{ "data": { "question": { "questionId": "2321", "questionFrontendId": "2203", "categoryTitle": "Algorithms", "boundTopicId": 1329523, "title": "Minimum Weighted Subgraph With the Required Paths", "titleSlug": "minimum-weighted-subgraph-with-the-required-paths", "content": "

You are given an integer n denoting the number of nodes of a weighted directed graph. The nodes are numbered from 0 to n - 1.

\n\n

You are also given a 2D integer array edges where edges[i] = [fromi, toi, weighti] denotes that there exists a directed edge from fromi to toi with weight weighti.

\n\n

Lastly, you are given three distinct integers src1, src2, and dest denoting three distinct nodes of the graph.

\n\n

Return the minimum weight of a subgraph of the graph such that it is possible to reach dest from both src1 and src2 via a set of edges of this subgraph. In case such a subgraph does not exist, return -1.

\n\n

A subgraph is a graph whose vertices and edges are subsets of the original graph. The weight of a subgraph is the sum of weights of its constituent edges.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 6, edges = [[0,2,2],[0,5,6],[1,0,3],[1,4,5],[2,1,1],[2,3,3],[2,3,4],[3,4,2],[4,5,1]], src1 = 0, src2 = 1, dest = 5\nOutput: 9\nExplanation:\nThe above figure represents the input graph.\nThe blue edges represent one of the subgraphs that yield the optimal answer.\nNote that the subgraph [[1,0,3],[0,5,6]] also yields the optimal answer. It is not possible to get a subgraph with less weight satisfying all the constraints.\n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 3, edges = [[0,1,1],[2,1,1]], src1 = 0, src2 = 1, dest = 2\nOutput: -1\nExplanation:\nThe above figure represents the input graph.\nIt can be seen that there does not exist any path from node 1 to node 2, hence there are no subgraphs satisfying all the constraints.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "得到要求路径的最小带权子图", "translatedContent": "

给你一个整数 n ，它表示一个 带权有向 图的节点数，节点编号为 0 到 n - 1 。

\n\n

同时给你一个二维整数数组 edges ，其中 edges[i] = [fromi, toi, weighti] ，表示从 fromi 到 toi 有一条边权为 weighti 的 有向 边。

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最后，给你三个 互不相同 的整数 src1 ，src2 和 dest ，表示图中三个不同的点。

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请你从图中选出一个 边权和最小 的子图，使得从 src1 和 src2 出发，在这个子图中，都 可以 到达 dest 。如果这样的子图不存在，请返回 -1 。

\n\n

子图 中的点和边都应该属于原图的一部分。子图的边权和定义为它所包含的所有边的权值之和。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：n = 6, edges = [[0,2,2],[0,5,6],[1,0,3],[1,4,5],[2,1,1],[2,3,3],[2,3,4],[3,4,2],[4,5,1]], src1 = 0, src2 = 1, dest = 5\n输出：9\n解释：\n上图为输入的图。\n蓝色边为最优子图之一。\n注意，子图 [[1,0,3],[0,5,6]] 也能得到最优解，但无法在满足所有限制的前提下，得到更优解。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：n = 3, edges = [[0,1,1],[2,1,1]], src1 = 0, src2 = 1, dest = 2\n输出：-1\n解释：\n上图为输入的图。\n可以看到，不存在从节点 1 到节点 2 的路径，所以不存在任何子图满足所有限制。\n
\n\n

 

\n\n

提示：

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