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Given a weighted tree and many queries (u, v), find the first node along the path from u to v where the cumulative edge weight from u reaches at least half the total path weight; this requires fast path-weight prefix queries using preprocessing (distances + LCA) and jump operations (e.g., binary lifting or HLD) to locate the median node efficiently.
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Leetcode 3585. Find Weighted Median Node in Tree
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Source snapshot: Nov 12, 2026
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