CustomCC0-1.0#P0041600
Partitioned GCD Sum
Summary
- •Phase 2 / DP, GCD
- •Reasoning-first competitive programming drill
Problem Description
Given an array of N positive integers, partition it into contiguous segments. For each segment, compute the GCD of all its elements and sum over all segments. What is the maximum possible sum you can achieve?
How to read this problem in plain language:
- This is a Phase 2 reasoning drill focused on DP, GCD.
- Typical lenses to test first: dp, gcd, partition.
- Constraints reminder: 1 ≤ , 1 ≤ A[i] ≤ 1e6
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] ≤ 1e6
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.
dpgcdpartition