CustomCC0-1.0#p0082300
Kth Smallest in Path
Summary
- •Phase 1 / tree, lca, path_query
- •Reasoning-first competitive programming drill
Problem Description
Given a tree with n nodes (labeled 1 to n) and values ..., answer q queries of the form (u, v, k): what is the k-th smallest value on the unique path from u to v?
How to read this problem in plain language:
- This is a Phase 1 reasoning drill focused on tree, lca, pat.
- Typical lenses to test first: tree, lca, path query.
- Constraints reminder: 1 ≤ n, , 1 ≤ , 1 ≤
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, , 1 ≤ , 1 ≤
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.
treelcapath queryorder statistics