# LeetCode 1913. Maximum Product Difference Between Two Pairs

## Description

https://leetcode.com/problems/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 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`

## Explanation

The max product difference is the different between the two max number pair and the two minimum number pair.

## Python Solution

``````class Solution:
def maxProductDifference(self, nums: List[int]) -> int:
nums = sorted(nums)

return nums[-1] * nums[-2] - nums * nums``````
• Time Complexity: O(Nlog(N)).
• Space Complexity: O(1).