CustomCC0-1.0#cp020-4902200
Minimal Product Cover
Summary
- •Phase 5 / number theory, primes, greedy
- •Reasoning-first competitive programming drill
Problem Description
Given an array of n positive integers, find the smallest set of indices such that the product of the selected elements is divisible by every element in the array.
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on number theory, primes, greedy.
- Typical lenses to test first: number theory, greedy, primes.
- Constraints reminder: 1 <= n <= 2*10^5, 1 <= ai <= 10^6
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 <= 10^6
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
number theorygreedyprimes