Comprehensive list of Data structures and Algorithms categorized by type and usage:

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Data Structures

Linear Data Structures

1. Array
2. Linked List
   • Singly Linked List
   • Doubly Linked List
   • Circular Linked List
3. Stack
4. Queue
   • Simple Queue
   • Circular Queue
   • Priority Queue
   • Deque (Double-Ended Queue)

Non-Linear Data Structures

5. Tree
   • Binary Tree
   • Binary Search Tree
   • AVL Tree
   • Red-Black Tree
   • B-Tree
   • B+ Tree
   • Segment Tree
   • Fenwick Tree (Binary Indexed Tree)
   • Suffix Tree
   • Trie (Prefix Tree)
   • Quad Tree
6. Graph
   • Adjacency List Representation
   • Adjacency Matrix Representation
   • Weighted Graph
   • Directed Graph
   • Undirected Graph
   • Directed Acyclic Graph (DAG)
7. Heap
   • Min Heap
   • Max Heap
   • Fibonacci Heap

Hash-Based Data Structures

8. Hash Table
   • Chaining
   • Open Addressing (Linear Probing, Quadratic Probing, Double Hashing)
   • Bloom Filter

Specialized Data Structures

9. Disjoint Set (Union-Find)
10. Matrix (2D arrays)
11. Skip List
12. Suffix Array
13. Interval Tree
14. Sparse Table

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Algorithms

Sorting Algorithms

1. Bubble Sort
2. Selection Sort
3. Insertion Sort
4. Merge Sort
5. Quick Sort
6. Heap Sort
7. Counting Sort
8. Radix Sort
9. Bucket Sort
10. Shell Sort
11. Tim Sort

Search Algorithms

12. Linear Search
13. Binary Search
14. Jump Search
15. Interpolation Search
16. Exponential Search

Graph Algorithms

17. Depth-First Search (DFS)
18. Breadth-First Search (BFS)
19. Dijkstra’s Algorithm
20. Bellman-Ford Algorithm
21. Floyd-Warshall Algorithm
22. Kruskal’s Algorithm (Minimum Spanning Tree)
23. Prim’s Algorithm (Minimum Spanning Tree)
24. Topological Sorting
25. A Search Algorithm*
26. Johnson’s Algorithm
27. Tarjan’s Algorithm (Strongly Connected Components)
28. Kosaraju’s Algorithm (Strongly Connected Components)
29. Ford-Fulkerson Algorithm (Maximum Flow)

Tree Algorithms

30. Tree Traversals
    • Inorder
    • Preorder
    • Postorder
    • Level Order
31. Lowest Common Ancestor (LCA)
32. Segment Tree Construction and Query
33. Fenwick Tree Updates and Query
34. Trie Operations (Insert, Search, Delete)

Dynamic Programming Algorithms

35. Knapsack Problem

• 0/1 Knapsack
• Fractional Knapsack

36. Longest Common Subsequence (LCS)
37. Longest Increasing Subsequence (LIS)
38. Matrix Chain Multiplication
39. Floyd-Warshall Algorithm
40. Subset Sum Problem
41. Rod Cutting Problem
42. Egg Dropping Problem
43. Coin Change Problem

Divide and Conquer Algorithms

44. Merge Sort
45. Quick Sort
46. Binary Search
47. Strassen’s Matrix Multiplication

Greedy Algorithms

48. Activity Selection Problem
49. Huffman Coding
50. Kruskal’s Algorithm
51. Prim’s Algorithm
52. Dijkstra’s Algorithm

Backtracking Algorithms

53. N-Queens Problem
54. Sudoku Solver
55. Rat in a Maze
56. Word Search
57. Hamiltonian Cycle
58. Knight’s Tour Problem

String Algorithms

59. KMP Algorithm (Knuth-Morris-Pratt)
60. Rabin-Karp Algorithm
61. Z Algorithm
62. Boyer-Moore Algorithm
63. Aho-Corasick Algorithm
64. Suffix Array Construction
65. Suffix Tree Operations

Mathematical Algorithms

66. Greatest Common Divisor (GCD)
67. Least Common Multiple (LCM)
68. Sieve of Eratosthenes
69. Prime Factorization
70. Modular Exponentiation
71. Euclidean Algorithm
72. Chinese Remainder Theorem
73. Fast Fourier Transform (FFT)

Bit Manipulation Algorithms

74. Bitwise AND/OR/XOR
75. Counting Set Bits (Hamming Weight)
76. Bit Masking
77. Checking Power of Two
78. Reversing Bits

Number Theory Algorithms

79. Modular Arithmetic
80. Miller-Rabin Primality Test
81. Elliptic Curve Cryptography (ECC)
82. Discrete Logarithm
83. Extended Euclidean Algorithm

Miscellaneous Algorithms

84. Flood Fill Algorithm
85. Union-Find Algorithm (for Disjoint Sets)
86. Reservoir Sampling
87. Fisher-Yates Shuffle
88. Manacher’s Algorithm (Longest Palindromic Substring)
89. Sliding Window Technique
90. Two Pointer Technique