CustomCC0-1.0#cp014-1801800
Range Bitwise Sum Query
Summary
- •Phase 5 / bitwise, prefix sums
- •Reasoning-first competitive programming drill
Problem Description
Given an array of n integers, answer q queries: for given range [l,r], what is the sum of bitwise ANDs of all possible pairs (i,j) with l <= i < j <= r?
How to read this problem in plain language:
- This is a Phase 5 reasoning drill focused on bitwise, prefix sums.
- Typical lenses to test first: bitwise, range query, prefix sums.
- Constraints reminder: 1 <= n, q <= 10^5, 0 <= ai <= 10^9
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 <= n, q <= 10^5, 0 <= ai <= 10^9
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
bitwiserange queryprefix sums