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Module Introduction to combinatorics

Introduction to combinatorics

**Frequency: 7/10** Combinatorics problems are quite common in Competitive Programming.

Resources

Tài liệu Tiếng Anh: - [CP Algorithms: Binomial Coefficients](https://cp-algorithms.com/combinatorics/binomial-coefficients.html) - [CP Algorithms: Stars and bars](https://cp-algorithms.com/combinatorics/stars_and_bars.html)

Problems

Binomial coefficient 383 / 445 1000
Fork and knife 324 / 331 1100
Binomial coefficient 2 261 / 296 1100
Equation 270 / 278 1300
Array rearrangement 259 / 265 1300
Value of subsequences 225 / 235 1400
Inequation 211 / 216 1400
Growing mushrooms 205 / 208 1500
Binary matrix 116 / 133 1600
Broken board 68 / 80 1600
Triangles counting 50 / 89 1800
Minecraft graph 22 / 26 1800
Restricted path 38 / 43 1900
Heavenly Peach Garden 13 / 18 2000

Graph

  • Shortest path
  • 0-1 BFS / Dial's algorithm
  • Multisource BFS / Dijkstra
  • DAG / Topological sort

Data structure

  • Introduction to Segment Tree and Binary Indexed Tree
  • Sparse table
  • Monotonic queue

Tree

  • Lowest common ancestor (LCA)
  • Euler tour

Dynamic Programming

  • Bitmask DP
  • Exchange labels DP
  • Game DP

Math

  • Introduction to combinatorics
  • Inclusion-exclusion principle