leetcode-problemset/leetcode-cn/originData/maximum-score-after-applying-operations-on-a-tree.json

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        "question": {
            "questionId": "3191",
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            "categoryTitle": "Algorithms",
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            "title": "Maximum Score After Applying Operations on a Tree",
            "titleSlug": "maximum-score-after-applying-operations-on-a-tree",
            "content": "<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given&nbsp;a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>\n\n<p>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node.</p>\n\n<p>You start with a score of <code>0</code>. In one operation, you can:</p>\n\n<ul>\n\t<li>Pick any node <code>i</code>.</li>\n\t<li>Add <code>values[i]</code> to your score.</li>\n\t<li>Set <code>values[i]</code> to <code>0</code>.</li>\n</ul>\n\n<p>A tree is <strong>healthy</strong> if the sum of values on the path from the root to any leaf node is different than zero.</p>\n\n<p>Return <em>the <strong>maximum score</strong> you can obtain after performing these operations on the tree any number of times so that it remains <strong>healthy</strong>.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/10/11/graph-13-1.png\" style=\"width: 515px; height: 443px;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1]\n<strong>Output:</strong> 11\n<strong>Explanation:</strong> We can choose nodes 1, 2, 3, 4, and 5. The value of the root is non-zero. Hence, the sum of values on the path from the root to any leaf is different than zero. Therefore, the tree is healthy and the score is values[1] + values[2] + values[3] + values[4] + values[5] = 11.\nIt can be shown that 11 is the maximum score obtainable after any number of operations on the tree.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/10/11/graph-14-2.png\" style=\"width: 522px; height: 245px;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5]\n<strong>Output:</strong> 40\n<strong>Explanation:</strong> We can choose nodes 0, 2, 3, and 4.\n- The sum of values on the path from 0 to 4 is equal to 10.\n- The sum of values on the path from 0 to 3 is equal to 10.\n- The sum of values on the path from 0 to 5 is equal to 3.\n- The sum of values on the path from 0 to 6 is equal to 5.\nTherefore, the tree is healthy and the score is values[0] + values[2] + values[3] + values[4] = 40.\nIt can be shown that 40 is the maximum score obtainable after any number of operations on the tree.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>values.length == n</code></li>\n\t<li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li>\n\t<li>The input is generated such that <code>edges</code> represents a valid tree.</li>\n</ul>\n",
            "translatedTitle": "在树上执行操作以后得到的最大分数",
            "translatedContent": "<p>有一棵 <code>n</code>&nbsp;个节点的无向树，节点编号为 <code>0</code>&nbsp;到 <code>n - 1</code>&nbsp;，根节点编号为 <code>0</code>&nbsp;。给你一个长度为 <code>n - 1</code>&nbsp;的二维整数数组&nbsp;<code>edges</code>&nbsp;表示这棵树，其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示树中节点&nbsp;<code>a<sub>i</sub></code>&nbsp;和&nbsp;<code>b<sub>i</sub></code>&nbsp;有一条边。</p>\n\n<p>同时给你一个长度为 <code>n</code>&nbsp;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;表示第 <code>i</code>&nbsp;个节点的值。</p>\n\n<p>一开始你的分数为 <code>0</code>&nbsp;，每次操作中，你将执行：</p>\n\n<ul>\n\t<li>选择节点&nbsp;<code>i</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>values[i]</code>&nbsp;加入你的分数。</li>\n\t<li>将&nbsp;<code>values[i]</code>&nbsp;变为&nbsp;<code>0</code>&nbsp;。</li>\n</ul>\n\n<p>如果从根节点出发，到任意叶子节点经过的路径上的节点值之和都不等于 0 ，那么我们称这棵树是 <strong>健康的</strong>&nbsp;。</p>\n\n<p>你可以对这棵树执行任意次操作，但要求执行完所有操作以后树是&nbsp;<strong>健康的</strong>&nbsp;，请你返回你可以获得的 <strong>最大分数</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/10/11/graph-13-1.png\" style=\"width: 515px; height: 443px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1]\n<b>输出：</b>11\n<b>解释：</b>我们可以选择节点 1 ，2 ，3 ，4 和 5 。根节点的值是非 0 的。所以从根出发到任意叶子节点路径上节点值之和都不为 0 。所以树是健康的。你的得分之和为 values[1] + values[2] + values[3] + values[4] + values[5] = 11 。\n11 是你对树执行任意次操作以后可以获得的最大得分之和。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/10/11/graph-14-2.png\" style=\"width: 522px; height: 245px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5]\n<b>输出：</b>40\n<b>解释：</b>我们选择节点 0 ，2 ，3 和 4 。\n- 从 0 到 4 的节点值之和为 10 。\n- 从 0 到 3 的节点值之和为 10 。\n- 从 0 到 5 的节点值之和为 3 。\n- 从 0 到 6 的节点值之和为 5 。\n所以树是健康的。你的得分之和为 values[0] + values[2] + values[3] + values[4] = 40 。\n40 是你对树执行任意次操作以后可以获得的最大得分之和。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>values.length == n</code></li>\n\t<li><code>1 &lt;= values[i] &lt;= 10<sup>9</sup></code></li>\n\t<li>输入保证&nbsp;<code>edges</code>&nbsp;构成一棵合法的树。</li>\n</ul>\n",
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                "Let <code>dp[i]</code> be the maximum score we can get on the subtree rooted at <code>i</code> and <code>sum[i]</code> be the sum of all the values of the subtree rooted at <code>i</code>.",
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