{ "data": { "question": { "questionId": "3908", "questionFrontendId": "3608", "categoryTitle": "Algorithms", "boundTopicId": 3714235, "title": "Minimum Time for K Connected Components", "titleSlug": "minimum-time-for-k-connected-components", "content": "
You are given an integer n and an undirected graph with n nodes labeled from 0 to n - 1. This is represented by a 2D array edges, where edges[i] = [ui, vi, timei] indicates an undirected edge between nodes ui and vi that can be removed at timei.
You are also given an integer k.
Initially, the graph may be connected or disconnected. Your task is to find the minimum time t such that after removing all edges with time <= t, the graph contains at least k connected components.
Return the minimum time t.
A connected component is a subgraph of a graph in which there exists a path between any two vertices, and no vertex of the subgraph shares an edge with a vertex outside of the subgraph.
\n\n\n
Example 1:
\n\nInput: n = 2, edges = [[0,1,3]], k = 2
\n\nOutput: 3
\n\nExplanation:
\n\n
{0, 1}.time = 1 or 2, the graph remains unchanged.time = 3, edge [0, 1] is removed, resulting in k = 2 connected components {0}, {1}. Thus, the answer is 3.Example 2:
\n\nInput: n = 3, edges = [[0,1,2],[1,2,4]], k = 3
\n\nOutput: 4
\n\nExplanation:
\n\n
{0, 1, 2}.time = 2, edge [0, 1] is removed, resulting in two connected components {0}, {1, 2}.time = 4, edge [1, 2] is removed, resulting in k = 3 connected components {0}, {1}, {2}. Thus, the answer is 4.Example 3:
\n\nInput: n = 3, edges = [[0,2,5]], k = 2
\n\nOutput: 0
\n\nExplanation:
\n\n
k = 2 disconnected components {1}, {0, 2}, no edge removal is needed. Thus, the answer is 0.\n
Constraints:
\n\n1 <= n <= 1050 <= edges.length <= 105edges[i] = [ui, vi, timei]0 <= ui, vi < nui != vi1 <= timei <= 1091 <= k <= n给你一个整数 n,表示一个包含 n 个节点(从 0 到 n - 1 编号)的无向图。该图由一个二维数组 edges 表示,其中 edges[i] = [ui, vi, timei] 表示一条连接节点 ui 和节点 vi 的无向边,该边会在时间 timei 被移除。
同时,另给你一个整数 k。
最初,图可能是连通的,也可能是非连通的。你的任务是找到一个 最小 的时间 t,使得在移除所有满足条件 time <= t 的边之后,该图包含 至少 k 个连通分量。
返回这个 最小 时间 t。
连通分量 是图的一个子图,其中任意两个顶点之间都存在路径,且子图中的任意顶点均不与子图外的顶点共享边。
\n\n\n\n
示例 1:
\n\n输入: n = 2, edges = [[0,1,3]], k = 2
\n\n输出: 3
\n\n解释:
\n\n
{0, 1}。time = 1 或 2 时,图保持不变。time = 3 时,边 [0, 1] 被移除,图中形成 k = 2 个连通分量:{0} 和 {1}。因此,答案是 3。示例 2:
\n\n输入: n = 3, edges = [[0,1,2],[1,2,4]], k = 3
\n\n输出: 4
\n\n解释:
\n\n
{0, 1, 2}。time = 2 时,边 [0, 1] 被移除,图中形成两个连通分量:{0} 和 {1, 2}。time = 4 时,边 [1, 2] 被移除,图中形成 k = 3 个连通分量:{0}、{1} 和 {2}。因此,答案是 4。示例 3:
\n\n输入: n = 3, edges = [[0,2,5]], k = 2
\n\n输出: 0
\n\n解释:
\n\n
k = 2 个连通分量 {1} 和 {0, 2},无需移除任何边。因此,答案是 0。\n\n
提示:
\n\n1 <= n <= 1050 <= edges.length <= 105edges[i] = [ui, vi, timei]0 <= ui, vi < nui != vi1 <= timei <= 1091 <= k <= nt such that, after removing all edges with time <= t, the graph splits into >= k connected components."
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