CustomCC0-1.0#ct-p1-021450
Modulo Prefix Pair Count
Summary
- •Phase 1 / prefix-sum
- •Reasoning-first competitive programming drill
Problem Description
Count subarrays whose sum is divisible by m. Your submission must justify algorithm choice, prove correctness, and test adversarial edge cases.
How to read this problem in plain language:
- This is a Phase 1 reasoning drill focused on prefix-sum.
- Typical lenses to test first: prefix-sum, hash-table, math.
- Constraints reminder: 1 <= n <= 2e5, 1 <= m <= 2e5
Mini examples for mental simulation:
1) Boundary example: Ensure normalized modulo works with negative prefixes.
2) Adversarial example: Every subarray is valid. Explain expected behavior and why naive logic may fail.
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, 1 <= m <= 2e5
Analysis
Key Insight
Quantifying complexity against constraints is mandatory for selecting the final approach and rejecting brute force formally.
prefix-sumhash-tablemath