algoadvance

Given the array nums, consisting of positive integers, find the maximum product of two elements in the array leveraging the specified rule. Specifically, you need to return the product of the two largest elements in the list, each decreased by 1. Formally, the task is to find max((nums[i]-1) * (nums[j]-1)) where 0 <= i < j < nums.length.

Example

Input: nums = [3,4,5,2]
Output: 12
Explanation: (5-1) * (4-1) = 4 * 3 = 12.

Input: nums = [1,5,4,5]
Output: 16
Explanation: (5-1) * (5-1) = 4 * 4 = 16.

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

Clarifying Questions

  1. Can the array have fewer than two elements?
    • No, based on the problem definition, the array will always have at least two elements.
  2. Are all numbers in the array guaranteed to be positive integers?
    • Yes, the problem states that the array consists of positive integers.
  3. Do we need to handle large integers for any specific edge cases?
    • Python handles large integers natively, but we should still keep potential performance considerations in mind.

Strategy

  1. First, we need to identify the two largest numbers in the array.
  2. One way is to sort the array and pick the two largest elements. However, this may not be efficient.
  3. A more efficient way in terms of time complexity is to iterate through the array once to find the two largest numbers.
  4. Once we have the largest and the second largest number, we compute and return the product (largest-1) * (secondLargest-1).

Code

def maxProduct(nums):
    first_max = second_max = -1
    for num in nums:
        if num > first_max:
            second_max = first_max
            first_max = num
        elif num > second_max:
            second_max = num
    return (first_max - 1) * (second_max - 1)

# Testing the function with given examples
print(maxProduct([3,4,5,2])) # Output: 12
print(maxProduct([1,5,4,5])) # Output: 16
print(maxProduct([3,7])) # Output: 12

Time Complexity

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