{ "data": { "question": { "questionId": "3720", "questionFrontendId": "3419", "categoryTitle": "Algorithms", "boundTopicId": 3043037, "title": "Minimize the Maximum Edge Weight of Graph", "titleSlug": "minimize-the-maximum-edge-weight-of-graph", "content": "
You are given two integers, n and threshold, as well as a directed weighted graph of n nodes numbered from 0 to n - 1. The graph is represented by a 2D integer array edges, where edges[i] = [Ai, Bi, Wi] indicates that there is an edge going from node Ai to node Bi with weight Wi.
You have to remove some edges from this graph (possibly none), so that it satisfies the following conditions:
\n\nthreshold outgoing edges.Return the minimum possible value of the maximum edge weight after removing the necessary edges. If it is impossible for all conditions to be satisfied, return -1.
\n\n\n
Example 1:
\n\nInput: n = 5, edges = [[1,0,1],[2,0,2],[3,0,1],[4,3,1],[2,1,1]], threshold = 2
\n\nOutput: 1
\n\nExplanation:
\n\n
Remove the edge 2 -> 0. The maximum weight among the remaining edges is 1.
Example 2:
\n\nInput: n = 5, edges = [[0,1,1],[0,2,2],[0,3,1],[0,4,1],[1,2,1],[1,4,1]], threshold = 1
\n\nOutput: -1
\n\nExplanation:
\n\nIt is impossible to reach node 0 from node 2.
\nExample 3:
\n\nInput: n = 5, edges = [[1,2,1],[1,3,3],[1,4,5],[2,3,2],[3,4,2],[4,0,1]], threshold = 1
\n\nOutput: 2
\n\nExplanation:
\n\n
Remove the edges 1 -> 3 and 1 -> 4. The maximum weight among the remaining edges is 2.
Example 4:
\n\nInput: n = 5, edges = [[1,2,1],[1,3,3],[1,4,5],[2,3,2],[4,0,1]], threshold = 1
\n\nOutput: -1
\n\n
Constraints:
\n\n2 <= n <= 1051 <= threshold <= n - 11 <= edges.length <= min(105, n * (n - 1) / 2).edges[i].length == 30 <= Ai, Bi < nAi != Bi1 <= Wi <= 106给你两个整数 n 和 threshold ,同时给你一个 n 个节点的 有向 带权图,节点编号为 0 到 n - 1 。这个图用 二维 整数数组 edges 表示,其中 edges[i] = [Ai, Bi, Wi] 表示节点 Ai 到节点 Bi 之间有一条边权为 Wi的有向边。
你需要从这个图中删除一些边(也可能 不 删除任何边),使得这个图满足以下条件:
\n\nthreshold 条出去的边。请你返回删除必要的边后,最大 边权的 最小值 为多少。如果无法满足所有的条件,请你返回 -1 。
\n\n\n\n
示例 1:
\n\n输入:n = 5, edges = [[1,0,1],[2,0,2],[3,0,1],[4,3,1],[2,1,1]], threshold = 2
\n\n输出:1
\n\n解释:
\n\n
删除边 2 -> 0 。剩余边中的最大值为 1 。
示例 2:
\n\n输入:n = 5, edges = [[0,1,1],[0,2,2],[0,3,1],[0,4,1],[1,2,1],[1,4,1]], threshold = 1
\n\n输出:-1
\n\n解释:
\n\n无法从节点 2 到节点 0 。
\n示例 3:
\n\n输入:n = 5, edges = [[1,2,1],[1,3,3],[1,4,5],[2,3,2],[3,4,2],[4,0,1]], threshold = 1
\n\n输出:2
\n\n解释:
\n\n
删除边 1 -> 3 和 1 -> 4 。剩余边中的最大值为 2 。
示例 4:
\n\n输入:n = 5, edges = [[1,2,1],[1,3,3],[1,4,5],[2,3,2],[4,0,1]], threshold = 1
\n\n输出:-1
\n\n\n
提示:
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