1913. Maximum Product Difference Between Two Pairs

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

Solution

/**
 * @param {number[]} nums
 * @return {number}
 */
var maxProductDifference = function(nums) {
    var maxIndex = -1;
    var secondMaxIndex = -1;
    var minIndex = -1;
    var secondMinIndex = -1;
    for (var i = 0; i < nums.length; i++) {
        if (minIndex === -1 || nums[i] < nums[minIndex]) {
            secondMinIndex = minIndex;
            minIndex = i;
        } else if (secondMinIndex === -1 || nums[i] < nums[secondMinIndex]) {
            secondMinIndex = i;
        }
        if (maxIndex === -1 || nums[i] > nums[maxIndex]) {
            secondMaxIndex = maxIndex;
            maxIndex = i;
        } else if (secondMaxIndex == -1 || nums[i] > nums[secondMaxIndex]) {
            secondMaxIndex = i;
        }
    }
    return nums[maxIndex] * nums[secondMaxIndex]
        - nums[minIndex] * nums[secondMinIndex];
};

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(1).