30 Fundamental Algorithms

1. Sorting Algorithms (Essential for Interviews)

1. Bubble Sort – Basic sorting algorithm, inefficient for large data.
2. Selection Sort – Selects the smallest element and places it in order.
3. Insertion Sort – Inserts elements into their correct position.
4. Merge Sort – Efficient, divide-and-conquer sorting with O(n log n) complexity.
5. Quick Sort – Fast sorting using partitioning, average O(n log n) complexity.
6. Heap Sort – Sorting using a heap, used in priority queues.
7. Counting Sort – Good for small range of numbers.
8. Radix Sort – Used for sorting numbers with multiple digits efficiently.

2. Searching Algorithms

9. Linear Search – Basic search, used in unsorted lists.
10. Binary Search – Fast O(log n) search, works only in sorted arrays.
11. Jump Search – Faster than binary search for sorted data.
12. Exponential Search – Good for unbounded lists.
13. Interpolation Search – Faster than binary search for uniformly distributed data.

3. Graph Algorithms

14. Breadth-First Search (BFS) – Traverses level-by-level, used in shortest path problems.
15. Depth-First Search (DFS) – Explores depth before breadth, used in tree/graph traversal.
16. Dijkstra’s Algorithm – Finds the shortest path from a source node (greedy approach).
17. Bellman-Ford Algorithm – Shortest path with negative weights.
18. Floyd-Warshall Algorithm – All-pairs shortest paths.
19. Kruskal’s Algorithm – Finds Minimum Spanning Tree (MST) using greedy approach.
20. Prim’s Algorithm – Another approach for MST.
21. Topological Sorting – Used in DAGs (Directed Acyclic Graphs) like dependency resolution.

4. Tree Algorithms

22. Binary Tree Traversal (Inorder, Preorder, Postorder, Level Order BFS)
23. Lowest Common Ancestor (LCA) – Finds the common ancestor of two nodes.
24. Morris Traversal – In-order traversal without recursion or stack.
25. Trie (Prefix Tree) – Used for searching strings efficiently (autocomplete systems).

5. Dynamic Programming & Recursion

26. Fibonacci Series (DP & Recursion) – Classic problem for understanding memoization.
27. Knapsack Problem (0/1 Knapsack & Fractional Knapsack) – Optimization problem.
28. Longest Common Subsequence (LCS) – Used in diff utilities, DNA sequencing.
29. Coin Change Problem – Find the minimum number of coins needed for a sum.
30. Subset Sum Problem – Determines if a subset sums to a given value.