{ "data": { "question": { "questionId": "3191", "questionFrontendId": "2925", "boundTopicId": null, "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.

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

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

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

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

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Example 1:

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\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
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Example 2:

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\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
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Constraints:

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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\": \"9.8K\", \"totalSubmission\": \"20.5K\", \"totalAcceptedRaw\": 9842, \"totalSubmissionRaw\": 20524, \"acRate\": \"48.0%\"}", "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, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"

Compiled with clang 11 using the latest C++ 20 standard.

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Most standard library headers are already included automatically for your convenience.

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OpenJDK 17. Java 8 features such as lambda expressions and stream API can be used.

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Python 2.7.12.

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C# 10 with .NET 6 runtime

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Node.js 16.13.2.

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Ruby 3.1

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Python 3.10.

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