mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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195 lines
28 KiB
JSON
195 lines
28 KiB
JSON
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"title": "Minimize Maximum Component Cost",
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"content": "<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>\n\n<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>\n\n<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>\n\n<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>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<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>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/04/19/minimizemaximumm.jpg\" style=\"width: 535px; height: 225px;\" /></p>\n\n<ul>\n\t<li data-end=\"1070\" data-start=\"1021\">Remove the edge between nodes 3 and 4 (weight 6).</li>\n\t<li data-end=\"1141\" data-start=\"1073\">The resulting components have costs of 0 and 4, so the overall maximum cost is 4.</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 4, edges = [[0,1,5],[1,2,5],[2,3,5]], k = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/04/19/minmax2.jpg\" style=\"width: 315px; height: 55px;\" /></p>\n\n<ul>\n\t<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>\n\t<li data-end=\"1389\" data-start=\"1318\">That single component’s cost equals its largest edge weight, which is 5.</li>\n</ul>\n</div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>0 <= edges.length <= 10<sup>5</sup></code></li>\n\t<li><code>edges[i].length == 3</code></li>\n\t<li><code>0 <= u<sub>i</sub>, v<sub>i</sub> < n</code></li>\n\t<li><code>1 <= w<sub>i</sub> <= 10<sup>6</sup></code></li>\n\t<li><code>1 <= k <= n</code></li>\n\t<li>The input graph is connected.</li>\n</ul>\n",
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"translatedTitle": "最小化连通分量的最大成本",
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"translatedContent": "<p data-end=\"331\" data-start=\"85\">给你一个无向连通图，包含 <code data-end=\"137\" data-start=\"134\">n</code> 个节点，节点编号从 0 到 <code data-end=\"171\" data-start=\"164\">n - 1</code>，以及一个二维整数数组 <code data-end=\"202\" data-start=\"195\">edges</code>，其中 <code data-end=\"234\" data-start=\"209\">edges[i] = [u<sub>i</sub>, v<sub>i</sub>, w<sub>i</sub>]</code> 表示一条连接节点 <code data-end=\"279\" data-start=\"275\">u<sub>i</sub></code> 和节点 <code data-end=\"293\" data-start=\"289\">v<sub>i</sub></code> 的无向边，边权为 <code data-end=\"310\" data-start=\"306\">w<sub>i</sub></code>，另有一个整数 <code data-end=\"330\" data-start=\"327\">k</code>。</p>\n\n<p data-end=\"461\" data-start=\"333\">你可以从图中移除任意数量的边，使得最终的图中 <strong>最多 </strong>只包含 <code data-end=\"439\" data-start=\"436\">k</code> 个连通分量。</p>\n\n<p data-end=\"589\" data-start=\"463\">连通分量的 <strong>成本 </strong>定义为该分量中边权的 <strong>最大值 </strong>。如果一个连通分量没有边，则其代价为 0。</p>\n\n<p data-end=\"760\" data-start=\"661\">请返回在移除这些边之后，在所有连通分量之中的 <strong>最大成本 </strong>的 <strong>最小可能值 </strong>。</p>\n\n<p> </p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">n = 5, edges = [[0,1,4],[1,2,3],[1,3,2],[3,4,6]], k = 2</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/04/19/minimizemaximumm.jpg\" style=\"width: 535px; height: 225px;\" /></p>\n\n<ul>\n\t<li data-end=\"1070\" data-start=\"1021\">移除节点 3 和节点 4 之间的边（权值为 6）。</li>\n\t<li data-end=\"1141\" data-start=\"1073\">最终的连通分量成本分别为 0 和 4，因此最大代价为 4。</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">n = 4, edges = [[0,1,5],[1,2,5],[2,3,5]], k = 1</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/04/19/minmax2.jpg\" style=\"width: 315px; height: 55px;\" /></p>\n\n<ul>\n\t<li data-end=\"1315\" data-start=\"1251\">无法移除任何边，因为只允许一个连通分量（<code>k = 1</code>），图必须保持完全连通。</li>\n\t<li data-end=\"1389\" data-start=\"1318\">该连通分量的成本等于其最大边权，即 5。</li>\n</ul>\n</div>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>0 <= edges.length <= 10<sup>5</sup></code></li>\n\t<li><code>edges[i].length == 3</code></li>\n\t<li><code>0 <= u<sub>i</sub>, v<sub>i</sub> < n</code></li>\n\t<li><code>1 <= w<sub>i</sub> <= 10<sup>6</sup></code></li>\n\t<li><code>1 <= k <= n</code></li>\n\t<li>输入图是连通图。</li>\n</ul>\n",
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