CustomCC0-1.0#cpq001-611450
Repeated XOR Path Sum
Summary
- •Phase 1 / prefix-xor, range-query
- •Reasoning-first competitive programming drill
Problem Description
Given an array of N integers, for each query (L, R), find the sum of XORs of all paths from L to R (inclusive), where a path is defined as any contiguous subarray starting at L and ending at any index between L and R.
How to read this problem in plain language:
- This is a Phase 1 reasoning drill focused on prefix-xor, range-query.
- Typical lenses to test first: prefix-xor, range-query, data-structures.
- Constraints reminder: 1 <= N, Q <= 2e5; 0 <= 1 <= L <= R <= N
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 <= 2e5; 0 <= 1 <= L <= R <= N
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.
prefix-xorrange-querydata-structures