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Module Euler tour

Euler tour

**Frequency: 7/10** Also known as DFS order. This is important for solving tree related problems from now on.

Resources

- [USACO: Euler Tour](https://usaco.guide/gold/tree-euler)

Problems

Subtree queries 453 / 459 1200
Subtree update 428 / 435 1400
Ancestor 380 / 383 1400
Shallow 342 / 348 1500
Remove subtree 218 / 269 1600
Queries on tree 172 / 263 1900
Queries on tree 2 117 / 140 1900
Library 68 / 86 1900
Tree rotation 48 / 52 1900
Black vertices 64 / 68 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