Introduction

In this blog post, we will explore how to solve the LeetCode problem "1913" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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

Here's a breakdown of the solution:

• Maximize the first product, minimize the second: The goal is to maximize (a * b) - (c * d). This is best achieved by selecting the two largest numbers from nums for a and b, and selecting the two smallest numbers from nums for c and d.
• Efficient Selection: We can find the two largest and two smallest numbers efficiently without fully sorting the array.

• Calculate and Return: Multiply the two largest and the two smallest, then subtract them to get the maximum product difference.

• Time & Space Complexity: O(n) runtime, O(1) storage.

Code

    def maxProductDifference(nums):
    """
    Finds the maximum product difference between two pairs in the given array.

    Args:
    nums (list[int]): An integer array.

    Returns:
    int: The maximum product difference.
    """

    max1 = 0
    max2 = 0
    min1 = float('inf')
    min2 = float('inf')

    for num in nums:
        if num > max1:
            max2 = max1
            max1 = num
        elif num > max2:
            max2 = num

        if num < min1:
            min2 = min1
            min1 = num
        elif num < min2:
            min2 = num

    return (max1 * max2) - (min1 * min2)