CustomCC0-1.0#P0192300
Range GCD Update and Query
Summary
- •Phase 2 / Segment Tree, Lazy Propagation
- •Reasoning-first competitive programming drill
Problem Description
Given an array of N integers, process Q queries: (1) add x to all elements in A[l..r], (2) report GCD of A[l..r].
How to read this problem in plain language:
- This is a Phase 2 reasoning drill focused on Segment Tree, Lazy Propagation.
- Typical lenses to test first: segment tree, range update, gcd.
- Constraints reminder: 1 ≤ N, , 1 ≤ A[i],
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, , 1 ≤ A[i],
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.
segment treerange updategcd