CustomCC0-1.0#cp007-7051900
Balanced Circular Subarray
Summary
- •Phase 5 / prefix sums, modular arithmetic
- •Reasoning-first competitive programming drill
Problem Description
Given a circular array of n integers, find the smallest length l > 0 such that there exists a subarray of length l whose sum is divisible by l.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on prefix sums, modular arithmetic.
- Typical lenses to test first: prefix sums, circular array, modular.
- Constraints reminder: 1 <= n <= 2*10^5, 1 <= ai <= 10^9
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 <= 2*10^5, 1 <= ai <= 10^9
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
prefix sumscircular arraymodular