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Graphs

  • Cycle detection in directed and undirected graphs
  • Shortest paths in DAGs via topological order
  • Johnson algorithm for APSP
  • Tarjan algorithm for SCC
  • Bridges, articulation points, and biconnected components
  • Dinic algorithm
  • Cut and separator problems

Interval and range queries

  • Fenwick tree
  • Segment tree with lazy propagation
  • Difference array

Strings

  • Suffix array and LCP array

Number theory and algebra

  • Gaussian elimination

Geometry

  • Point in polygon
  • Distance and projection primitives
  • Rotating calipers

Subsets and combinatorics

  • Meet in the middle