CustomCC0-1.0#ct-p5-022300
Lower-Bound Flow Feasibility
Summary
- •Phase 5 / flows
- •Reasoning-first competitive programming drill
Problem Description
Directed edges have lower/upper capacity. Determine if feasible circulation exists and output one.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on flows.
- Typical lenses to test first: flow, graph, invariant.
- Constraints reminder: n,m <= 2e5
Mini examples for mental simulation:
1) Boundary example: When l=r, fixed flow edge. Explain expected behavior and why naive logic may fail.
2) Adversarial example: Immediate infeasibility if total demand mismatch.
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
- •n,m <= 2e5
Analysis
Key Insight
Quantifying complexity against constraints is mandatory for selecting the final approach and rejecting brute force formally.
flowgraphinvariant