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Formatted question description: https://leetcode.ca/all/1874.html

# 1874. Minimize Product Sum of Two Arrays

Medium

## 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.

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 34 + 52 + 42 + 25 = 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 53 + 72 + 44 + 18 + 2*6 = 65.

Constraints:

• n == nums1.length == nums2.length
• 1 <= n <= 10^5
• 1 <= nums1[i], nums2[i] <= 100

## Solution

Sort both nums1 and nums2. Then for each 0 <= i < n, nums1[i] is multiplied with nums2[n - 1 - i]. In this way, the product sum is minimized.

• class Solution {
public int minProductSum(int[] nums1, int[] nums2) {
Arrays.sort(nums1);
Arrays.sort(nums2);
int sum = 0;
int length = nums1.length;
for (int i = 0; i < length; i++)
sum += nums1[i] * nums2[length - 1 - i];
return sum;
}
}

############

class Solution {
public int minProductSum(int[] nums1, int[] nums2) {
Arrays.sort(nums1);
Arrays.sort(nums2);
int n = nums1.length, res = 0;
for (int i = 0; i < n; ++i) {
res += nums1[i] * nums2[n - i - 1];
}
return res;
}
}

• // OJ: https://leetcode.com/problems/minimize-product-sum-of-two-arrays/
// Time: O(NlogN)
// Space: O(1)
class Solution {
public:
int minProductSum(vector<int>& A, vector<int>& B) {
sort(begin(A), end(A));
sort(begin(B), end(B), greater<>());
int ans = 0;
for (int i = 0; i < A.size(); ++i) ans += A[i] * B[i];
return ans;
}
};

• class Solution:
def minProductSum(self, nums1: List[int], nums2: List[int]) -> int:
nums1.sort()
nums2.sort()
n, res = len(nums1), 0
for i in range(n):
res += nums1[i] * nums2[n - i - 1]
return res


• func minProductSum(nums1 []int, nums2 []int) int {
sort.Ints(nums1)
sort.Ints(nums2)
res, n := 0, len(nums1)
for i, num := range nums1 {
res += num * nums2[n-i-1]
}
return res
}