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1913. Maximum Product Difference Between Two Pairs

Description

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

Solutions

Solution 1

Thinking

Enumerating four indices is \(O(n^4)\). Maximizing \(ab-cd\) means taking the largest product minus the smallest product.

After sorting, that is the product of the two largest minus the product of the two smallest, which uses four distinct indices.

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

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class Solution {
    public int maxProductDifference(int[] nums) {
        Arrays.sort(nums);
        int n = nums.length;
        return nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
    }
}

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class Solution {
public:
    int maxProductDifference(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int n = nums.size();
        return nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
    }
};

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func maxProductDifference(nums []int) int {
    sort.Ints(nums)
    n := len(nums)
    return nums[n-1]*nums[n-2] - nums[0]*nums[1]
}

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/**
 * @param {number[]} nums
 * @return {number}
 */
var maxProductDifference = function (nums) {
    nums.sort((a, b) => a - b);
    let n = nums.length;
    let ans = nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
    return ans;
};

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