CustomCC0-1.0#cp-tp3-0041700
Monochrome Component Removals
Summary
- •Phase 3 / graph-components
- •Reasoning-first competitive programming drill
Problem Description
Given a connected undirected graph with n nodes and m edges, each node colored black or white, you may remove a connected monochrome component at each step. What is the minimum number of steps to remove all nodes? Output it.
How to read this problem in plain language:
- This is a Phase 3 reasoning drill focused on graph-components.
- Typical lenses to test first: graph, components, coloring.
- Constraints reminder: 1 ≤ n-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 ≤ n-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.
graphcomponentscoloringgreedy