{ "data": { "question": { "questionId": "1946", "questionFrontendId": "1818", "categoryTitle": "Algorithms", "boundTopicId": 694937, "title": "Minimum Absolute Sum Difference", "titleSlug": "minimum-absolute-sum-difference", "content": "

You are given two positive integer arrays nums1 and nums2, both of length n.

\n\n

The absolute sum difference of arrays nums1 and nums2 is defined as the sum of |nums1[i] - nums2[i]| for each 0 <= i < n (0-indexed).

\n\n

You can replace at most one element of nums1 with any other element in nums1 to minimize the absolute sum difference.

\n\n

Return the minimum absolute sum difference after replacing at most one element in the array nums1. Since the answer may be large, return it modulo 109 + 7.

\n\n

|x| is defined as:

\n\n\n\n

 

\n

Example 1:

\n\n
\nInput: nums1 = [1,7,5], nums2 = [2,3,5]\nOutput: 3\nExplanation: There are two possible optimal solutions:\n- Replace the second element with the first: [1,7,5] => [1,1,5], or\n- Replace the second element with the third: [1,7,5] => [1,5,5].\nBoth will yield an absolute sum difference of |1-2| + (|1-3| or |5-3|) + |5-5| = 3.\n
\n\n

Example 2:

\n\n
\nInput: nums1 = [2,4,6,8,10], nums2 = [2,4,6,8,10]\nOutput: 0\nExplanation: nums1 is equal to nums2 so no replacement is needed. This will result in an \nabsolute sum difference of 0.\n
\n\n

Example 3:

\n\n
\nInput: nums1 = [1,10,4,4,2,7], nums2 = [9,3,5,1,7,4]\nOutput: 20\nExplanation: Replace the first element with the second: [1,10,4,4,2,7] => [10,10,4,4,2,7].\nThis yields an absolute sum difference of |10-9| + |10-3| + |4-5| + |4-1| + |2-7| + |7-4| = 20\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "绝对差值和", "translatedContent": "

给你两个正整数数组 nums1 和 nums2 ，数组的长度都是 n 。

\n\n

数组 nums1 和 nums2 的 绝对差值和 定义为所有 |nums1[i] - nums2[i]|（0 <= i < n）的 总和（下标从 0 开始）。

\n\n

你可以选用 nums1 中的 任意一个 元素来替换 nums1 中的 至多 一个元素，以 最小化 绝对差值和。

\n\n

在替换数组 nums1 中最多一个元素 之后 ，返回最小绝对差值和。因为答案可能很大，所以需要对 109 + 7 取余 后返回。

\n\n

|x| 定义为：

\n\n\n\n

 

\n\n

示例 1：

\n\n
\n输入：nums1 = [1,7,5], nums2 = [2,3,5]\n输出：3\n解释：有两种可能的最优方案：\n- 将第二个元素替换为第一个元素：[1,7,5] => [1,1,5] ，或者\n- 将第二个元素替换为第三个元素：[1,7,5] => [1,5,5]\n两种方案的绝对差值和都是 |1-2| + (|1-3| 或者 |5-3|) + |5-5| = 3\n
\n\n

示例 2：

\n\n
\n输入：nums1 = [2,4,6,8,10], nums2 = [2,4,6,8,10]\n输出：0\n解释：nums1 和 nums2 相等，所以不用替换元素。绝对差值和为 0\n
\n\n

示例 3：

\n\n
\n输入：nums1 = [1,10,4,4,2,7], nums2 = [9,3,5,1,7,4]\n输出：20\n解释：将第一个元素替换为第二个元素：[1,10,4,4,2,7] => [10,10,4,4,2,7]\n绝对差值和为 |10-9| + |10-3| + |4-5| + |4-1| + |2-7| + |7-4| = 20\n
\n\n

 

\n\n

提示：

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