Class Solution
java.lang.Object
g2001_2100.s2065_maximum_path_quality_of_a_graph.Solution
2065 - Maximum Path Quality of a Graph.<p>Hard</p>
<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>, 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>
<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>
<p>Return <em>the <strong>maximum</strong> quality of a valid path</em>.</p>
<p><strong>Note:</strong> There are <strong>at most four</strong> edges connected to each node.</p>
<p><strong>Example 1:</strong></p>
<p><img src="https://assets.leetcode.com/uploads/2021/10/19/ex1drawio.png" alt="" /></p>
<p><strong>Input:</strong> values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49</p>
<p><strong>Output:</strong> 75</p>
<p><strong>Explanation:</strong></p>
<p>One possible path is 0 -> 1 -> 0 -> 3 -> 0.</p>
<p>The total time taken is 10 + 10 + 10 + 10 = 40 <= 49.</p>
<p>The nodes visited are 0, 1, and 3, giving a maximal path quality of 0 + 32 + 43 = 75.</p>
<p><strong>Example 2:</strong></p>
<p><img src="https://assets.leetcode.com/uploads/2021/10/19/ex2drawio.png" alt="" /></p>
<p><strong>Input:</strong> values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30</p>
<p><strong>Output:</strong> 25</p>
<p><strong>Explanation:</strong></p>
<p>One possible path is 0 -> 3 -> 0.</p>
<p>The total time taken is 10 + 10 = 20 <= 30.</p>
<p>The nodes visited are 0 and 3, giving a maximal path quality of 5 + 20 = 25.</p>
<p><strong>Example 3:</strong></p>
<p><img src="https://assets.leetcode.com/uploads/2021/10/19/ex31drawio.png" alt="" /></p>
<p><strong>Input:</strong> values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50</p>
<p><strong>Output:</strong> 7</p>
<p><strong>Explanation:</strong></p>
<p>One possible path is 0 -> 1 -> 3 -> 1 -> 0.</p>
<p>The total time taken is 10 + 13 + 13 + 10 = 46 <= 50.</p>
<p>The nodes visited are 0, 1, and 3, giving a maximal path quality of 1 + 2 + 4 = 7.</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>n == values.length</code></li>
<li><code>1 <= n <= 1000</code></li>
<li><code>0 <= values[i] <= 10<sup>8</sup></code></li>
<li><code>0 <= edges.length <= 2000</code></li>
<li><code>edges[j].length == 3</code></li>
<li><code>0 <= u<sub>j</sub> < v<sub>j</sub> <= n - 1</code></li>
<li><code>10 <= time<sub>j</sub>, maxTime <= 100</code></li>
<li>All the pairs <code>[u<sub>j</sub>, v<sub>j</sub>]</code> are <strong>unique</strong>.</li>
<li>There are <strong>at most four</strong> edges connected to each node.</li>
<li>The graph may not be connected.</li>
</ul>
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Constructor Summary
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Method Summary
Modifier and TypeMethodDescriptionintmaximalPathQuality(int[] values, int[][] edges, int maxTime)
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Solution
public Solution()
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Method Details
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maximalPathQuality
public int maximalPathQuality(int[] values, int[][] edges, int maxTime)
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