1913 Maximum Product Difference Between Two Pairs - Easy

Problem:

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

Problem Analysis:

• Sorting the array has a time complexity of O(nlogn), where n is the length of the array.
• The space complexity is O(1) since the sorting is performed in-place.

Solutions:

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

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