CustomCC0-1.0#cpq0122000

Weighted Range Median Query

Summary

•Phase 6 / segment-tree/order-statistics
•Reasoning-first competitive programming drill

Problem Description

Given an array of n elements with integer weights, answer q queries: for each query l r, return the weighted median of the subarray

a_{l}

a_{r}

. How to read this problem in plain language: - This is a Phase 6 reasoning drill focused on segment-tree/order-statistics. - Typical lenses to test first: median, weighted, segment-tree. - Constraints reminder: 1 ≤ n,

q \leq 1 0^{5}

, 1 ≤

a_{i}

w_{i} \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 ≤ $a_{i}$ , $w_{i} \leq 1 0^{6}$

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.

medianweightedsegment-treequeries