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Graph Ladders

These ladders follow the graph teaching spine from modeling to standard algorithms.

  1. graph modeling
  2. BFS / DFS
  3. shortest paths
  4. minimum spanning tree
  5. toposort and SCC
  6. bridges / articulation / low-link on undirected graphs
  7. Eulerian path / cycle once "use every edge exactly once" becomes a repeated pattern
  8. de Bruijn sequence once overlap-string constructions clearly reduce to hidden Eulerian cycles
  9. 2-SAT once implication graphs and SCCs feel natural
  10. trees and subtree flattening
  11. tree isomorphism when unordered rooted shape itself becomes the task
  12. LCA
  13. virtual tree when each query only marks a small subset of vertices but the union of marked paths still matters
  14. heavy-light decomposition when path queries need a range structure
  15. centroid decomposition when balanced recursive splits become the main tool
  16. link-cut tree when the tree topology itself changes online
  17. Euler tour tree when the topology changes online but the live query is still subtree-side
  18. flow
  19. global min-cut when one undirected weighted graph has no designated s-t and you only want the cheapest disconnection cut
  20. Gomory-Hu once many undirected min-cuts must be compressed into one tree
  21. stable marriage once one-to-one pairing is about blocking pairs under strict preferences, not size or cost
  22. weighted assignment once one-to-one pairing is no longer only about cardinality
  23. general matching once odd cycles kill the bipartite-first route

Subtopic Ladders

Representative Solved Notes