How do you solve Maximum Product of Two Elements in an Array on LeetCode?

Maximum Product of Two Elements in an Array (LeetCode #1464) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The product is maximized by selecting the two largest numbers in the array.

What is the brute force solution for Maximum Product of Two Elements in an Array?

The brute force approach for Maximum Product of Two Elements in an Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible pair of elements in the array to find the maximum product of (nums[i]-1)*(nums[j]-1). This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Product of Two Elements in an Array?

Maximum Product of Two Elements in an Array uses the following concepts: Array, Sorting, Heap (Priority Queue). The recommended patterns to study are: Array, Sorting.

What are the interview tips for Maximum Product of Two Elements in an Array?

Always clarify the problem constraints and edge cases. Think about the efficiency of your solution — can it be improved? Explain your thought process clearly while coding.

What are common mistakes when solving Maximum Product of Two Elements in an Array?

Not considering the case where the two largest numbers are the same. Overlooking the need to check pairs of indices correctly.

#1464

Maximum Product of Two Elements in an Array

Easy

ArraySortingHeap (Priority Queue)ArraySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution focuses on finding the two largest numbers in the array. Since the product is maximized when both numbers are as large as possible, we can simply find the two largest numbers and compute the product directly.

⚙️

Algorithm

3 steps

1Step 1: Initialize two variables, first_max and second_max, to track the two largest numbers.
2Step 2: Iterate through the array to find the two largest numbers.
3Step 3: Calculate the maximum product using the formula (first_max - 1) * (second_max - 1).

solution.py11 lines

1# Full working Python code
2
3def maxProduct(nums):
4    first_max, second_max = float('-inf'), float('-inf')
5    for num in nums:
6        if num > first_max:
7            second_max = first_max
8            first_max = num
9        elif num > second_max:
10            second_max = num
11    return (first_max - 1) * (second_max - 1)

ℹ

Complexity note: The time complexity is O(n) because we only need to traverse the array once to find the two largest numbers. The space complexity is O(1) since we are using a constant amount of extra space.

1The product is maximized by selecting the two largest numbers in the array.
2Subtracting 1 from each number before multiplying helps avoid zero products.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.