leetcode-problemset/leetcode-cn/originData/maximum-path-quality-of-a-graph.json

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            "title": "Maximum Path Quality of a Graph",
            "titleSlug": "maximum-path-quality-of-a-graph",
            "content": "<p>There is an <strong>undirected</strong> graph with <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> (<strong>inclusive</strong>). You are given a <strong>0-indexed</strong> integer array <code>values</code> where <code>values[i]</code> is the <strong>value </strong>of the <code>i<sup>th</sup></code> node. You are also given a <strong>0-indexed</strong> 2D integer array <code>edges</code>, where each <code>edges[j] = [u<sub>j</sub>, v<sub>j</sub>, time<sub>j</sub>]</code> indicates that there is an undirected edge between the nodes <code>u<sub>j</sub></code> and <code>v<sub>j</sub></code>,<sub> </sub>and it takes <code>time<sub>j</sub></code> seconds to travel between the two nodes. Finally, you are given an integer <code>maxTime</code>.</p>\n\n<p>A <strong>valid</strong> <strong>path</strong> in the graph is any path that starts at node <code>0</code>, ends at node <code>0</code>, and takes <strong>at most</strong> <code>maxTime</code> seconds to complete. You may visit the same node multiple times. The <strong>quality</strong> of a valid path is the <strong>sum</strong> of the values of the <strong>unique nodes</strong> visited in the path (each node&#39;s value is added <strong>at most once</strong> to the sum).</p>\n\n<p>Return <em>the <strong>maximum</strong> quality of a valid path</em>.</p>\n\n<p><strong>Note:</strong> There are <strong>at most four</strong> edges connected to each node.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex1drawio.png\" style=\"width: 269px; height: 170px;\" />\n<pre>\n<strong>Input:</strong> values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49\n<strong>Output:</strong> 75\n<strong>Explanation:</strong>\nOne possible path is 0 -&gt; 1 -&gt; 0 -&gt; 3 -&gt; 0. The total time taken is 10 + 10 + 10 + 10 = 40 &lt;= 49.\nThe nodes visited are 0, 1, and 3, giving a maximal path quality of 0 + 32 + 43 = 75.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex2drawio.png\" style=\"width: 269px; height: 170px;\" />\n<pre>\n<strong>Input:</strong> values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30\n<strong>Output:</strong> 25\n<strong>Explanation:</strong>\nOne possible path is 0 -&gt; 3 -&gt; 0. The total time taken is 10 + 10 = 20 &lt;= 30.\nThe nodes visited are 0 and 3, giving a maximal path quality of 5 + 20 = 25.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex31drawio.png\" style=\"width: 236px; height: 170px;\" />\n<pre>\n<strong>Input:</strong> values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50\n<strong>Output:</strong> 7\n<strong>Explanation:</strong>\nOne possible path is 0 -&gt; 1 -&gt; 3 -&gt; 1 -&gt; 0. The total time taken is 10 + 13 + 13 + 10 = 46 &lt;= 50.\nThe nodes visited are 0, 1, and 3, giving a maximal path quality of 1 + 2 + 4 = 7.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == values.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n\t<li><code>0 &lt;= values[i] &lt;= 10<sup>8</sup></code></li>\n\t<li><code>0 &lt;= edges.length &lt;= 2000</code></li>\n\t<li><code>edges[j].length == 3 </code></li>\n\t<li><code>0 &lt;= u<sub>j </sub>&lt; v<sub>j</sub> &lt;= n - 1</code></li>\n\t<li><code>10 &lt;= time<sub>j</sub>, maxTime &lt;= 100</code></li>\n\t<li>All the pairs <code>[u<sub>j</sub>, v<sub>j</sub>]</code> are <strong>unique</strong>.</li>\n\t<li>There are <strong>at most four</strong> edges connected to each node.</li>\n\t<li>The graph may not be connected.</li>\n</ul>\n",
            "translatedTitle": "最大化一张图中的路径价值",
            "translatedContent": "<p>给你一张 <strong>无向</strong>&nbsp;图，图中有 <code>n</code>&nbsp;个节点，节点编号从 <code>0</code>&nbsp;到 <code>n - 1</code>&nbsp;（<strong>都包括</strong>）。同时给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>values</code>&nbsp;，其中&nbsp;<code>values[i]</code>&nbsp;是第 <code>i</code>&nbsp;个节点的 <strong>价值</strong>&nbsp;。同时给你一个下标从 <strong>0</strong>&nbsp;开始的二维整数数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[j] = [u<sub>j</sub>, v<sub>j</sub>, time<sub>j</sub>]</code>&nbsp;表示节点&nbsp;<code>u<sub>j</sub></code> 和&nbsp;<code>v<sub>j</sub></code>&nbsp;之间有一条需要&nbsp;<code>time<sub>j</sub></code>&nbsp;秒才能通过的无向边。最后，给你一个整数&nbsp;<code>maxTime</code>&nbsp;。</p>\n\n<p><strong>合法路径</strong>&nbsp;指的是图中任意一条从节点&nbsp;<code>0</code>&nbsp;开始，最终回到节点 <code>0</code>&nbsp;，且花费的总时间 <strong>不超过</strong>&nbsp;<code>maxTime</code> 秒的一条路径。你可以访问一个节点任意次。一条合法路径的 <b>价值</b>&nbsp;定义为路径中 <strong>不同节点</strong>&nbsp;的价值 <strong>之和</strong>&nbsp;（每个节点的价值 <strong>至多</strong>&nbsp;算入价值总和中一次）。</p>\n\n<p>请你返回一条合法路径的 <strong>最大</strong>&nbsp;价值。</p>\n\n<p><strong>注意：</strong>每个节点 <strong>至多</strong>&nbsp;有 <strong>四条</strong>&nbsp;边与之相连。</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/2021/10/19/ex1drawio.png\" style=\"width: 269px; height: 170px;\" /></p>\n\n<pre>\n<b>输入：</b>values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49\n<b>输出：</b>75\n<strong>解释：</strong>\n一条可能的路径为：0 -&gt; 1 -&gt; 0 -&gt; 3 -&gt; 0 。总花费时间为 10 + 10 + 10 + 10 = 40 &lt;= 49 。\n访问过的节点为 0 ，1 和 3 ，最大路径价值为 0 + 32 + 43 = 75 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex2drawio.png\" style=\"width: 269px; height: 170px;\" /></p>\n\n<pre>\n<b>输入：</b>values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30\n<b>输出：</b>25\n<strong>解释：</strong>\n一条可能的路径为：0 -&gt; 3 -&gt; 0 。总花费时间为 10 + 10 = 20 &lt;= 30 。\n访问过的节点为 0 和 3 ，最大路径价值为 5 + 20 = 25 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex31drawio.png\" style=\"width: 236px; height: 170px;\" /></p>\n\n<pre>\n<b>输入：</b>values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50\n<b>输出：</b>7\n<strong>解释：</strong>\n一条可能的路径为：0 -&gt; 1 -&gt; 3 -&gt; 1 -&gt; 0 。总花费时间为 10 + 13 + 13 + 10 = 46 &lt;= 50 。\n访问过的节点为 0 ，1 和 3 ，最大路径价值为 1 + 2 + 4 = 7 。</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/21/ex4drawio.png\" style=\"width: 270px; height: 71px;\" /></strong></p>\n\n<pre>\n<b>输入：</b>values = [0,1,2], edges = [[1,2,10]], maxTime = 10\n<b>输出：</b>0\n<b>解释：</b>\n唯一一条路径为 0 。总花费时间为 0 。\n唯一访问过的节点为 0 ，最大路径价值为 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == values.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n\t<li><code>0 &lt;= values[i] &lt;= 10<sup>8</sup></code></li>\n\t<li><code>0 &lt;= edges.length &lt;= 2000</code></li>\n\t<li><code>edges[j].length == 3 </code></li>\n\t<li><code>0 &lt;= u<sub>j </sub>&lt; v<sub>j</sub> &lt;= n - 1</code></li>\n\t<li><code>10 &lt;= time<sub>j</sub>, maxTime &lt;= 100</code></li>\n\t<li><code>[u<sub>j</sub>, v<sub>j</sub>]</code>&nbsp;所有节点对 <strong>互不相同</strong>&nbsp;。</li>\n\t<li>每个节点 <strong>至多有四条&nbsp;</strong>边。</li>\n\t<li>图可能不连通。</li>\n</ul>\n",
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