Maximum Product Difference Between Two Pairs

Problem Description

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

Key Insights

• To maximize the product difference, we should focus on the largest and smallest numbers in the array.
• The maximum product can be achieved using the two largest numbers for one pair and the two smallest numbers for the other pair.
• Sorting the array helps in easily accessing the largest and smallest elements.

Space and Time Complexity

Time Complexity: O(n log n), where n is the length of the array due to the sorting step. Space Complexity: O(1), as we only need a constant amount of extra space.

Solution

To solve the problem, we can follow these steps:

1. Sort the array.
2. Identify the two largest numbers and the two smallest numbers.
3. Calculate the product of the two largest numbers and the product of the two smallest numbers.
4. Return the difference between these two products.

The algorithm primarily uses sorting to rearrange the numbers, which allows us to efficiently pick the required elements for our calculations.

Code Solutions