CustomCC0-1.0#ct-p6-012300
Constructive Modulo Permutation
Summary
- •Phase 6 / constructive-math
- •Reasoning-first competitive programming drill
Problem Description
Construct permutation p of 1..n maximizing count of indices i with (p[i]+i) mod m = 0.
How to read this problem in plain language:
- This is a Phase 6 reasoning drill focused on constructive-math.
- Typical lenses to test first: constructive, math, greedy.
- Constraints reminder: 1 <= n <= 2e5
Mini examples for mental simulation:
1) Boundary example: All indices are matchable. Explain expected behavior and why naive logic may fail.
2) Adversarial example: Residue m/2 when m even requires internal pairing.
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 <= 2e5
Analysis
Key Insight
Quantifying complexity against constraints is mandatory for selecting the final approach and rejecting brute force formally.
constructivemathgreedy