{ "data": { "question": { "questionId": "3179", "questionFrontendId": "2920", "categoryTitle": "Algorithms", "boundTopicId": 2501670, "title": "Maximum Points After Collecting Coins From All Nodes", "titleSlug": "maximum-points-after-collecting-coins-from-all-nodes", "content": "

There exists an undirected tree rooted at node 0 with n nodes labeled from 0 to n - 1. 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. You are also given a 0-indexed array coins of size n where coins[i] indicates the number of coins in the vertex i, and an integer k.

\n\n

Starting from the root, you have to collect all the coins such that the coins at a node can only be collected if the coins of its ancestors have been already collected.

\n\n

Coins at nodei can be collected in one of the following ways:

\n\n\n\n

Return the maximum points you can get after collecting the coins from all the tree nodes.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: edges = [[0,1],[1,2],[2,3]], coins = [10,10,3,3], k = 5\nOutput: 11                        \nExplanation: \nCollect all the coins from node 0 using the first way. Total points = 10 - 5 = 5.\nCollect all the coins from node 1 using the first way. Total points = 5 + (10 - 5) = 10.\nCollect all the coins from node 2 using the second way so coins left at node 3 will be floor(3 / 2) = 1. Total points = 10 + floor(3 / 2) = 11.\nCollect all the coins from node 3 using the second way. Total points = 11 + floor(1 / 2) = 11.\nIt can be shown that the maximum points we can get after collecting coins from all the nodes is 11. \n
\n\n

Example 2:

\n \"\"\n\n
\nInput: edges = [[0,1],[0,2]], coins = [8,4,4], k = 0\nOutput: 16\nExplanation: \nCoins will be collected from all the nodes using the first way. Therefore, total points = (8 - 0) + (4 - 0) + (4 - 0) = 16.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "收集所有金币可获得的最大积分", "translatedContent": "

有一棵由 n 个节点组成的无向树，以 0  为根节点，节点编号从 0 到 n - 1 。给你一个长度为 n - 1 的二维 整数 数组 edges ，其中 edges[i] = [ai, bi] 表示在树上的节点 ai 和 bi 之间存在一条边。另给你一个下标从 0 开始、长度为 n 的数组 coins 和一个整数 k ，其中 coins[i] 表示节点 i 处的金币数量。

\n\n

从根节点开始，你必须收集所有金币。要想收集节点上的金币，必须先收集该节点的祖先节点上的金币。

\n\n

节点 i 上的金币可以用下述方法之一进行收集：

\n\n\n\n

返回收集 所有 树节点的金币之后可以获得的最大积分。

\n\n

 

\n\n

示例 1：

\n\"\"\n
\n输入：edges = [[0,1],[1,2],[2,3]], coins = [10,10,3,3], k = 5\n输出：11                        \n解释：\n使用第一种方法收集节点 0 上的所有金币。总积分 = 10 - 5 = 5 。\n使用第一种方法收集节点 1 上的所有金币。总积分 = 5 + (10 - 5) = 10 。\n使用第二种方法收集节点 2 上的所有金币。所以节点 3 上的金币将会变为 floor(3 / 2) = 1 ，总积分 = 10 + floor(3 / 2) = 11 。\n使用第二种方法收集节点 3 上的所有金币。总积分 =  11 + floor(1 / 2) = 11.\n可以证明收集所有节点上的金币能获得的最大积分是 11 。 \n
\n\n

示例 2：

\n \"\"\n\n
\n输入：edges = [[0,1],[0,2]], coins = [8,4,4], k = 0\n输出：16\n解释：\n使用第一种方法收集所有节点上的金币，因此，总积分 = (8 - 0) + (4 - 0) + (4 - 0) = 16 。\n
\n\n

 

\n\n

提示：

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(listof exact-integer?) exact-integer? exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximum_points(Edges :: [[integer()]], Coins :: [integer()], K :: integer()) -> integer().\nmaximum_points(Edges, Coins, K) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximum_points(edges :: [[integer]], coins :: [integer], k :: integer) :: integer\n def maximum_points(edges, coins, k) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"2.6K\", \"totalSubmission\": \"6.3K\", \"totalAcceptedRaw\": 2623, \"totalSubmissionRaw\": 6289, \"acRate\": \"41.7%\"}", "hints": [ "Let dp[x][t] be the maximum points we can get from the subtree rooted at node x and the second operation has been used t times in its ancestors.", "Note that the value of each node <= 104, so when t >= 14 dp[x][t] is always 0.", "General equation will be: dp[x][t] = max((coins[x] >> t) - k + sigma(dp[y][t]), (coins[x] >> (t + 1)) + sigma(dp[y][t + 1])) where nodes denoted by y in the sigma, are the direct children of node x." ], "solution": null, "status": null, "sampleTestCase": "[[0,1],[1,2],[2,3]]\n[10,10,3,3]\n5", "metaData": "{\n \"name\": \"maximumPoints\",\n \"params\": [\n {\n \"name\": \"edges\",\n \"type\": \"integer[][]\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"coins\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"k\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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