# 1913. Maximum Product Difference Between Two Pairs

## Description

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 1:

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.


Example 2:

Input: nums = [4,2,5,9,7,4,8]
Output: 64
Explanation: We can choose indices 3 and 6 for the first pair (9, 8) and indices 1 and 5 for the second pair (2, 4).
The product difference is (9 * 8) - (2 * 4) = 64.


Constraints:

• 4 <= nums.length <= 104
• 1 <= nums[i] <= 104

## Solutions

• class Solution {
public int maxProductDifference(int[] nums) {
Arrays.sort(nums);
int n = nums.length;
return nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
}
}

• class Solution {
public:
int maxProductDifference(vector<int>& nums) {
sort(nums.begin(), nums.end());
int n = nums.size();
return nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
}
};

• class Solution:
def maxProductDifference(self, nums: List[int]) -> int:
nums.sort()
return nums[-1] * nums[-2] - nums[0] * nums[1]


• func maxProductDifference(nums []int) int {
sort.Ints(nums)
n := len(nums)
return nums[n-1]*nums[n-2] - nums[0]*nums[1]
}

• /**
* @param {number[]} nums
* @return {number}
*/
var maxProductDifference = function (nums) {
nums.sort((a, b) => a - b);
let n = nums.length;
let ans = nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
return ans;
};