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"title": "Maximum Total Importance of Roads",
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"content": "<p>You are given an integer <code>n</code> denoting the number of cities in a country. The cities are numbered from <code>0</code> to <code>n - 1</code>.</p>\n\n<p>You are also given a 2D integer array <code>roads</code> where <code>roads[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists a <strong>bidirectional</strong> road connecting cities <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>\n\n<p>You need to assign each city with an integer value from <code>1</code> to <code>n</code>, where each value can only be used <strong>once</strong>. The <strong>importance</strong> of a road is then defined as the <strong>sum</strong> of the values of the two cities it connects.</p>\n\n<p>Return <em>the <strong>maximum total importance</strong> of all roads possible after assigning the values optimally.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/07/ex1drawio.png\" style=\"width: 290px; height: 215px;\" />\n<pre>\n<strong>Input:</strong> n = 5, roads = [[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]\n<strong>Output:</strong> 43\n<strong>Explanation:</strong> The figure above shows the country and the assigned values of [2,4,5,3,1].\n- The road (0,1) has an importance of 2 + 4 = 6.\n- The road (1,2) has an importance of 4 + 5 = 9.\n- The road (2,3) has an importance of 5 + 3 = 8.\n- The road (0,2) has an importance of 2 + 5 = 7.\n- The road (1,3) has an importance of 4 + 3 = 7.\n- The road (2,4) has an importance of 5 + 1 = 6.\nThe total importance of all roads is 6 + 9 + 8 + 7 + 7 + 6 = 43.\nIt can be shown that we cannot obtain a greater total importance than 43.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/07/ex2drawio.png\" style=\"width: 281px; height: 151px;\" />\n<pre>\n<strong>Input:</strong> n = 5, roads = [[0,3],[2,4],[1,3]]\n<strong>Output:</strong> 20\n<strong>Explanation:</strong> The figure above shows the country and the assigned values of [4,3,2,5,1].\n- The road (0,3) has an importance of 4 + 5 = 9.\n- The road (2,4) has an importance of 2 + 1 = 3.\n- The road (1,3) has an importance of 3 + 5 = 8.\nThe total importance of all roads is 9 + 3 + 8 = 20.\nIt can be shown that we cannot obtain a greater total importance than 20.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= roads.length &lt;= 5 * 10<sup>4</sup></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> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>There are no duplicate roads.</li>\n</ul>\n",
"translatedTitle": "道路的最大总重要性",
"translatedContent": "<p>给你一个整数&nbsp;<code>n</code>&nbsp;,表示一个国家里的城市数目。城市编号为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;。</p>\n\n<p>给你一个二维整数数组&nbsp;<code>roads</code>&nbsp;,其中&nbsp;<code>roads[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示城市&nbsp;<code>a<sub>i</sub></code>&nbsp;和&nbsp;<code>b<sub>i</sub></code>&nbsp;之间有一条&nbsp;<strong>双向</strong>&nbsp;道路。</p>\n\n<p>你需要给每个城市安排一个从 <code>1</code>&nbsp;到 <code>n</code>&nbsp;之间的整数值,且每个值只能被使用 <strong>一次</strong>&nbsp;。道路的 <strong>重要性</strong>&nbsp;定义为这条道路连接的两座城市数值 <strong>之和</strong>&nbsp;。</p>\n\n<p>请你返回在最优安排下,<strong>所有道路重要性</strong> 之和 <strong>最大</strong>&nbsp;为多少。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/07/ex1drawio.png\" style=\"width: 290px; height: 215px;\"></p>\n\n<pre><b>输入:</b>n = 5, roads = [[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]\n<b>输出:</b>43\n<b>解释:</b>上图展示了国家图和每个城市被安排的值 [2,4,5,3,1] 。\n- 道路 (0,1) 重要性为 2 + 4 = 6 。\n- 道路 (1,2) 重要性为 4 + 5 = 9 。\n- 道路 (2,3) 重要性为 5 + 3 = 8 。\n- 道路 (0,2) 重要性为 2 + 5 = 7 。\n- 道路 (1,3) 重要性为 4 + 3 = 7 。\n- 道路 (2,4) 重要性为 5 + 1 = 6 。\n所有道路重要性之和为 6 + 9 + 8 + 7 + 7 + 6 = 43 。\n可以证明重要性之和不可能超过 43 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/07/ex2drawio.png\" style=\"width: 281px; height: 151px;\"></p>\n\n<pre><b>输入:</b>n = 5, roads = [[0,3],[2,4],[1,3]]\n<b>输出:</b>20\n<b>解释:</b>上图展示了国家图和每个城市被安排的值 [4,3,2,5,1] 。\n- 道路 (0,3) 重要性为 4 + 5 = 9 。\n- 道路 (2,4) 重要性为 2 + 1 = 3 。\n- 道路 (1,3) 重要性为 3 + 5 = 8 。\n所有道路重要性之和为 9 + 3 + 8 = 20 。\n可以证明重要性之和不可能超过 20 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= roads.length &lt;= 5 * 10<sup>4</sup></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> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>没有重复道路。</li>\n</ul>\n",
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