1.2 Algorithm Knowledge

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.

AlgorithmSpecific TypeRelated ProblemsExplanatory Articles
Sorting Algorithms1. 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 Conquer1. Binary Search/Lookup
2. Multiplication of Large Integers
3. Strassen Matrix Multiplication
4. Chessboard Covering
5. Merge Sort
6. Quick Sort
7. Linear-Time Selection
8. Closest Pair of Points Problem
9. Round-Robin Tournament Schedule
Dynamic Programming1. Matrix Chain Multiplication Problem
2. Longest Common Subsequence
3. Maximum Subarray Sum
4. Optimal Triangulation of Convex Polygons
5. Polygon Game
6. Image Compression
7. Circuit Wiring
8. Flow Shop Scheduling
9. 0-1 Knapsack Problem/Nine Lectures on Knapsack
10. Optimal Binary Search Tree
11. Principles of Dynamic Programming Acceleration
12. Tree DP
Greedy1. Activity Selection Problem
2. Optimal Loading
3. Huffman Coding
4. Single-Source Shortest Path
5. Minimum Spanning Tree
6. Multi-Machine Scheduling Problem
Backtracking1. Loading Problem
2. Batch Processing Job Scheduling
3. Symbol Triangle Problem
4. n-Queens Problem
5. 0-1 Knapsack Problem
6. Maximum Clique Problem
7. m-Coloring Problem of Graphs
8. Traveling Salesman Problem
9. Circle Arrangement Problem
10. Circuit Board Arrangement Problem
11. Continuous Postage Problem
Search1. Enumeration
2. DFS
3. BFS
4. Heuristic Search
Randomization1. Random Numbers
2. Numerical Randomized Algorithms
3. Sherwood Algorithm
4. Las Vegas Algorithm
5. Monte Carlo Algorithm
1. Calculate the Value of π
2. Calculate Definite Integrals
3. Solve Systems of Nonlinear Equations
4. Linear-Time Selection Algorithm
5. Skip List
6. n-Queens Problem
7. Integer Factorization
8. Majority Element Problem
9. Primality Testing
Graph Theory1. Traversal DFS / BFS
2. AOV / AOE Network
3. Kruskal Algorithm(Minimum Spanning Tree)
4. Prim Algorithm(Minimum Spanning Tree)
5. Boruvka Algorithm(Minimum Spanning Tree)
6. Dijkstra Algorithm(Single-Source Shortest Path)
7. Bellman-Ford Algorithm(Single-Source Shortest Path)
8. SPFA Algorithm(Single-Source Shortest Path)
9. Floyd Algorithm(All-Pairs Shortest Path)
10. Johnson Algorithm(All-Pairs Shortest Path)
11. Fleury Algorithm(Eulerian Circuit)
12. Ford-Fulkerson Algorithm(Augmenting Path for Maximum Network Flow)
13. Edmonds-Karp Algorithm(Maximum Network Flow)
14. Dinic Algorithm(Maximum Network Flow)
15. General Preflow-Push Algorithm
16. Highest-Label Preflow-Push HLPP Algorithm
17. Primal-Dual Algorithm(Minimum Cost Flow)18. Kosaraju Algorithm(Strongly Connected Components of Directed Graphs)
19. Tarjan Algorithm(Strongly Connected Components of Directed Graphs)
20. Gabow Algorithm(Strongly Connected Components of Directed Graphs)
21. Hungarian Algorithm(Bipartite Graph Matching)
22. Hopcroft－Karp Algorithm(Bipartite Graph Matching)
23. kuhn munkras Algorithm(Best Bipartite Matching)
24. Edmonds’ Blossom-Contraction Algorithm(General Graph Matching)
1. Graph Traversal
2. Strong and Weak Connectivity of Directed and Undirected Graphs
3. Cut Vertices/Cut Edges
3. AOV Network and Topological Sorting
4. AOE Network and Critical Path
5. Minimum-Cost Spanning Tree/Second-Best Minimum Spanning Tree
6. Shortest Path Problem/K-th Shortest Path Problem
7. Maximum Network Flow Problem
8. Minimum Cost Flow Problem
9. Graph Coloring Problem
10. Difference Constraints System
11. Eulerian Circuit
12. Chinese Postman Problem
13. Hamiltonian Circuit
14. Optimal Edge Cut Set/Optimal Vertex Cut Set/Minimum Edge Cut Set/Minimum Vertex Cut Set/Minimum Path Cover/Minimum Vertex Set Cover
15. Edge Cover Set
16. Perfect Matching and Maximum Matching Problems in Bipartite Graphs
17. Cactus Graph
18. Chordal Graph
19. Stable Marriage Problem
20. Maximum Clique Problem
Number Theory1. Greatest Common Divisor
2. Least Common Multiple
3. Prime Factorization
4. Primality Testing
5. Base Conversion
6. High-Precision Computation
7. Divisibility Problems
8. Congruence Problems
9. Euler’s Totient Function
10. Extended Euclidean Algorithm
11. Permutation Group
12. Generating Function
13. Discrete Transform
14. Cantor Expansion
15. Matrix
16. Vector
17. System of Linear Equations
18. Linear Programming
Geometry1. Convex Hull - Gift wrapping
2. Convex Hull - Graham scan
3. Line Segment Problems
4. Problems Related to Polygons and Polyhedra
NP-Complete1. Computational Model
2. P-Class and NP-Class Problems
3. NP-Complete Problems
4. Approximation Algorithms for NP-Complete Problems
1. Random Access Machine RAM
2. Random Access Stored Program Machine RASP
3. Turing Machine
4. Nondeterministic Turing Machine
5. P-Class and NP-Class Languages
6. Polynomial-Time Verification
7. Polynomial-Time Transformation
8. Cook’s Theorem
9. Satisfiability Problem of Conjunctive Normal Form CNF-SAT
10. Satisfiability Problem of 3-Conjunctive Normal Form 3-SAT
11. Clique Problem CLIQUE
12. Vertex Cover Problem VERTEX-COVER
13. Subset Sum Problem SUBSET-SUM
14. Hamiltonian Circuit Problem HAM-CYCLE
15. Traveling Salesman Problem TSP
16. Approximation Algorithm for the Vertex Cover Problem
17. Approximation Algorithm for the Traveling Salesman Problem
18. Traveling Salesman Problem with the Triangle Inequality Property
19. General Traveling Salesman Problem
20. Approximation Algorithm for the Set Cover Problem
21. Approximation Algorithm for the Subset Sum Problem
22. Exponential-Time Algorithm for the Subset Sum Problem
23. Polynomial-Time Approximation Scheme for the Subset Sum Problem
Bit OperationsBit operations include:
1. NOT
2. Bitwise OR（OR）
3. Bitwise XOR（XOR）
4. Bitwise AND（AND）
5. 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
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