Graph Ladders¶
These ladders follow the graph teaching spine from modeling to standard algorithms.
Recommended Order¶
- graph modeling
- BFS / DFS
- shortest paths
- minimum spanning tree
- toposort and SCC
- bridges / articulation / low-link on undirected graphs
- Eulerian path / cycle once "use every edge exactly once" becomes a repeated pattern
- de Bruijn sequence once overlap-string constructions clearly reduce to hidden Eulerian cycles
- 2-SAT once implication graphs and SCCs feel natural
- trees and subtree flattening
- tree isomorphism when unordered rooted shape itself becomes the task
- LCA
- virtual tree when each query only marks a small subset of vertices but the union of marked paths still matters
- heavy-light decomposition when path queries need a range structure
- centroid decomposition when balanced recursive splits become the main tool
- link-cut tree when the tree topology itself changes online
- Euler tour tree when the topology changes online but the live query is still subtree-side
- flow
- global min-cut when one undirected weighted graph has no designated
s-tand you only want the cheapest disconnection cut - Gomory-Hu once many undirected min-cuts must be compressed into one tree
- stable marriage once one-to-one pairing is about blocking pairs under strict preferences, not size or cost
- weighted assignment once one-to-one pairing is no longer only about cardinality
- general matching once odd cycles kill the bipartite-first route
Subtopic Ladders¶
- Graph modeling
- BFS / DFS
- Bridges / articulation / BCC
- Eulerian path / cycle
- De Bruijn Sequence
- Shortest paths
- Minimum spanning tree
- Toposort and SCC
- Two-SAT
- Trees
- Tree Isomorphism
- Euler Tour / Subtree Queries
- LCA
- Virtual Tree / Auxiliary Tree
- Heavy-light decomposition
- Centroid decomposition
- Link-cut tree
- Euler tour tree
- Flow
- Randomized / Global Min-Cut
- Gomory-Hu tree
- Matching
- Stable Marriage
- Hungarian / Assignment Problem
- Edmonds Blossom / General Matching
- Tree DP notes
Representative Solved Notes¶
- Counting Rooms
- Building Roads
- Necessary Roads
- Mail Delivery
- De Bruijn Sequence
- QOS
- Giant Pizza
- Tree Isomorphism I
- Subtree Queries
- Kingdom and its Cities
- Ciel the Commander
- Dynamic Tree Vertex Add Path Sum
- Dynamic Tree Vertex Add Subtree Sum
- FFLOW
- Minimum Cut
- MCQUERY
- MINCOST
- Path Queries II
- QBFLOWER
- Stable Marriage
- Task Assignment
- General Matching
- VOSTRIP