# 1874. Minimize Product Sum of Two Arrays

https://leetcode.com/problems/minimize-product-sum-of-two-arrays

## Description

The **product sum** of two equal-length arrays `a` and `b` is equal to the sum of `a[i] * b[i]` for all `0 <= i < a.length` (**0-indexed**).

* For example, if `a = [1,2,3,4]` and `b = [5,2,3,1]`, the **product sum** would be `1*5 + 2*2 + 3*3 + 4*1 = 22`.

Given two arrays `nums1` and `nums2` of length `n`, return _the **minimum product sum** if you are allowed to **rearrange** the **order** of the elements in_ `nums1`.&#x20;

**Example 1:**

```

**Input:** nums1 = [5,3,4,2], nums2 = [4,2,2,5]
**Output:** 40
**Explanation:** We can rearrange nums1 to become [3,5,4,2]. The product sum of [3,5,4,2] and [4,2,2,5] is 3*4 + 5*2 + 4*2 + 2*5 = 40.
```

**Example 2:**

```

**Input:** nums1 = [2,1,4,5,7], nums2 = [3,2,4,8,6]
**Output:** 65
**Explanation:** We can rearrange nums1 to become [5,7,4,1,2]. The product sum of [5,7,4,1,2] and [3,2,4,8,6] is 5*3 + 7*2 + 4*4 + 1*8 + 2*6 = 65.
```

**Constraints:**

* `n == nums1.length == nums2.length`
* `1 <= n <= 105`
* `1 <= nums1[i], nums2[i] <= 100`

## ac

```java
```
