CustomCC0-1.0#cptp0162500
K-th Smallest XOR in Range
Summary
- •Phase 6 / persistent_trie, offline_queries
- •Reasoning-first competitive programming drill
Problem Description
Given an array of n integers, answer q queries. Each is of the form (l, r, k): Find the k-th smallest XOR value among all pairs (i, j) with ≤ r.
How to read this problem in plain language:
- This is a Phase 6 reasoning drill focused on persisten, offlin.
- Typical lenses to test first: offline, trie, queries.
- Constraints reminder: 1 ≤ n, , 0 ≤ , 1 ≤ , 1 ≤ k ≤ (r-l+1)*(r-l)/2
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, , 0 ≤ , 1 ≤ , 1 ≤ k ≤ (r-l+1)*(r-l)/2
Analysis
Key Insight
The goal is to force explicit intermediate reasoning before revealing more.
offlinetriequeriesXOR