{ "data": { "question": { "questionId": "2627", "questionFrontendId": "2538", "categoryTitle": "Algorithms", "boundTopicId": 2060313, "title": "Difference Between Maximum and Minimum Price Sum", "titleSlug": "difference-between-maximum-and-minimum-price-sum", "content": "

There exists an undirected and initially unrooted tree with n nodes indexed from 0 to n - 1. You are given the integer n and 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

Each node has an associated price. You are given an integer array price, where price[i] is the price of the ith node.

\n\n

The price sum of a given path is the sum of the prices of all nodes lying on that path.

\n\n

The tree can be rooted at any node root of your choice. The incurred cost after choosing root is the difference between the maximum and minimum price sum amongst all paths starting at root.

\n\n

Return the maximum possible cost amongst all possible root choices.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 6, edges = [[0,1],[1,2],[1,3],[3,4],[3,5]], price = [9,8,7,6,10,5]\nOutput: 24\nExplanation: The diagram above denotes the tree after rooting it at node 2. The first part (colored in red) shows the path with the maximum price sum. The second part (colored in blue) shows the path with the minimum price sum.\n- The first path contains nodes [2,1,3,4]: the prices are [7,8,6,10], and the sum of the prices is 31.\n- The second path contains the node [2] with the price [7].\nThe difference between the maximum and minimum price sum is 24. It can be proved that 24 is the maximum cost.\n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 3, edges = [[0,1],[1,2]], price = [1,1,1]\nOutput: 2\nExplanation: The diagram above denotes the tree after rooting it at node 0. The first part (colored in red) shows the path with the maximum price sum. The second part (colored in blue) shows the path with the minimum price sum.\n- The first path contains nodes [0,1,2]: the prices are [1,1,1], and the sum of the prices is 3.\n- The second path contains node [0] with a price [1].\nThe difference between the maximum and minimum price sum is 2. It can be proved that 2 is the maximum cost.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "最大价值和与最小价值和的差值", "translatedContent": "

给你一个 n 个节点的无向无根图，节点编号为 0 到 n - 1 。给你一个整数 n 和一个长度为 n - 1 的二维整数数组 edges ，其中 edges[i] = [ai, bi] 表示树中节点 ai 和 bi 之间有一条边。

\n\n

每个节点都有一个价值。给你一个整数数组 price ，其中 price[i] 是第 i 个节点的价值。

\n\n

一条路径的 价值和 是这条路径上所有节点的价值之和。

\n\n

你可以选择树中任意一个节点作为根节点 root 。选择 root 为根的 开销 是以 root 为起点的所有路径中，价值和 最大的一条路径与最小的一条路径的差值。

\n\n

请你返回所有节点作为根节点的选择中，最大 的 开销 为多少。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：n = 6, edges = [[0,1],[1,2],[1,3],[3,4],[3,5]], price = [9,8,7,6,10,5]\n输出：24\n解释：上图展示了以节点 2 为根的树。左图（红色的节点）是最大价值和路径，右图（蓝色的节点）是最小价值和路径。\n- 第一条路径节点为 [2,1,3,4]：价值为 [7,8,6,10] ，价值和为 31 。\n- 第二条路径节点为 [2] ，价值为 [7] 。\n最大路径和与最小路径和的差值为 24 。24 是所有方案中的最大开销。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：n = 3, edges = [[0,1],[1,2]], price = [1,1,1]\n输出：2\n解释：上图展示了以节点 0 为根的树。左图（红色的节点）是最大价值和路径，右图（蓝色的节点）是最小价值和路径。\n- 第一条路径包含节点 [0,1,2]：价值为 [1,1,1] ，价值和为 3 。\n- 第二条路径节点为 [0] ，价值为 [1] 。\n最大路径和与最小路径和的差值为 2 。2 是所有方案中的最大开销。\n
\n\n

 

\n\n

提示：

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(listof (listof exact-integer?)) (listof exact-integer?) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec max_output(N :: integer(), Edges :: [[integer()]], Price :: [integer()]) -> integer().\nmax_output(N, Edges, Price) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec max_output(n :: integer, edges :: [[integer]], price :: [integer]) :: integer\n def max_output(n, edges, price) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"3.7K\", \"totalSubmission\": \"7.5K\", \"totalAcceptedRaw\": 3653, \"totalSubmissionRaw\": 7537, \"acRate\": \"48.5%\"}", "hints": [ "The minimum price sum is always the price of a rooted node.", "Let’s root the tree at vertex 0 and find the answer from this perspective.", "In the optimal answer maximum price is the sum of the prices of nodes on the path from “u” to “v” where either “u” or “v” is the parent of the second one or neither is a parent of the second one.", "The first case is easy to find. For the second case, notice that in the optimal path, “u” and “v” are both leaves. Then we can use dynamic programming to find such a path.", "Let DP(v,1) denote “the maximum price sum from node v to leaf, where v is a parent of that leaf” and let DP(v,0) denote “the maximum price sum from node v to leaf, where v is a parent of that leaf - price[leaf]”. Then the answer is maximum of DP(u,0) + DP(v,1) + price[parent] where u, v are directly connected to vertex “parent”." ], "solution": null, "status": null, "sampleTestCase": "6\n[[0,1],[1,2],[1,3],[3,4],[3,5]]\n[9,8,7,6,10,5]", "metaData": "{\n \"name\": \"maxOutput\",\n \"params\": [\n {\n \"name\": \"n\",\n \"type\": \"integer\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"edges\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"price\"\n }\n ],\n \"return\": {\n \"type\": \"long\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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            "book": null,
            "isSubscribed": false,
            "isDailyQuestion": false,
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            "editorType": "CKEDITOR",
            "ugcQuestionId": null,
            "style": "LEETCODE",
            "exampleTestcases": "6\n[[0,1],[1,2],[1,3],[3,4],[3,5]]\n[9,8,7,6,10,5]\n3\n[[0,1],[1,2]]\n[1,1,1]",
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}