CustomCC0-1.0#cp002-1572100
Graph Reversal Path Cost
Summary
- •Phase 5 / graphs, shortest paths
- •Reasoning-first competitive programming drill
Problem Description
Given a directed weighted graph with n nodes and m edges, you may reverse at most one edge (flipping its direction but keeping its weight) before starting your path. Find the minimum possible cost to go from node 1 to node n.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on graphs, shortest paths.
- Typical lenses to test first: graphs, dijkstra, reverse edge.
- Constraints reminder: 1 <= n <= 2*10^5, 1 <= m <= 3*10^5, 1 <= u,v <= n, 1 <= w <= 10^9
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
- •1 <= n <= 2*10^5, 1 <= m <= 3*10^5, 1 <= u,v <= n, 1 <= w <= 10^9
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
graphsdijkstrareverse edge