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"title": "Maximal Network Rank",
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"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 <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> </p>\n<p><strong>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>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>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> </p>\n<p><strong>Constraints:</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>Each pair of cities has <strong>at most one</strong> road connecting them.</li>\n</ul>\n",
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"code": "class Solution(object):\n def maximalNetworkRank(self, n, roads):\n \"\"\"\n :type n: int\n :type roads: List[List[int]]\n :rtype: int\n \"\"\"\n ",
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"code": "(define/contract (maximal-network-rank n roads)\n (-> exact-integer? (listof (listof exact-integer?)) exact-integer?)\n\n )",
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"hints": [
"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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