mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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174 lines
19 KiB
JSON
174 lines
19 KiB
JSON
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"title": "Maximum Path Quality of a Graph",
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"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'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> </p>\n<p><strong>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 -> 1 -> 0 -> 3 -> 0. The total time taken is 10 + 10 + 10 + 10 = 40 <= 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>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 -> 3 -> 0. The total time taken is 10 + 10 = 20 <= 30.\nThe nodes visited are 0 and 3, giving a maximal path quality of 5 + 20 = 25.\n</pre>\n\n<p><strong>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 -> 1 -> 3 -> 1 -> 0. The total time taken is 10 + 13 + 13 + 10 = 46 <= 50.\nThe nodes visited are 0, 1, and 3, giving a maximal path quality of 1 + 2 + 4 = 7.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == values.length</code></li>\n\t<li><code>1 <= n <= 1000</code></li>\n\t<li><code>0 <= values[i] <= 10<sup>8</sup></code></li>\n\t<li><code>0 <= edges.length <= 2000</code></li>\n\t<li><code>edges[j].length == 3 </code></li>\n\t<li><code>0 <= u<sub>j </sub>< v<sub>j</sub> <= n - 1</code></li>\n\t<li><code>10 <= time<sub>j</sub>, maxTime <= 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",
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