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"categoryTitle": "Algorithms",
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"title": "Maximal Network Rank",
"titleSlug": "maximal-network-rank",
"content": "<p>There is an infrastructure of <code>n</code> cities with some number of <code>roads</code> connecting these cities. Each <code>roads[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is a bidirectional road between cities <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>\n\n<p>The <strong>network rank</strong><em> </em>of <strong>two different cities</strong> is defined as the total number of&nbsp;<strong>directly</strong> connected roads to <strong>either</strong> city. If a road is directly connected to both cities, it is only counted <strong>once</strong>.</p>\n\n<p>The <strong>maximal network rank </strong>of the infrastructure is the <strong>maximum network rank</strong> of all pairs of different cities.</p>\n\n<p>Given the integer <code>n</code> and the array <code>roads</code>, return <em>the <strong>maximal network rank</strong> of the entire infrastructure</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/21/ex1.png\" style=\"width: 292px; height: 172px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, roads = [[0,1],[0,3],[1,2],[1,3]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The network rank of cities 0 and 1 is 4 as there are 4 roads that are connected to either 0 or 1. The road between 0 and 1 is only counted once.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/21/ex2.png\" style=\"width: 292px; height: 172px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, roads = [[0,1],[0,3],[1,2],[1,3],[2,3],[2,4]]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> There are 5 roads that are connected to cities 1 or 2.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 8, roads = [[0,1],[1,2],[2,3],[2,4],[5,6],[5,7]]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The network rank of 2 and 5 is 5. Notice that all the cities do not have to be connected.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 100</code></li>\n\t<li><code>0 &lt;= roads.length &lt;= n * (n - 1) / 2</code></li>\n\t<li><code>roads[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub>&nbsp;&lt;= n-1</code></li>\n\t<li><code>a<sub>i</sub>&nbsp;!=&nbsp;b<sub>i</sub></code></li>\n\t<li>Each&nbsp;pair of cities has <strong>at most one</strong> road connecting them.</li>\n</ul>\n",
"translatedTitle": "最大网络秩",
"translatedContent": "<p><code>n</code> 座城市和一些连接这些城市的道路 <code>roads</code> 共同组成一个基础设施网络。每个 <code>roads[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> 都表示在城市 <code>a<sub>i</sub></code> 和 <code>b<sub>i</sub></code> 之间有一条双向道路。</p>\n\n<p>两座不同城市构成的 <strong>城市对</strong> 的 <strong>网络秩</strong> 定义为:与这两座城市 <strong>直接</strong> 相连的道路总数。如果存在一条道路直接连接这两座城市,则这条道路只计算 <strong>一次</strong> 。</p>\n\n<p>整个基础设施网络的 <strong>最大网络秩</strong> 是所有不同城市对中的 <strong>最大网络秩</strong> 。</p>\n\n<p>给你整数 <code>n</code> 和数组 <code>roads</code>,返回整个基础设施网络的 <strong>最大网络秩</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/11/ex1.png\" style=\"width: 292px; height: 172px;\" /></strong></p>\n\n<pre>\n<strong>输入:</strong>n = 4, roads = [[0,1],[0,3],[1,2],[1,3]]\n<strong>输出:</strong>4\n<strong>解释:</strong>城市 0 和 1 的网络秩是 4因为共有 4 条道路与城市 0 或 1 相连。位于 0 和 1 之间的道路只计算一次。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/11/ex2.png\" style=\"width: 292px; height: 172px;\" /></strong></p>\n\n<pre>\n<strong>输入:</strong>n = 5, roads = [[0,1],[0,3],[1,2],[1,3],[2,3],[2,4]]\n<strong>输出:</strong>5\n<strong>解释:</strong>共有 5 条道路与城市 1 或 2 相连。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 8, roads = [[0,1],[1,2],[2,3],[2,4],[5,6],[5,7]]\n<strong>输出:</strong>5\n<strong>解释:</strong>2 和 5 的网络秩为 5注意并非所有的城市都需要连接起来。\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 100</code></li>\n\t<li><code>0 <= roads.length <= n * (n - 1) / 2</code></li>\n\t<li><code>roads[i].length == 2</code></li>\n\t<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> <= n-1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>每对城市之间 <strong>最多只有一条</strong> 道路相连</li>\n</ul>\n",
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"Try every pair of different cities and calculate its network rank.",
"The network rank of two vertices is <i>almost</i> the sum of their degrees.",
"How can you efficiently check if there is a road connecting two different cities?"
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