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{
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"question": {
"questionId": "1121",
"questionFrontendId": "1043",
"categoryTitle": "Algorithms",
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"title": "Partition Array for Maximum Sum",
"titleSlug": "partition-array-for-maximum-sum",
"content": "<p>Given an integer array <code>arr</code>, partition the array into (contiguous) subarrays of length <strong>at most</strong> <code>k</code>. After partitioning, each subarray has their values changed to become the maximum value of that subarray.</p>\n\n<p>Return <em>the largest sum of the given array after partitioning. Test cases are generated so that the answer fits in a <strong>32-bit</strong> integer.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,15,7,9,2,5,10], k = 3\n<strong>Output:</strong> 84\n<strong>Explanation:</strong> arr becomes [15,15,15,9,10,10,10]\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,4,1,5,7,3,6,1,9,9,3], k = 4\n<strong>Output:</strong> 83\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1], k = 1\n<strong>Output:</strong> 1\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr.length &lt;= 500</code></li>\n\t<li><code>0 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= arr.length</code></li>\n</ul>\n",
"translatedTitle": "分隔数组以得到最大和",
"translatedContent": "<p>给你一个整数数组 <code>arr</code>,请你将该数组分隔为长度 <strong>最多 </strong>为 k 的一些(连续)子数组。分隔完成后,每个子数组的中的所有值都会变为该子数组中的最大值。</p>\n\n<p>返回将数组分隔变换后能够得到的元素最大和。本题所用到的测试用例会确保答案是一个 32 位整数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>arr = [1,15,7,9,2,5,10], k = 3\n<strong>输出:</strong>84\n<strong>解释:</strong>数组变为 [15,15,15,9,10,10,10]</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>arr = [1,4,1,5,7,3,6,1,9,9,3], k = 4\n<strong>输出:</strong>83\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>arr = [1], k = 1\n<strong>输出:</strong>1\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr.length &lt;= 500</code></li>\n\t<li><code>0 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= arr.length</code></li>\n</ul>\n",
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"Think dynamic programming: dp[i] will be the answer for array A[0], ..., A[i-1].",
"For j = 1 .. k that keeps everything in bounds, dp[i] is the maximum of dp[i-j] + max(A[i-1], ..., A[i-j]) * j ."
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