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55 lines
3.6 KiB
HTML
<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>
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<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>
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<p>Return <em>the <strong>maximum</strong> quality of a valid path</em>.</p>
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<p><strong>Note:</strong> There are <strong>at most four</strong> edges connected to each node.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/10/19/ex1drawio.png" style="width: 269px; height: 170px;" />
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<pre>
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<strong>Input:</strong> values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49
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<strong>Output:</strong> 75
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<strong>Explanation:</strong>
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One possible path is 0 -> 1 -> 0 -> 3 -> 0. The total time taken is 10 + 10 + 10 + 10 = 40 <= 49.
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The nodes visited are 0, 1, and 3, giving a maximal path quality of 0 + 32 + 43 = 75.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/10/19/ex2drawio.png" style="width: 269px; height: 170px;" />
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<pre>
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<strong>Input:</strong> values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30
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<strong>Output:</strong> 25
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<strong>Explanation:</strong>
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One possible path is 0 -> 3 -> 0. The total time taken is 10 + 10 = 20 <= 30.
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The nodes visited are 0 and 3, giving a maximal path quality of 5 + 20 = 25.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/10/19/ex31drawio.png" style="width: 236px; height: 170px;" />
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<pre>
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<strong>Input:</strong> values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50
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<strong>Output:</strong> 7
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<strong>Explanation:</strong>
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One possible path is 0 -> 1 -> 3 -> 1 -> 0. The total time taken is 10 + 13 + 13 + 10 = 46 <= 50.
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The nodes visited are 0, 1, and 3, giving a maximal path quality of 1 + 2 + 4 = 7.
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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>n == values.length</code></li>
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<li><code>1 <= n <= 1000</code></li>
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<li><code>0 <= values[i] <= 10<sup>8</sup></code></li>
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<li><code>0 <= edges.length <= 2000</code></li>
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<li><code>edges[j].length == 3 </code></li>
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<li><code>0 <= u<sub>j </sub>< v<sub>j</sub> <= n - 1</code></li>
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<li><code>10 <= time<sub>j</sub>, maxTime <= 100</code></li>
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<li>All the pairs <code>[u<sub>j</sub>, v<sub>j</sub>]</code> are <strong>unique</strong>.</li>
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<li>There are <strong>at most four</strong> edges connected to each node.</li>
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<li>The graph may not be connected.</li>
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</ul>
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