CustomCC0-1.0#cp006-601600
Unique Path Lengths in Grid
Summary
- •Phase 5 / dp, path counting
- •Reasoning-first competitive programming drill
Problem Description
Given an n x m grid of obstacles ('.' = empty, '#' = blocked), find the number of distinct path lengths from (1,1) to (n,m) moving only right or down.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on dp, path counting.
- Typical lenses to test first: dp, grid, path counting.
- Constraints reminder: 1 <= n,m <= 500, grid contains only '.' or '#'
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 <= 500, grid contains only '.' or '#'
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
dpgridpath counting