Package g3501_3600.s3585_find_weighted_median_node_in_tree

Class Solution

java.lang.Object

g3501_3600.s3585_find_weighted_median_node_in_tree.Solution

public class Solution
extends Object

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 edges[i] = [ui, vi, wi] indicates an edge from node ui to vi with weight wi.

The weighted median node is defined as the first node x on the path from ui to vi such that the sum of edge weights from ui to x is greater than or equal to half of the total path weight.

You are given a 2D integer array queries. For each queries[j] = [uj, vj], determine the weighted median node along the path from uj to vj.

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:

Query	Path	Edge Weights	Total Path Weight	Half	Explanation	Answer
[1, 0]	1 \u2192 0	[7]	7	3.5	Sum from 1 \u2192 0 = 7 >= 3.5, median is node 0.	0
[0, 1]	0 \u2192 1	[7]	7	3.5	Sum from 0 \u2192 1 = 7 >= 3.5, median is node 1.	1

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:

Query	Path	Edge Weights	Total Path Weight	Half	Explanation	Answer
[0, 1]	0 \u2192 1	[2]	2	1	Sum from 0 \u2192 1 = 2 >= 1, median is node 1.	1
[2, 0]	2 \u2192 0	[4]	4	2	Sum from 2 \u2192 0 = 4 >= 2, median is node 0.	0
[1, 2]	1 \u2192 0 \u2192 2	[2, 4]	6	3	Sum from 1 \u2192 0 = 2 < 3. <br> Sum from 1 \u2192 2 = 2 + 4 = 6 >= 3, median is node 2.	2

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:

Query	Path	Edge Weights	Total Path Weight	Half	Explanation	Answer
[3, 4]	3 \u2192 1 \u2192 0 \u2192 2 \u2192 4	[1, 2, 5, 3]	11	5.5	Sum from 3 \u2192 1 = 1 < 5.5.<br> Sum from 3 \u2192 0 = 1 + 2 = 3 < 5.5.<br> Sum from 3 \u2192 2 = 1 + 2 + 5 = 8 >= 5.5, median is node 2.	2
[1, 2]	1 \u2192 0 \u2192 2	[2, 5]	7	3.5	Sum from 1 \u2192 0 = 2 < 3.5.<br> Sum from 1 \u2192 2 = 2 + 5 = 7 >= 3.5, median is node 2.	2

Constraints:

• 2 <= n <= 105
• edges.length == n - 1
• edges[i] == [ui, vi, wi]
• 0 <= ui, vi < n
• 1 <= wi <= 109
• 1 <= queries.length <= 105
• queries[j] == [uj, vj]
• 0 <= uj, vj < n
• The input is generated such that edges represents a valid tree.

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
int[]	findMedian(int n, int[][] edges, int[][] queries)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

findMedian

public int[] findMedian(int n,
 int[][] edges,
 int[][] queries)