CustomCC0-1.0#P013-2412200
K-Longest Paths in Grid
Summary
- •Phase 5 / dp/kth_path/grid
- •Reasoning-first competitive programming drill
Problem Description
Given an N x M grid of positive integers, find the sum of the k longest simple path sums from the top-left (1,1) to bottom-right (N,M), moving only right or down. Paths may revisit cells but not revisit any cell in the same path.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on dp/kt/grid.
- Typical lenses to test first: dp, kth path, grid.
- Constraints reminder: 1 ≤ N, 1 ≤ 1 ≤ grid[i][j] ≤ 100
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 ≤ 1 ≤ grid[i][j] ≤ 100
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.
dpkth pathgrid