Problem URL: Minimize product sum of two arrays

We will sort the two arrays, first one in ascending order and second one in descending order. That will make sure the product of both array's item will be minimized. Then we will iterate over the arrays and calculate the product sum. Finally, we will return the product sum.

class Solution:
    def minProductSum(self, nums1: List[int], nums2: List[int]) -> int:
        nums1.sort()
        nums2.sort(reverse=True)

        productSum = 0
        for i in range(len(nums1)):
            productSum += nums1[i] * nums2[i]

        return productSum

Time complexity: O(nlog(n)), n is the number of items in the nums1
Space complexity: O(1)

We can achieve the same result by using python's built-in function.

class Solution:
    def minProductSum(self, nums1: List[int], nums2: List[int]) -> int:
        nums1.sort()
        nums2.sort(reverse=True)
        return sum([n1*n2 for n1, n2 in zip(nums1, nums2)])