3613 - Minimize Maximum Component Cost.

Medium

You are given an undirected connected graph with n nodes labeled from 0 to n - 1 and a 2D integer array edges where <code>edgesi = u_i, v_i, w_i</code> denotes an undirected edge between node <code>u_i</code> and node <code>v_i</code> with weight <code>w_i</code>, 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.

Return the minimum possible value of the maximum cost among all components after such removals.

Example 1:

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

Output: 4

Explanation:

• Remove the edge between nodes 3 and 4 (weight 6).

• The resulting components have costs of 0 and 4, so the overall maximum cost is 4.

Example 2:

Input: n = 4, edges = [0,1,5,1,2,5,2,3,5], k = 1

Output: 5

Explanation:

• No edge can be removed, since allowing only one component (k = 1) requires the graph to stay fully connected.

• That single component’s cost equals its largest edge weight, which is 5.

Constraints:

• <code>1 <= n <= 5 * 10⁴</code>

• <code>0 <= edges.length <= 10⁵</code>

• edges[i].length == 3

• <code>0 <= u_i, v_i< n</code>

• <code>1 <= w_i<= 10⁶</code>

• 1 <= k <= n

• The input graph is connected.