CustomCC0-1.0#cptp0052200
Directed Graph Two-Edge Connectivity
Summary
- •Phase 5 / graph_theory, connectivity
- •Reasoning-first competitive programming drill
Problem Description
Given a directed graph with n nodes and m edges, determine whether every pair of nodes is connected by at least two edge-disjoint paths (not necessarily simple) in both directions.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on grap, connectivity.
- Typical lenses to test first: graphs, connectivity, edge-disjoint paths.
- Constraints reminder: 2 ≤ , 1 ≤
Mini examples for mental simulation:
1) Boundary example: Describe why this case is tricky. Explain expected behavior and why naive logic may fail.
2) Adversarial example: Adversarial case where naive greedy/local decision looks correct but fails globally.
Lite-mode writing target:
- Write 1~2 observations that shrink the search space.
- Name one final algorithm and state target complexity explicitly.
- Validate with at least 2 edge cases and one hand simulation.
Constraints
- •2 ≤ , 1 ≤
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
graphsconnectivityedge-disjoint pathsstrongly-connected