{ "data": { "question": { "questionId": "3881", "questionFrontendId": "3613", "categoryTitle": "Algorithms", "boundTopicId": 3719871, "title": "Minimize Maximum Component Cost", "titleSlug": "minimize-maximum-component-cost", "content": "
You are given an undirected connected graph with n nodes labeled from 0 to n - 1 and a 2D integer array edges where edges[i] = [ui, vi, wi] denotes an undirected edge between node ui and node vi with weight wi, and an integer k.
You are allowed to remove any number of edges from the graph such that the resulting graph has at most k connected components.
The cost of a component is defined as the maximum edge weight in that component. If a component has no edges, its cost is 0.
\n\nReturn the minimum possible value of the maximum cost among all components after such removals.
\n\n\n
Example 1:
\n\nInput: n = 5, edges = [[0,1,4],[1,2,3],[1,3,2],[3,4,6]], k = 2
\n\nOutput: 4
\n\nExplanation:
\n\n
Example 2:
\n\nInput: n = 4, edges = [[0,1,5],[1,2,5],[2,3,5]], k = 1
\n\nOutput: 5
\n\nExplanation:
\n\n
k = 1) requires the graph to stay fully connected.\n
Constraints:
\n\n1 <= n <= 5 * 1040 <= edges.length <= 105edges[i].length == 30 <= ui, vi < n1 <= wi <= 1061 <= k <= n给你一个无向连通图,包含 n 个节点,节点编号从 0 到 n - 1,以及一个二维整数数组 edges,其中 edges[i] = [ui, vi, wi] 表示一条连接节点 ui 和节点 vi 的无向边,边权为 wi,另有一个整数 k。
你可以从图中移除任意数量的边,使得最终的图中 最多 只包含 k 个连通分量。
连通分量的 成本 定义为该分量中边权的 最大值 。如果一个连通分量没有边,则其代价为 0。
\n\n请返回在移除这些边之后,在所有连通分量之中的 最大成本 的 最小可能值 。
\n\n\n\n
示例 1:
\n\n输入: n = 5, edges = [[0,1,4],[1,2,3],[1,3,2],[3,4,6]], k = 2
\n\n输出: 4
\n\n解释:
\n\n
示例 2:
\n\n输入: n = 4, edges = [[0,1,5],[1,2,5],[2,3,5]], k = 1
\n\n输出: 5
\n\n解释:
\n\n
k = 1),图必须保持完全连通。\n\n
提示:
\n\n1 <= n <= 5 * 1040 <= edges.length <= 105edges[i].length == 30 <= ui, vi < n1 <= wi <= 1061 <= k <= nedges and do binary search on the candidate maximum weight",
"Use DFS or DSU to count the number of connected components when keeping only edges with weight <= mid"
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