{ "data": { "question": { "questionId": "3113", "questionFrontendId": "2866", "categoryTitle": "Algorithms", "boundTopicId": 2453609, "title": "Beautiful Towers II", "titleSlug": "beautiful-towers-ii", "content": "

You are given a 0-indexed array maxHeights of n integers.

\n\n

You are tasked with building n towers in the coordinate line. The ith tower is built at coordinate i and has a height of heights[i].

\n\n

A configuration of towers is beautiful if the following conditions hold:

\n\n
    \n\t
  1. 1 <= heights[i] <= maxHeights[i]
    2. \n\t
  2. heights is a mountain array.
    3. \n
\n\n

Array heights is a mountain if there exists an index i such that:

\n\n\n\n

Return the maximum possible sum of heights of a beautiful configuration of towers.

\n\n

 

\n

Example 1:

\n\n
\nInput: maxHeights = [5,3,4,1,1]\nOutput: 13\nExplanation: One beautiful configuration with a maximum sum is heights = [5,3,3,1,1]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]  \n- heights is a mountain of peak i = 0.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 13.
\n\n

Example 2:

\n\n
\nInput: maxHeights = [6,5,3,9,2,7]\nOutput: 22\nExplanation: One beautiful configuration with a maximum sum is heights = [3,3,3,9,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 3.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 22.
\n\n

Example 3:

\n\n
\nInput: maxHeights = [3,2,5,5,2,3]\nOutput: 18\nExplanation: One beautiful configuration with a maximum sum is heights = [2,2,5,5,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 2. \nNote that, for this configuration, i = 3 can also be considered a peak.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 18.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "美丽塔 II", "translatedContent": "

给你一个长度为 n 下标从 0 开始的整数数组 maxHeights 。

\n\n

你的任务是在坐标轴上建 n 座塔。第 i 座塔的下标为 i ，高度为 heights[i] 。

\n\n

如果以下条件满足，我们称这些塔是 美丽 的：

\n\n
    \n\t
  1. 1 <= heights[i] <= maxHeights[i]
    2. \n\t
  2. heights 是一个 山脉 数组。
    3. \n
\n\n

如果存在下标 i 满足以下条件，那么我们称数组 heights 是一个 山脉 数组：

\n\n\n\n

请你返回满足 美丽塔 要求的方案中，高度和的最大值 。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：maxHeights = [5,3,4,1,1]\n输出：13\n解释：和最大的美丽塔方案为 heights = [5,3,3,1,1] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]  \n- heights 是个山脉数组，峰值在 i = 0 处。\n13 是所有美丽塔方案中的最大高度和。
\n\n

示例 2：

\n\n
\n输入：maxHeights = [6,5,3,9,2,7]\n输出：22\n解释： 和最大的美丽塔方案为 heights = [3,3,3,9,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山脉数组，峰值在 i = 3 处。\n22 是所有美丽塔方案中的最大高度和。
\n\n

示例 3：

\n\n
\n输入：maxHeights = [3,2,5,5,2,3]\n输出：18\n解释：和最大的美丽塔方案为 heights = [2,2,5,5,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山脉数组，最大值在 i = 2 处。\n注意，在这个方案中，i = 3 也是一个峰值。\n18 是所有美丽塔方案中的最大高度和。\n
\n\n

 

\n\n

提示：

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\"kotlin\": false, \"dart\": false, \"golang\": false, \"ruby\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"rust\": false, \"racket\": false, \"erlang\": false, \"elixir\": false, \"pythondata\": false, \"react\": false, \"vanillajs\": false, \"postgresql\": false, \"cangjie\": false}", "topicTags": [ { "name": "Stack", "slug": "stack", "translatedName": "栈", "__typename": "TopicTagNode" }, { "name": "Array", "slug": "array", "translatedName": "数组", "__typename": "TopicTagNode" }, { "name": "Monotonic Stack", "slug": "monotonic-stack", "translatedName": "单调栈", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n long long maximumSumOfHeights(vector& maxHeights) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public long maximumSumOfHeights(List maxHeights) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def maximumSumOfHeights(self, maxHeights):\n \"\"\"\n :type maxHeights: List[int]\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def maximumSumOfHeights(self, maxHeights: List[int]) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "long long maximumSumOfHeights(int* maxHeights, int maxHeightsSize) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public long MaximumSumOfHeights(IList maxHeights) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[]} maxHeights\n * @return {number}\n */\nvar maximumSumOfHeights = function(maxHeights) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function maximumSumOfHeights(maxHeights: number[]): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[] $maxHeights\n * @return Integer\n */\n function maximumSumOfHeights($maxHeights) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func maximumSumOfHeights(_ maxHeights: [Int]) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun maximumSumOfHeights(maxHeights: List): Long {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int maximumSumOfHeights(List maxHeights) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func maximumSumOfHeights(maxHeights []int) int64 {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[]} max_heights\n# @return {Integer}\ndef maximum_sum_of_heights(max_heights)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def maximumSumOfHeights(maxHeights: List[Int]): Long = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn maximum_sum_of_heights(max_heights: Vec) -> i64 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (maximum-sum-of-heights maxHeights)\n (-> (listof exact-integer?) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximum_sum_of_heights(MaxHeights :: [integer()]) -> integer().\nmaximum_sum_of_heights(MaxHeights) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximum_sum_of_heights(max_heights :: [integer]) :: integer\n def maximum_sum_of_heights(max_heights) do\n \n end\nend", "__typename": "CodeSnippetNode" }, { "lang": "Cangjie", "langSlug": "cangjie", "code": "class Solution {\n func maximumSumOfHeights(maxHeights: ArrayList): Int64 {\n\n }\n}", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"18.3K\", \"totalSubmission\": \"39.4K\", \"totalAcceptedRaw\": 18309, \"totalSubmissionRaw\": 39447, \"acRate\": \"46.4%\"}", "hints": [ "Try all the possible indices i as the peak.", "Let left[i] be the maximum sum of heights for the prefix 0, …, i when index i is the peak.", "Let right[i] be the maximum sum of heights for suffix i, …, (n - 1) when i is the peak", "Compute values of left[i] from left to right using DP.\r\nFor each i from 0 to n - 1, left[i] = maxHeights * (i - j) + answer[j], where j is the rightmost index to the left of i such that maxHeights[j] < maxHeights[i] .", "For each i from n - 1 to 0, right[i] = maxHeights * (j - i) + answer[j], where j is the leftmost index to the right of i such that maxHeights[j] < maxHeights[i] ." ], "solution": null, "status": null, "sampleTestCase": "[5,3,4,1,1]", "metaData": "{\n \"name\": \"maximumSumOfHeights\",\n \"params\": [\n {\n \"name\": \"maxHeights\",\n \"type\": \"list\"\n }\n ],\n \"return\": {\n \"type\": \"long\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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