CustomCC0-1.0#P020-3412500
Weighted Subset XOR Query
Summary
- •Phase 6 / xor/subset_dp/weighted
- •Reasoning-first competitive programming drill
Problem Description
You are given N numbers and Q queries. Each query (L, R, X) asks for the maximal sum of weights of a subset of A[L:R] whose XOR is exactly X. Each A[i] has a weight W[i].
How to read this problem in plain language:
- This is a Phase 6 reasoning drill focused on xor/subse/weighted.
- Typical lenses to test first: xor, dp, subset.
- Constraints reminder: 1 ≤ 1 ≤ 0 ≤ A[i] < 2^{20}; 1 ≤ W[i] ≤ 10^6
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 ≤ 0 ≤ A[i] < 2^{20}; 1 ≤ W[i] ≤ 10^6
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.
xordpsubsetquery