CustomCC0-1.0#P007-7201450
Minimal Prime Gaps
Summary
- •Phase 4 / number_theory/primes/difference
- •Reasoning-first competitive programming drill
Problem Description
Given an array A of N unique integers (1 ≤ A[i] ≤ 10^6), find the smallest difference between any two primes in the array. Output -1 if there are fewer than two primes.
How to read this problem in plain language:
- This is a Phase 4 reasoning drill focused on numbe/primes/difference.
- Typical lenses to test first: number theory, primes, sorting.
- Constraints reminder: 1 ≤ 1 ≤ A[i] ≤ 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 ≤ 1 ≤ A[i] ≤ 10^6
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.
number theoryprimessorting