CustomCC0-1.0#cpq007-5361800
Grid Minimum Cost Painting
Summary
- •Phase 2 / dp, coloring, grid
- •Reasoning-first competitive programming drill
Problem Description
Given an NxM grid of integers, you can repaint any cell to any color at cost 1, but no two adjacent cells (up, down, left, right) can have the same color. Find the minimal total cost to transform the grid into a valid coloring.
How to read this problem in plain language:
- This is a Phase 2 reasoning drill focused on dp, coloring, grid.
- Typical lenses to test first: dp, grid, coloring.
- Constraints reminder: 1 <= N, M <= 200; initial colors are integers between 1 and 1e6.
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, M <= 200; initial colors are integers between 1 and 1e6.
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.
dpgridcoloring