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49 lines
2.4 KiB
HTML
<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>
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<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>
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<p>The <strong>maximal network rank </strong>of the infrastructure is the <strong>maximum network rank</strong> of all pairs of different cities.</p>
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<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>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/ex1.png" style="width: 292px; height: 172px;" /></strong></p>
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<pre>
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<strong>Input:</strong> n = 4, roads = [[0,1],[0,3],[1,2],[1,3]]
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<strong>Output:</strong> 4
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<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.
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</pre>
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<p><strong>Example 2:</strong></p>
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<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/ex2.png" style="width: 292px; height: 172px;" /></strong></p>
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<pre>
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<strong>Input:</strong> n = 5, roads = [[0,1],[0,3],[1,2],[1,3],[2,3],[2,4]]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> There are 5 roads that are connected to cities 1 or 2.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> n = 8, roads = [[0,1],[1,2],[2,3],[2,4],[5,6],[5,7]]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> The network rank of 2 and 5 is 5. Notice that all the cities do not have to be connected.
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</pre>
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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>2 <= n <= 100</code></li>
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<li><code>0 <= roads.length <= n * (n - 1) / 2</code></li>
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<li><code>roads[i].length == 2</code></li>
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<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> <= n-1</code></li>
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<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
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<li>Each pair of cities has <strong>at most one</strong> road connecting them.</li>
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</ul>
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