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