes (prime numbers), Fast Exponentiation.
• Purpose: Cryptography, numerical optimization, number theory.

10. Machine Learning Algorithms

These learn patterns from data and make predictions or decisions.

• Common Examples: Linear Regression, Decision Trees, Neural Networks, K-Means Clustering, Gradient Descent.
• Purpose: AI and data-driven decision-making.

11. Cryptographic Algorithms

These secure communication and data.

• Common Examples: RSA, AES, SHA (hashing), Diffie-Hellman.
• Purpose: Data encryption, authentication.

12. Miscellaneous Algorithms

These serve niche or highly specific applications.

• Examples: Monte Carlo Simulation, Bloom Filters, Reservoir Sampling.
• Purpose: Statistical analysis, approximation, randomness.

Commonly Used Algorithms in Programming

While there are thousands of algorithms, most programming scenarios require mastery of 20–30 core algorithms across these categories. These include:

• Sorting: Quick Sort, Merge Sort
• Searching: Binary Search
• Dynamic Programming: Knapsack Problem, Longest Common Subsequence
• Graphs: Dijkstra’s Algorithm, DFS, BFS
• Strings: KMP, Rabin-Karp

Suggested Resources for Learning Algorithms

• Grokking Data Structures & Algorithms for Coding Interviews (Learn More): Comprehensive coverage of algorithms in programming.
• Grokking the Coding Interview: Patterns for Coding Questions (Learn More): Focus on essential algorithms and problem-solving techniques.
• Mastering the 20 Coding Patterns (Explore): Learn how algorithms fit into common coding patterns.

In summary, there are countless algorithms, but mastering a well-curated set of core algorithms and their variations is sufficient for most programming and interview needs.