# LeetCode 1464. Maximum Product of Two Elements in an Array

## Description

https://leetcode.com/problems/maximum-product-of-two-elements-in-an-array/

Given the array of integers `nums`, you will choose two different indices `i` and `j` of that array. Return the maximum value of`(nums[i]-1)*(nums[j]-1)`.

Example 1:

```Input: nums = [3,4,5,2]
Output: 12
Explanation: If you choose the indices i=1 and j=2 (indexed from 0), you will get the maximum value, that is, (nums[1]-1)*(nums[2]-1) = (4-1)*(5-1) = 3*4 = 12.
```

Example 2:

```Input: nums = [1,5,4,5]
Output: 16
Explanation: Choosing the indices i=1 and j=3 (indexed from 0), you will get the maximum value of (5-1)*(5-1) = 16.
```

Example 3:

```Input: nums = [3,7]
Output: 12
```

Constraints:

• `2 <= nums.length <= 500`
• `1 <= nums[i] <= 10^3`

## Explanation

Find the first largest number and the second-largest number, then calculate the product.

## Python Solution

``````class Solution:
def maxProduct(self, nums: List[int]) -> int:

max_num_index = -1
for i, num in enumerate(nums):
if max_num_index == -1 or num > nums[max_num_index]:
max_num_index = i

second_num_index = -1
for i, num in enumerate(nums):
if (i != max_num_index and (num > nums[second_num_index] or second_num_index == -1)):
second_num_index = i

return (nums[max_num_index] - 1) * (nums[second_num_index] - 1)``````
• Time Complexity: ~N
• Space Complexity: ~1