{ "data": { "question": { "questionId": "3191", "questionFrontendId": "2925", "categoryTitle": "Algorithms", "boundTopicId": 2510617, "title": "Maximum Score After Applying Operations on a Tree", "titleSlug": "maximum-score-after-applying-operations-on-a-tree", "content": "

There is an undirected tree with n nodes labeled from 0 to n - 1, and rooted at node 0. You are given a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.

\n\n

You are also given a 0-indexed integer array values of length n, where values[i] is the value associated with the ith node.

\n\n

You start with a score of 0. In one operation, you can:

\n\n\n\n

A tree is healthy if the sum of values on the path from the root to any leaf node is different than zero.

\n\n

Return the maximum score you can obtain after performing these operations on the tree any number of times so that it remains healthy.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1]\nOutput: 11\nExplanation: 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
\n\n

Example 2:

\n\"\"\n
\nInput: edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5]\nOutput: 40\nExplanation: 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
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "在树上执行操作以后得到的最大分数", "translatedContent": "

有一棵 n 个节点的无向树，节点编号为 0 到 n - 1 ，根节点编号为 0 。给你一个长度为 n - 1 的二维整数数组 edges 表示这棵树，其中 edges[i] = [ai, bi] 表示树中节点 ai 和 bi 有一条边。

\n\n

同时给你一个长度为 n 下标从 0 开始的整数数组 values ，其中 values[i] 表示第 i 个节点的值。

\n\n

一开始你的分数为 0 ，每次操作中，你将执行：

\n\n\n\n

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 健康的 。

\n\n

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 健康的 ，请你返回你可以获得的 最大分数 。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1]\n输出：11\n解释：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
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5]\n输出：40\n解释：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
\n\n

 

\n\n

提示：

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(listof exact-integer?) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximum_score_after_operations(Edges :: [[integer()]], Values :: [integer()]) -> integer().\nmaximum_score_after_operations(Edges, Values) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximum_score_after_operations(edges :: [[integer]], values :: [integer]) :: integer\n def maximum_score_after_operations(edges, values) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"3.7K\", \"totalSubmission\": \"7.9K\", \"totalAcceptedRaw\": 3696, \"totalSubmissionRaw\": 7906, \"acRate\": \"46.7%\"}", "hints": [ "Let dp[i] be the maximum score we can get on the subtree rooted at i and sum[i] be the sum of all the values of the subtree rooted at i.", "If we don’t take value[i] into the final score, we can take all the nodes of the subtrees rooted at i’s children.", "If we take value[i] into the score, then each subtree rooted at its children should satisfy the constraints.", "dp[x] = max(value[x] + sigma(dp[y]), sigma(sum[y])), where y is a direct child of x." ], "solution": null, "status": null, "sampleTestCase": "[[0,1],[0,2],[0,3],[2,4],[4,5]]\n[5,2,5,2,1,1]", "metaData": "{\n \"name\": \"maximumScoreAfterOperations\",\n \"params\": [\n {\n \"name\": \"edges\",\n \"type\": \"integer[][]\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"values\"\n }\n ],\n \"return\": {\n \"type\": \"long\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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            "exampleTestcases": "[[0,1],[0,2],[0,3],[2,4],[4,5]]\n[5,2,5,2,1,1]\n[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]\n[20,10,9,7,4,3,5]",
            "__typename": "QuestionNode"
        }
    }
}