mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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165 lines
21 KiB
JSON
165 lines
21 KiB
JSON
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"questionId": "1887",
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"categoryTitle": "Algorithms",
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"boundTopicId": 601249,
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"title": "Minimum Degree of a Connected Trio in a Graph",
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"content": "<p>You are given an undirected graph. You are given an integer <code>n</code> which is the number of nodes in the graph and an array <code>edges</code>, where each <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an undirected edge between <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>.</p>\n\n<p>A <strong>connected trio</strong> is a set of <strong>three</strong> nodes where there is an edge between <b>every</b> pair of them.</p>\n\n<p>The <strong>degree of a connected trio</strong> is the number of edges where one endpoint is in the trio, and the other is not.</p>\n\n<p>Return <em>the <strong>minimum</strong> degree of a connected trio in the graph, or</em> <code>-1</code> <em>if the graph has no connected trios.</em></p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/01/26/trios1.png\" style=\"width: 388px; height: 164px;\" />\n<pre>\n<strong>Input:</strong> n = 6, edges = [[1,2],[1,3],[3,2],[4,1],[5,2],[3,6]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> There is exactly one trio, which is [1,2,3]. The edges that form its degree are bolded in the figure above.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/01/26/trios2.png\" style=\"width: 388px; height: 164px;\" />\n<pre>\n<strong>Input:</strong> n = 7, edges = [[1,3],[4,1],[4,3],[2,5],[5,6],[6,7],[7,5],[2,6]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are exactly three trios:\n1) [1,4,3] with degree 0.\n2) [2,5,6] with degree 2.\n3) [5,6,7] with degree 2.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 400</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>1 <= edges.length <= n * (n-1) / 2</code></li>\n\t<li><code>1 <= u<sub>i</sub>, v<sub>i</sub> <= n</code></li>\n\t<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>\n\t<li>There are no repeated edges.</li>\n</ul>\n",
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"translatedTitle": "一个图中连通三元组的最小度数",
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"translatedContent": "<p>给你一个无向图，整数 <code>n</code> 表示图中节点的数目，<code>edges</code> 数组表示图中的边，其中 <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> ，表示 <code>u<sub>i</sub></code> 和 <code>v<sub>i</sub></code><sub> </sub>之间有一条无向边。</p>\n\n<p>一个 <strong>连通三元组</strong> 指的是 <strong>三个</strong> 节点组成的集合且这三个点之间 <strong>两两</strong> 有边。</p>\n\n<p><strong>连通三元组的度数</strong> 是所有满足此条件的边的数目：一个顶点在这个三元组内，而另一个顶点不在这个三元组内。</p>\n\n<p>请你返回所有连通三元组中度数的 <strong>最小值</strong> ，如果图中没有连通三元组，那么返回 <code>-1</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/02/14/trios1.png\" style=\"width: 388px; height: 164px;\" />\n<pre>\n<b>输入：</b>n = 6, edges = [[1,2],[1,3],[3,2],[4,1],[5,2],[3,6]]\n<b>输出：</b>3\n<b>解释：</b>只有一个三元组 [1,2,3] 。构成度数的边在上图中已被加粗。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/02/14/trios2.png\" style=\"width: 388px; height: 164px;\" />\n<pre>\n<b>输入：</b>n = 7, edges = [[1,3],[4,1],[4,3],[2,5],[5,6],[6,7],[7,5],[2,6]]\n<b>输出：</b>0\n<b>解释：</b>有 3 个三元组：\n1) [1,4,3]，度数为 0 。\n2) [2,5,6]，度数为 2 。\n3) [5,6,7]，度数为 2 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 400</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>1 <= edges.length <= n * (n-1) / 2</code></li>\n\t<li><code>1 <= u<sub>i</sub>, v<sub>i</sub> <= n</code></li>\n\t<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>\n\t<li>图中没有重复的边。</li>\n</ul>\n",
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"Consider a trio with nodes u, v, and w. The degree of the trio is just degree(u) + degree(v) + degree(w) - 6. The -6 comes from subtracting the edges u-v, u-w, and v-w, which are counted twice each in the vertex degree calculation.",
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"To get the trios (u,v,w), you can iterate on u, then iterate on each w,v such that w and v are neighbors of u and are neighbors of each other."
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