3585 - Find Weighted Median Node in Tree.

Hard

You are given an integer n and an undirected, weighted tree rooted at node 0 with n nodes numbered from 0 to n - 1. This is represented by a 2D array edges of length n - 1, where <code>edgesi = u_i, v_i, w_i</code> indicates an edge from node <code>u_i</code> to <code>v_i</code> with weight <code>w_i</code>.

The weighted median node is defined as the first node x on the path from <code>u_i</code> to <code>v_i</code> such that the sum of edge weights from <code>u_i</code> to x is greater than or equal to half of the total path weight.

You are given a 2D integer array queries. For each <code>queriesj = u_j, v_j</code>, determine the weighted median node along the path from <code>u_j</code> to <code>v_j</code>.

Return an array ans, where ans[j] is the node index of the weighted median for queries[j].

Example 1:

Input: n = 2, edges = [0,1,7], queries = [1,0,0,1]

Output: 0,1

Explanation:

Example 2:

Input: n = 3, edges = [0,1,2,2,0,4], queries = [0,1,2,0,1,2]

Output: 1,0,2

E****xplanation:

Example 3:

Input: n = 5, edges = [0,1,2,0,2,5,1,3,1,2,4,3], queries = [3,4,1,2]

Output: 2,2

Explanation:

Constraints:

• <code>2 <= n <= 10⁵</code>

• edges.length == n - 1

• <code>edgesi == u_i, v_i, w_i</code>

• <code>0 <= u_i, v_i< n</code>

• <code>1 <= w_i<= 10⁹</code>

• <code>1 <= queries.length <= 10⁵</code>

• <code>queriesj == u_j, v_j</code>

• <code>0 <= u_j, v_j< n</code>

• The input is generated such that edges represents a valid tree.