CustomCC0-1.0#P0132000
Swap to Sort with Constraints
Summary
- •Phase 2 / Graphs, Permutations
- •Reasoning-first competitive programming drill
Problem Description
Given an array of N distinct integers and a set of allowed indices pairs (i,j), you may swap A[i] and A[j] if (i,j) is in the set. What is the minimal number of swaps needed, using only allowed swaps, to sort the array in increasing order?
How to read this problem in plain language:
- This is a Phase 2 reasoning drill focused on Graphs, Permutations.
- Typical lenses to test first: graph, permutation, swapping.
- Constraints reminder: 1 ≤ , 0 ≤ , 1 ≤ A[i] ≤ 1e9
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 ≤ , 0 ≤ , 1 ≤ A[i] ≤ 1e9
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.
graphpermutationswapping