CustomCC0-1.0#cp016-3652100
Grid Row-Column Swap Sort
Summary
- •Phase 5 / permutations, cycles, grid
- •Reasoning-first competitive programming drill
Problem Description
Given an n x n grid of distinct integers, you can swap any two rows or any two columns (but not both at the same time). What is the minimal number of swaps to fully sort the grid in row-major order?
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on permutations, cycles, grid.
- Typical lenses to test first: permutation, grid, cycle decomposition.
- Constraints reminder: 1 <= n <= 500, all grid values unique and in 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 <= 500, all grid values unique and in 1..
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
permutationgridcycle decomposition