CustomCC0-1.0#P006-3662100
Graph Path Swap Parity
Summary
- •Phase 5 / graphs/parity/path_reversal
- •Reasoning-first competitive programming drill
Problem Description
Given a directed graph with N nodes and M edges, answer Q queries: for each (u,v), can the parity of the length of the shortest path from u to v be swapped by reversing one edge anywhere in the graph?
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on graphs/parity/pat.
- Typical lenses to test first: graph, bfs, parity.
- Constraints reminder: 1 ≤ 1 ≤ 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
- •1 ≤ 1 ≤ 1 ≤
Analysis
Key Insight
Use this hint to refine your reasoning. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.
graphbfsparityquery