Toposort And SCC Ladder¶
This ladder should make directed-graph structure feel cleaner: first order a DAG, then learn how SCC compression turns a cyclic graph into a DAG.
Who This Is For¶
Use this ladder if:
- directed dependencies still feel messy
- you know the algorithms, but not when SCC must come before DP
- cycles in directed graphs still lead to ad hoc reasoning
Warm-Up¶
- topological order in a DAG
- cycle detection in a directed graph
Target skill:
- know when a DAG order exists and when it cannot
Core¶
- Kahn topological sort
- SCC decomposition
- condensation DAG reasoning
Target skill:
- move from original graph to component DAG cleanly
Stretch¶
- DAG DP after SCC compression
- compare Kosaraju and Tarjan conceptually
Target skill:
- use SCC as a preprocessing step for later graph logic
Exit Criteria¶
You are ready to move on when:
- you can detect a failed toposort as a cycle signal
- you can explain why SCC condensation is acyclic
- you no longer attempt DAG DP directly on a cyclic graph