{ "data": { "question": { "questionId": "3114", "questionFrontendId": "2865", "categoryTitle": "Algorithms", "boundTopicId": 2453610, "title": "Beautiful Towers I", "titleSlug": "beautiful-towers-i", "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 I", "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 山状 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 山状 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 是个山状数组，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 是个山状数组，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 是个山状数组，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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