CustomCC0-1.0#cpq0061400

Sliding Window GCD Coverage

Summary

•Phase 6 / gcd/sliding-window
•Reasoning-first competitive programming drill

Problem Description

Given an array of n positive integers and an integer k, find the number of subarrays of length k whose GCD is equal to a given integer g. How to read this problem in plain language: - This is a Phase 6 reasoning drill focused on gcd/sliding-window. - Typical lenses to test first: gcd, sliding-window, array. - Constraints reminder: 1 ≤

k \leq n \leq 2 \times 1 0^{5}

, 1 ≤

g \leq 1 0^{9}

, 1 ≤

a_{i} \leq 1 0^{9}

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 ≤ $k \leq n \leq 2 \times 1 0^{5}$ , 1 ≤ $g \leq 1 0^{9}$ , 1 ≤ $a_{i} \leq 1 0^{9}$

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.

gcdsliding-windowarray