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56 lines
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56 lines
3.1 KiB
HTML
<p data-end="331" data-start="85">You are given an undirected connected graph with <code data-end="137" data-start="134">n</code> nodes labeled from 0 to <code data-end="171" data-start="164">n - 1</code> and a 2D integer array <code data-end="202" data-start="195">edges</code> where <code data-end="234" data-start="209">edges[i] = [u<sub>i</sub>, v<sub>i</sub>, w<sub>i</sub>]</code> denotes an undirected edge between node <code data-end="279" data-start="275">u<sub>i</sub></code> and node <code data-end="293" data-start="289">v<sub>i</sub></code> with weight <code data-end="310" data-start="306">w<sub>i</sub></code>, and an integer <code data-end="330" data-start="327">k</code>.</p>
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<p data-end="461" data-start="333">You are allowed to remove any number of edges from the graph such that the resulting graph has <strong>at most</strong> <code data-end="439" data-start="436">k</code> connected components.</p>
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<p data-end="589" data-start="463">The <strong>cost</strong> of a component is defined as the <strong>maximum</strong> edge weight in that component. If a component has no edges, its cost is 0.</p>
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<p data-end="760" data-start="661">Return the <strong>minimum</strong> possible value of the <strong>maximum</strong> cost among all components <strong data-end="759" data-start="736">after such removals</strong>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 5, edges = [[0,1,4],[1,2,3],[1,3,2],[3,4,6]], k = 2</span></p>
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<p><strong>Output:</strong> <span class="example-io">4</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img alt="" src="https://assets.leetcode.com/uploads/2025/04/19/minimizemaximumm.jpg" style="width: 535px; height: 225px;" /></p>
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<ul>
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<li data-end="1070" data-start="1021">Remove the edge between nodes 3 and 4 (weight 6).</li>
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<li data-end="1141" data-start="1073">The resulting components have costs of 0 and 4, so the overall maximum cost is 4.</li>
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</ul>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 4, edges = [[0,1,5],[1,2,5],[2,3,5]], k = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">5</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img alt="" src="https://assets.leetcode.com/uploads/2025/04/19/minmax2.jpg" style="width: 315px; height: 55px;" /></p>
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<ul>
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<li data-end="1315" data-start="1251">No edge can be removed, since allowing only one component (<code>k = 1</code>) requires the graph to stay fully connected.</li>
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<li data-end="1389" data-start="1318">That single component’s cost equals its largest edge weight, which is 5.</li>
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</ul>
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</div>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= n <= 5 * 10<sup>4</sup></code></li>
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<li><code>0 <= edges.length <= 10<sup>5</sup></code></li>
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<li><code>edges[i].length == 3</code></li>
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<li><code>0 <= u<sub>i</sub>, v<sub>i</sub> < n</code></li>
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<li><code>1 <= w<sub>i</sub> <= 10<sup>6</sup></code></li>
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<li><code>1 <= k <= n</code></li>
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<li>The input graph is connected.</li>
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</ul>
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