Algorithm Knowledge

The following is algorithm-related knowledge compiled by the author. I hope to enumerate all common algorithms exhaustively. If anything is missing, everyone is welcome to give advice and submit PRs. Related problems are still being gradually organized, and explanatory articles are still being created.

Solving problems is only a means to improve algorithmic ability; the ultimate goal should be to improve one's thinking ability. Knowledge needs to be condensed into blocks, so summarize these in the two sections of Chapter 1 and let it be sublimated~ I hope readers will come back to look at this table after finishing problem practice, so they can clearly organize their own knowledge system, check for gaps, and improve it as soon as possible.

Algorithm	Specific Type	Related Problems	Explanatory Articles
Sorting Algorithms	1. Bubble Sort

2. Insertion Sort
3. Selection Sort
4. Shell Sort
5. Quick Sort
6. Merge Sort
7. Heap Sort
8. Linear Sorting Algorithms
9. Introsort
10. Indirect Sort
11. Counting Sort
12. Radix Sort
13. Bucket Sort
14. External Sorting - k-Way Merge Loser Tree
15. External Sorting - Optimal Merge Tree||| |Recursion and Divide and Conquer||1. Binary Search/Lookup
16. Multiplication of Large Integers
17. Strassen Matrix Multiplication
18. Chessboard Covering
19. Merge Sort
20. Quick Sort
21. Linear-Time Selection
22. Closest Pair of Points Problem
23. Round-Robin Tournament Schedule || |Dynamic Programming||1. Matrix Chain Multiplication Problem
24. Longest Common Subsequence
25. Maximum Subarray Sum
26. Optimal Triangulation of Convex Polygons
27. Polygon Game
28. Image Compression
29. Circuit Wiring
30. Flow Shop Scheduling
31. 0-1 Knapsack Problem/Nine Lectures on Knapsack
32. Optimal Binary Search Tree
33. Principles of Dynamic Programming Acceleration
34. Tree DP || |Greedy||1. Activity Selection Problem
35. Optimal Loading
36. Huffman Coding
37. Single-Source Shortest Path
38. Minimum Spanning Tree
39. Multi-Machine Scheduling Problem || |Backtracking||1. Loading Problem
40. Batch Processing Job Scheduling
41. Symbol Triangle Problem
42. n-Queens Problem
43. 0-1 Knapsack Problem
44. Maximum Clique Problem
45. m-Coloring Problem of Graphs
46. Traveling Salesman Problem
47. Circle Arrangement Problem
48. Circuit Board Arrangement Problem
49. Continuous Postage Problem || |Search|1. Enumeration
50. DFS
51. BFS
52. Heuristic Search ||| |Randomization|1. Random Numbers
53. Numerical Randomized Algorithms
54. Sherwood Algorithm
55. Las Vegas Algorithm
56. Monte Carlo Algorithm |1. Calculate the Value of π
57. Calculate Definite Integrals
58. Solve Systems of Nonlinear Equations
59. Linear-Time Selection Algorithm
60. Skip List
61. n-Queens Problem
62. Integer Factorization
63. Majority Element Problem
64. Primality Testing || |Graph Theory|1. Traversal DFS / BFS
65. AOV / AOE Network
66. Kruskal Algorithm(Minimum Spanning Tree)
67. Prim Algorithm(Minimum Spanning Tree)
68. Boruvka Algorithm(Minimum Spanning Tree)
69. Dijkstra Algorithm(Single-Source Shortest Path)
70. Bellman-Ford Algorithm(Single-Source Shortest Path)
71. SPFA Algorithm(Single-Source Shortest Path)
72. Floyd Algorithm(All-Pairs Shortest Path)
73. Johnson Algorithm(All-Pairs Shortest Path)
74. Fleury Algorithm(Eulerian Circuit)
75. Ford-Fulkerson Algorithm(Augmenting Path for Maximum Network Flow)
76. Edmonds-Karp Algorithm(Maximum Network Flow)
77. Dinic Algorithm(Maximum Network Flow)
78. General Preflow-Push Algorithm
79. Highest-Label Preflow-Push HLPP Algorithm
80. Primal-Dual Algorithm(Minimum Cost Flow)18. Kosaraju Algorithm(Strongly Connected Components of Directed Graphs)
81. Tarjan Algorithm(Strongly Connected Components of Directed Graphs)
82. Gabow Algorithm(Strongly Connected Components of Directed Graphs)
83. Hungarian Algorithm(Bipartite Graph Matching)
84. Hopcroft－Karp Algorithm(Bipartite Graph Matching)
85. kuhn munkras Algorithm(Best Bipartite Matching)
86. Edmonds’ Blossom-Contraction Algorithm(General Graph Matching) |1. Graph Traversal
87. Strong and Weak Connectivity of Directed and Undirected Graphs
88. Cut Vertices/Cut Edges
89. AOV Network and Topological Sorting
90. AOE Network and Critical Path
91. Minimum-Cost Spanning Tree/Second-Best Minimum Spanning Tree
92. Shortest Path Problem/K-th Shortest Path Problem
93. Maximum Network Flow Problem
94. Minimum Cost Flow Problem
95. Graph Coloring Problem
96. Difference Constraints System
97. Eulerian Circuit
98. Chinese Postman Problem
99. Hamiltonian Circuit
100. Optimal Edge Cut Set/Optimal Vertex Cut Set/Minimum Edge Cut Set/Minimum Vertex Cut Set/Minimum Path Cover/Minimum Vertex Set Cover
101. Edge Cover Set
102. Perfect Matching and Maximum Matching Problems in Bipartite Graphs
103. Cactus Graph
104. Chordal Graph
105. Stable Marriage Problem
106. Maximum Clique Problem || |Number Theory||1. Greatest Common Divisor
107. Least Common Multiple
108. Prime Factorization
109. Primality Testing
110. Base Conversion
111. High-Precision Computation
112. Divisibility Problems
113. Congruence Problems
114. Euler's Totient Function
115. Extended Euclidean Algorithm
116. Permutation Group
117. Generating Function
118. Discrete Transform
119. Cantor Expansion
120. Matrix
121. Vector
122. System of Linear Equations
123. Linear Programming || |Geometry||1. Convex Hull - Gift wrapping
124. Convex Hull - Graham scan
125. Line Segment Problems
126. Problems Related to Polygons and Polyhedra || |NP-Complete|1. Computational Model
127. P-Class and NP-Class Problems
128. NP-Complete Problems
129. Approximation Algorithms for NP-Complete Problems |1. Random Access Machine RAM
130. Random Access Stored Program Machine RASP
131. Turing Machine
132. Nondeterministic Turing Machine
133. P-Class and NP-Class Languages
134. Polynomial-Time Verification
135. Polynomial-Time Transformation
136. Cook's Theorem
137. Satisfiability Problem of Conjunctive Normal Form CNF-SAT
138. Satisfiability Problem of 3-Conjunctive Normal Form 3-SAT
139. Clique Problem CLIQUE
140. Vertex Cover Problem VERTEX-COVER
141. Subset Sum Problem SUBSET-SUM
142. Hamiltonian Circuit Problem HAM-CYCLE
143. Traveling Salesman Problem TSP
144. Approximation Algorithm for the Vertex Cover Problem
145. Approximation Algorithm for the Traveling Salesman Problem
146. Traveling Salesman Problem with the Triangle Inequality Property
147. General Traveling Salesman Problem
148. Approximation Algorithm for the Set Cover Problem
149. Approximation Algorithm for the Subset Sum Problem
150. Exponential-Time Algorithm for the Subset Sum Problem
151. Polynomial-Time Approximation Scheme for the Subset Sum Problem || |Bit Operations| Bit operations include:
152. NOT
153. Bitwise OR（OR）
154. Bitwise XOR（XOR）
155. Bitwise AND（AND）
156. Shift: It is a binary operator used to move every bit in a binary number in one direction by a specified number of positions; the overflowing part will be discarded, and the vacant part will be filled with a certain value. | 1.Bitwise AND of Numbers Range 2.UTF-8 Validation 3.Convert a Number to Hexadecimal 4.Find Longest Awesome Substring 5.XOR Operation in an Array 6.Power Set 7.Number of 1 Bits 8.Prime Number of Set Bits in Binary Representation 9.XOR Queries of a Subarray | LeetCode: Bit Manipulation| |------------|------------------------------------------------------------------|-----------------------------------------------------------------|--------------------|