LeetCode 1874: Minimize Product Sum of Two Arrays Solution

Master LeetCode problem 1874 (Minimize Product Sum of Two Arrays), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1874. Minimize Product Sum of Two Arrays

Medium

Array Greedy Sorting

Problem Explanation

Explanation

To minimize the product sum of two arrays, we need to pair elements from the two arrays in a way that the sum of products of corresponding elements is minimized. One way to achieve this is by sorting both arrays in ascending order and multiplying the smallest element from one array with the largest element from the other array, and so on. This way, we pair the smallest with the largest elements to minimize the product sum.

Algorithm:

Sort both arrays in ascending order.
Initialize a variable productSum to store the sum of products.
Iterate over the arrays simultaneously from start to end.
For each iteration, multiply the current elements from both arrays and add the product to productSum.
Return productSum as the minimum product sum.

Time complexity: O(nlogn) where n is the size of the arrays due to the sorting step. Space complexity: O(1) as we are not using any extra space other than some variables.

Solution Code

import java.util.Arrays;

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

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