All contents and pictures on this website come from the Internet and are updated regularly every week. They are for personal study and research only, and should not be used for commercial purposes. Thank you for your cooperation.

# 1818. Minimum Absolute Sum Difference

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

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

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`.

`|x|` is defined as:

• `x` if `x >= 0`, or
• `-x` if `x < 0`.

Example 1:

```Input: nums1 = [1,7,5], nums2 = [2,3,5]
Output: 3
Explanation: There are two possible optimal solutions:
- Replace the second element with the first: [1,7,5] => [1,1,5], or
- Replace the second element with the third: [1,7,5] => [1,5,5].
Both will yield an absolute sum difference of `|1-2| + (|1-3| or |5-3|) + |5-5| = `3.
```

Example 2:

```Input: nums1 = [2,4,6,8,10], nums2 = [2,4,6,8,10]
Output: 0
Explanation: nums1 is equal to nums2 so no replacement is needed. This will result in an
absolute sum difference of 0.
```

Example 3:

```Input: nums1 = [1,10,4,4,2,7], nums2 = [9,3,5,1,7,4]
Output: 20
Explanation: Replace the first element with the second: [1,10,4,4,2,7] => [10,10,4,4,2,7].
This yields an absolute sum difference of `|10-9| + |10-3| + |4-5| + |4-1| + |2-7| + |7-4| = 20`
```

Constraints:

• `n == nums1.length`
• `n == nums2.length`
• `1 <= n <= 105`
• `1 <= nums1[i], nums2[i] <= 105`

Medium

Normal

Uber

leetcode.ca