{ "id": 3113, "name": "beautiful_towers_ii", "difficulty": "Medium", "link": "https://leetcode.com/problems/beautiful-towers-ii/", "date": "2023-09-17 00:00:00", "task_description": "You are given a **0-indexed** array `maxHeights` of `n` integers. 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]`. A configuration of towers is **beautiful** if the following conditions hold: `1 <= heights[i] <= maxHeights[i]` `heights` is a **mountain** array. Array `heights` is a **mountain** if there exists an index `i` such that: For all `0 < j <= i`, `heights[j - 1] <= heights[j]` For all `i <= k < n - 1`, `heights[k + 1] <= heights[k]` Return _the **maximum possible sum of heights** of a beautiful configuration of towers_. **Example 1:** ``` **Input:** maxHeights = [5,3,4,1,1] **Output:** 13 **Explanation:** One beautiful configuration with a maximum sum is heights = [5,3,3,1,1]. This configuration is beautiful since: - 1 <= heights[i] <= maxHeights[i] - heights is a mountain of peak i = 0. It can be shown that there exists no other beautiful configuration with a sum of heights greater than 13. ``` **Example 2:** ``` **Input:** maxHeights = [6,5,3,9,2,7] **Output:** 22 **Explanation:** One beautiful configuration with a maximum sum is heights = [3,3,3,9,2,2]. This configuration is beautiful since: - 1 <= heights[i] <= maxHeights[i] - heights is a mountain of peak i = 3. It can be shown that there exists no other beautiful configuration with a sum of heights greater than 22. ``` **Example 3:** ``` **Input:** maxHeights = [3,2,5,5,2,3] **Output:** 18 **Explanation:** One beautiful configuration with a maximum sum is heights = [2,2,5,5,2,2]. This configuration is beautiful since: - 1 <= heights[i] <= maxHeights[i] - heights is a mountain of peak i = 2. Note that, for this configuration, i = 3 can also be considered a peak. It can be shown that there exists no other beautiful configuration with a sum of heights greater than 18. ``` **Constraints:** `1 <= n == maxHeights.length <= 105` `1 <= maxHeights[i] <= 109`", "public_test_cases": [ { "label": "Example 1", "input": "maxHeights = [5,3,4,1,1]", "output": "13 " }, { "label": "Example 2", "input": "maxHeights = [6,5,3,9,2,7]", "output": "22 " }, { "label": "Example 3", "input": "maxHeights = [3,2,5,5,2,3]", "output": "18 " } ], "private_test_cases": [ { "input": [ 818285741, 607617451, 735866601, 598930260, 899460492, 2660828, 681419595, 382919309, 242080287, 388065900, 323211807, 956267513, 677700970, 520928405, 346173939, 837978437, 248064270, 111712576, 527845439, 427290128, 112497440, 415269802, 44851045, 945931176, 224293580, 493570801, 181595623, 279427297, 974284345, 361915861, 557846220, 573073192, 662548241, 866043187, 746404240, 263643381, 109799700, 209982734, 476993083, 657520904, 958025636, 904357542, 950624906, 908851112, 79870897, 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505992223, 635761320, 684357911, 125395844, 111263078, 671244820, 402538388, 973016017, 123092347, 399125997, 50576533, 492396847, 484952488, 207093741 ], "output": 36941689946 } ], "haskell_template": "maximumSumOfHeights :: [Int] -> Int\nmaximumSumOfHeights maxHeights ", "ocaml_template": "let maximumSumOfHeights (maxHeights: int list) : int = ", "scala_template": "def maximumSumOfHeights(maxHeights: List[Int]): Int = { \n \n}", "java_template": "class Solution {\n public long maximumSumOfHeights(List maxHeights) {\n \n }\n}", "python_template": "class Solution(object):\n def maximumSumOfHeights(self, maxHeights):\n \"\"\"\n :type maxHeights: List[int]\n :rtype: int\n \"\"\"\n " }