Maximum Product Difference Between Two Pairs

The product difference between two pairs (a, b) and (c, d) is defined as (a * b) - (c * d).

• For example, the product difference between (5, 6) and (2, 7) is (5 * 6) - (2 * 7) = 16.

Given an integer array nums, choose four distinct indices w, x, y, and z such that the product difference between pairs (nums[w], nums[x]) and (nums[y], nums[z]) is maximized.

Return the maximum such product difference.

Example:

Input: nums = [5,6,2,7,4]
Output: 34
Explanation: We can choose indices 1 and 3 for the first pair (6, 7) and indices 2 and 4 for the second pair (2, 4).
The product difference is (6 * 7) - (2 * 4) = 34.

Approach

C++

#include <bits/stdc++.h>
using namespace std;

int maxProductDifference(vector<int> &nums)
{

    //sort the array
    sort(nums.begin(), nums.end());

    //size of array
    int n = nums.size();

    //result will be the difference
    //of product of largest two elements
    //product of smallest two elements
    return (nums[n - 1] * nums[n - 2] - nums[0] * nums[1]);
}
int main()
{
    vector<int> nums = {5, 6, 2, 7, 4};

    cout << maxProductDifference(nums) << "\n";

    return 0;
}