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Colorful Path Queries

Thinking Mode

Summary

  • •Phase 6 / tree, lca, path, color counting
  • •Reasoning-first competitive programming drill

Problem Description

Given a tree with n nodes, each edge colored with a color. For q queries, each asks for the number of unique colors along the path between two nodes u and v. How to read this problem in plain language: - This is a Phase 6 reasoning drill focused on tree, lca, path, color counting. - Typical lenses to test first: tree, lca, color. - Constraints reminder: 1 ≤ n, q≤1e5; 1 ≤ c≤1e9 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≤1e5; 1 ≤ c≤1e9

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.

treelcacoloroffline query
treelcacoloroffline query