CustomCC0-1.0#ct-p3-031900
Shortest Path with Free Coupons
Summary
- •Phase 3 / graph-shortest-path
- •Reasoning-first competitive programming drill
Problem Description
In weighted graph, you may apply up to c coupons making an edge cost zero. Find min cost s->t.
How to read this problem in plain language:
- This is a Phase 3 reasoning drill focused on graph-shortest-path.
- Typical lenses to test first: graph, dijkstra, state-space.
- Constraints reminder: n,m <= 2e5, c <= 30
Mini examples for mental simulation:
1) Boundary example: Must reduce to normal shortest path.
2) Adversarial example: Return unreachable marker. Explain expected behavior and why naive logic may fail.
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, c <= 30
Analysis
Key Insight
Any used count up to c is valid end state. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.
graphdijkstrastate-space