leetcode-problemset/leetcode-cn/originData/make-k-subarray-sums-equal.json

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            "title": "Make K-Subarray Sums Equal",
            "titleSlug": "make-k-subarray-sums-equal",
            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>arr</code> and an integer <code>k</code>. The array <code>arr</code> is circular. In other words, the first element of the array is the next element of the last element, and the last element of the array is the previous element of the first element.</p>\n\n<p>You can do the following operation any number of times:</p>\n\n<ul>\n\t<li>Pick any element from <code>arr</code> and increase or decrease it by <code>1</code>.</li>\n</ul>\n\n<p>Return <em>the minimum number of operations such that the sum of each <strong>subarray</strong> of length </em><code>k</code><em> is equal</em>.</p>\n\n<p>A <strong>subarray</strong> is a contiguous part of the array.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,4,1,3], k = 2\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> we can do one operation on index 1 to make its value equal to 3.\nThe array after the operation is [1,3,1,3]\n- Subarray starts at index 0 is [1, 3], and its sum is 4 \n- Subarray starts at index 1 is [3, 1], and its sum is 4 \n- Subarray starts at index 2 is [1, 3], and its sum is 4 \n- Subarray starts at index 3 is [3, 1], and its sum is 4 \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [2,5,5,7], k = 3\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> we can do three operations on index 0 to make its value equal to 5 and two operations on index 3 to make its value equal to 5.\nThe array after the operations is [5,5,5,5]\n- Subarray starts at index 0 is [5, 5, 5], and its sum is 15\n- Subarray starts at index 1 is [5, 5, 5], and its sum is 15\n- Subarray starts at index 2 is [5, 5, 5], and its sum is 15\n- Subarray starts at index 3 is [5, 5, 5], and its sum is 15 \n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= arr.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "使子数组元素和相等",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的整数数组 <code>arr</code> 和一个整数 <code>k</code> 。数组 <code>arr</code> 是一个循环数组。换句话说，数组中的最后一个元素的下一个元素是数组中的第一个元素，数组中第一个元素的前一个元素是数组中的最后一个元素。</p>\n\n<p>你可以执行下述运算任意次：</p>\n\n<ul>\n\t<li>选中 <code>arr</code> 中任意一个元素，并使其值加上 <code>1</code> 或减去 <code>1</code> 。</li>\n</ul>\n\n<p>执行运算使每个长度为 <code>k</code> 的 <strong>子数组</strong> 的元素总和都相等，返回所需要的最少运算次数。</p>\n\n<p><strong>子数组</strong> 是数组的一个连续部分。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>arr = [1,4,1,3], k = 2\n<strong>输出：</strong>1\n<strong>解释：</strong>在下标为 1 的元素那里执行一次运算，使其等于 3 。\n执行运算后，数组变为 [1,3,1,3] 。\n- 0 处起始的子数组为 [1, 3] ，元素总和为 4 \n- 1 处起始的子数组为 [3, 1] ，元素总和为 4 \n- 2 处起始的子数组为 [1, 3] ，元素总和为 4 \n- 3 处起始的子数组为 [3, 1] ，元素总和为 4 \n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>arr = [2,5,5,7], k = 3\n<strong>输出：</strong>5\n<strong>解释：</strong>在下标为 0 的元素那里执行三次运算，使其等于 5 。在下标为 3 的元素那里执行两次运算，使其等于 5 。\n执行运算后，数组变为 [5,5,5,5] 。\n- 0 处起始的子数组为 [5, 5, 5] ，元素总和为 15\n- 1 处起始的子数组为 [5, 5, 5] ，元素总和为 15\n- 2 处起始的子数组为 [5, 5, 5] ，元素总和为 15\n- 3 处起始的子数组为 [5, 5, 5] ，元素总和为 15\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k &lt;= arr.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "Think about gcd(n, k). How will it help to calculate the answer?",
                "indices i and j are in the same group if gcd(n, k) mod i = gcd(n, k) mod j. Each group should have equal elements. Think about the minimum number of operations for each group",
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