CustomCC0-1.0#cpq0151700

Tree Path Sum With Multipliers

Summary

•Phase 6 / tree/path-query
•Reasoning-first competitive programming drill

Problem Description

Given a tree with n nodes and a value

a_{i}

at each node, you have q queries; each gives two nodes u,v, and a multiplier m. Output the sum of

a_{i}

along the path from u to v, each multiplied by m. How to read this problem in plain language: - This is a Phase 6 reasoning drill focused on tree/path-query. - Typical lenses to test first: tree, lca, queries. - Constraints reminder: 1 ≤ n,

q \leq 1 0^{5}

, 1 ≤

a_{i}

m \leq 1 0^{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 ≤ n, $q \leq 1 0^{5}$ , 1 ≤ $a_{i}$ , $m \leq 1 0^{6}$

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.

treelcaqueriespath-sum