CustomCC0-1.0#cp0101800
Matrix Path with Alternating Parity
Summary
- •Phase 5 / dp, grid, parity
- •Reasoning-first competitive programming drill
Problem Description
Given an n × m grid of integers, find the maximal sum path from the top-left to the bottom-right corner, moving only right or down, such that the parity of cell values along the path alternates.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on dp, grid, parity.
- Typical lenses to test first: dp, grid, parity.
- Constraints reminder: 1 ≤ n, ≤ 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, ≤ 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.
dpgridparity