Class Solution
java.lang.Object
g2401_2500.s2421_number_of_good_paths.Solution
2421 - Number of Good Paths.<p>Hard</p>
<p>There is a tree (i.e. a connected, undirected graph with no cycles) consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> and exactly <code>n - 1</code> edges.</p>
<p>You are given a <strong>0-indexed</strong> integer array <code>vals</code> of length <code>n</code> where <code>vals[i]</code> denotes the value of the <code>i<sup>th</sup></code> node. You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>
<p>A <strong>good path</strong> is a simple path that satisfies the following conditions:</p>
<ol>
<li>The starting node and the ending node have the <strong>same</strong> value.</li>
<li>All nodes between the starting node and the ending node have values <strong>less than or equal to</strong> the starting node (i.e. the starting node’s value should be the maximum value along the path).</li>
</ol>
<p>Return <em>the number of distinct good paths</em>.</p>
<p>Note that a path and its reverse are counted as the <strong>same</strong> path. For example, <code>0 -> 1</code> is considered to be the same as <code>1 -> 0</code>. A single node is also considered as a valid path.</p>
<p><strong>Example 1:</strong></p>
<p><img src="https://assets.leetcode.com/uploads/2022/08/04/f9caaac15b383af9115c5586779dec5.png" alt="" /></p>
<p><strong>Input:</strong> vals = [1,3,2,1,3], edges = [[0,1],[0,2],[2,3],[2,4]]</p>
<p><strong>Output:</strong> 6</p>
<p><strong>Explanation:</strong> There are 5 good paths consisting of a single node.</p>
<p>There is 1 additional good path: 1 -> 0 -> 2 -> 4.</p>
<p>(The reverse path 4 -> 2 -> 0 -> 1 is treated as the same as 1 -> 0 -> 2 -> 4.)</p>
<p>Note that 0 -> 2 -> 3 is not a good path because vals[2] > vals[0].</p>
<p><strong>Example 2:</strong></p>
<p><img src="https://assets.leetcode.com/uploads/2022/08/04/149d3065ec165a71a1b9aec890776ff.png" alt="" /></p>
<p><strong>Input:</strong> vals = [1,1,2,2,3], edges = [[0,1],[1,2],[2,3],[2,4]]</p>
<p><strong>Output:</strong> 7</p>
<p><strong>Explanation:</strong> There are 5 good paths consisting of a single node.</p>
<p>There are 2 additional good paths: 0 -> 1 and 2 -> 3.</p>
<p><strong>Example 3:</strong></p>
<p><img src="https://assets.leetcode.com/uploads/2022/08/04/31705e22af3d9c0a557459bc7d1b62d.png" alt="" /></p>
<p><strong>Input:</strong> vals = [1], edges = []</p>
<p><strong>Output:</strong> 1</p>
<p><strong>Explanation:</strong> The tree consists of only one node, so there is one good path.</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>n == vals.length</code></li>
<li><code>1 <= n <= 3 * 10<sup>4</sup></code></li>
<li><code>0 <= vals[i] <= 10<sup>5</sup></code></li>
<li><code>edges.length == n - 1</code></li>
<li><code>edges[i].length == 2</code></li>
<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> < n</code></li>
<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
<li><code>edges</code> represents a valid tree.</li>
</ul>
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Constructor Summary
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Solution
public Solution()
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Method Details
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numberOfGoodPaths
public int numberOfGoodPaths(int[] vals, int[][] edges)
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