Dynamic Programming

1. LCS (Longest Common Subsequence)
2. LIS (Longest Increasing Subsequence)
3. Knapsack
4. Monotonic DP
5. Circular DP
6. Tree DP
7. State Compression DP

Search

1. Enumeration
2. Search with Pruning
3. Heuristic Search
4. DLX (Dancing Links)
5. Bidirectional Search
6. Meet-in-the-Middle
7. Memoized Search
8. Simulated Annealing

Computational Geometry

1. Half-Plane Intersection
2. Convex Hull
3. Intersection and Union of Geometric Shapes
4. Rotating Calipers
5. Point Location
6. Coordinate Transformation
7. Discretization and Sweep Line
8. Inversion
9. Voronoi Diagram
10. Dual Graph of Planar Graphs
11. Triangulation
12. Trapezoidal Decomposition
13. Geometry Fundamentals

Greedy

Tree Structures

1. Lowest Common Ancestor (LCA)
2. Spanning Tree
3. Second Minimum Spanning Tree
4. DFS Order
5. Binary Lifting on Trees
6. Tree Divide and Conquer
7. Heavy-Light Decomposition
8. Link-Cut Tree

Graph Structures

1. Floyd
2. Dijkstra
3. SPFA
4. Negative Weight Edges
5. Planar Graphs
6. Bipartite Graphs
7. Bipartite Matching
8. Shortest Path
9. Difference Constraints
10. Topological Sorting
11. Network Flow
12. Strongly Connected Components
13. Articulation Points and Bridges
14. Eulerian Circuit
15. 2-SAT

Number Theory

1. Primality Testing
2. Euclidean Algorithm
3. Diophantine Equations
4. Digit DP / Digit Counting
5. Solving Linear Congruence Equations
6. Baby-Step Giant-Step
7. Pell Equation
8. Large Integer Prime Factorization
9. Pythagorean Equations
10. Multiplicative Functions
11. Fibonacci Sequence

Simulation

Data Structures

1. Stack
2. Queue
3. Linked List
4. Monotonic Queue
5. Disjoint Set Union (Union-Find)
6. Heap
7. Balanced Tree
8. Segment Tree
9. Binary Indexed Tree (Fenwick Tree)
10. Tree of Trees
11. Quadtree
12. Partition Tree
13. Merge Sort Tree
14. Scapegoat Tree
15. Leftist Heap
16. k-d Tree
17. Block Linked List
18. Hashing
19. Functional Programming

Game Theory

1. Bash Game
2. Nim Game
3. Wythoff Game
4. Fibonacci Game
5. Sprague–Grundy Theorem

Strings

1. KMP
2. Suffix Data Structures
3. Trie
4. Aho–Corasick Automaton
5. Manacher
6. Expression Processing
7. Minimal Representation

Combinatorics

1. Pigeonhole Principle
2. Generating Functions
3. Inclusion–Exclusion Principle
4. Cantor Expansion
5. Catalan Numbers
6. Stirling Numbers
7. Differences
8. Pólya’s Enumeration Theorem

Linear Algebra

1. Matrix Multiplication
2. Gaussian Elimination
3. Linear Programming

High Precision

1. FFT

Recurrence

Probability Theory

1. Randomization

NPC

Others

1. Binary Search
2. Ternary Search
3. Two-Pointer Technique
4. Divide and Conquer
5. Block Decomposition
6. RMQ (Range Minimum Query)
7. Fast Exponentiation
8. Mathematics
9. Sorting
10. Construction
11. Precomputation / Table Building
12. Bit Manipulation
13. Discretization
14. Mo’s Algorithm