{ "data": { "question": { "questionId": "3853", "questionFrontendId": "3553", "categoryTitle": "Algorithms", "boundTopicId": 3677846, "title": "Minimum Weighted Subgraph With the Required Paths II", "titleSlug": "minimum-weighted-subgraph-with-the-required-paths-ii", "content": "

You are given an undirected weighted tree with n nodes, numbered from 0 to n - 1. It is represented by a 2D integer array edges of length n - 1, where edges[i] = [ui, vi, wi] indicates that there is an edge between nodes ui and vi with weight wi.​

\n\n

Additionally, you are given a 2D integer array queries, where queries[j] = [src1j, src2j, destj].

\n\n

Return an array answer of length equal to queries.length, where answer[j] is the minimum total weight of a subtree such that it is possible to reach destj from both src1j and src2j using edges in this subtree.

\n\n

A subtree here is any connected subset of nodes and edges of the original tree forming a valid tree.

\n\n

 

\n

Example 1:

\n\n
\n

Input: edges = [[0,1,2],[1,2,3],[1,3,5],[1,4,4],[2,5,6]], queries = [[2,3,4],[0,2,5]]

\n\n

Output: [12,11]

\n\n

Explanation:

\n\n

The blue edges represent one of the subtrees that yield the optimal answer.

\n\n

\"\"

\n\n\n
\n\n

Example 2:

\n\n
\n

Input: edges = [[1,0,8],[0,2,7]], queries = [[0,1,2]]

\n\n

Output: [15]

\n\n

Explanation:

\n\n

\"\"

\n\n\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "包含给定路径的最小带权子树 II", "translatedContent": "

给你一个 无向带权 树，共有 n 个节点，编号从 0 到 n - 1。这棵树由一个二维整数数组 edges 表示，长度为 n - 1，其中 edges[i] = [ui, vi, wi] 表示存在一条连接节点 ui 和 vi 的边，权重为 wi。

\n\n

此外，给你一个二维整数数组 queries，其中 queries[j] = [src1j, src2j, destj]。

\n\n

返回一个长度等于 queries.length 的数组 answer，其中 answer[j] 表示一个子树的 最小总权重 ，使用该子树的边可以从 src1j 和 src2j 到达 destj 。

\n\n

这里的 子树 是指原树中任意节点和边组成的连通子集形成的一棵有效树。

\n\n

 

\n\n

示例 1：

\n\n
\n

输入： edges = [[0,1,2],[1,2,3],[1,3,5],[1,4,4],[2,5,6]], queries = [[2,3,4],[0,2,5]]

\n\n

输出： [12,11]

\n\n

解释：

\n\n

蓝色边表示可以得到最优答案的子树之一。

\n\n

\"\"

\n\n\n
\n\n

示例 2：

\n\n
\n

输入： edges = [[1,0,8],[0,2,7]], queries = [[0,1,2]]

\n\n

输出： [15]

\n\n

解释：

\n\n

\"\"

\n\n\n
\n\n

 

\n\n

提示：

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        }
    }
}