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

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

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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].

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

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    \n\t
  1. 1 <= heights[i] <= maxHeights[i]
    2. \n\t
  2. heights is a mountain array.
    3. \n
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Array heights is a mountain if there exists an index i such that:

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

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Example 1:

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\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.
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Example 2:

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\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.
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Example 3:

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\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
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Constraints:

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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, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"

Compiled with clang 11 using the latest C++ 20 standard.

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Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

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Most standard library headers are already included automatically for your convenience.

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OpenJDK 17. Java 8 features such as lambda expressions and stream API can be used.

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Most standard library headers are already included automatically for your convenience.

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Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

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Python 2.7.12.

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Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

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For Map/TreeMap data structure, you may use sortedcontainers library.

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Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

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Compiled with gcc 8.2 using the gnu11 standard.

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Your code is compiled with level one optimization (-O1). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

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Most standard library headers are already included automatically for your convenience.

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For hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:

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1. Adding an item to a hash.\\r\\n

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\\r\\n\\r\\n

3. Deleting an item in a hash:\\r\\n

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C# 10 with .NET 6 runtime

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Node.js 16.13.2.

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Your code is run with --harmony flag, enabling new ES6 features.

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lodash.js library is included by default.

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For Priority Queue / Queue data structures, you may use 5.3.0 version of datastructures-js/priority-queue and 4.2.1 version of datastructures-js/queue.

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Ruby 3.1

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Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

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Swift 5.5.2.

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Go 1.21

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Support https://godoc.org/github.com/emirpasic/gods@v1.18.1 library.

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Python 3.10.

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Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

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For Map/TreeMap data structure, you may use sortedcontainers library.

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Scala 2.13.7.

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Kotlin 1.9.0.

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Rust 1.58.1

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PHP 8.1.

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With bcmath module

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TypeScript 5.1.6, Node.js 16.13.2.

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Run with Racket 8.3.

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Dart 2.17.3

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