How do you solve Maximum Product of Three Numbers on LeetCode?

Maximum Product of Three Numbers (LeetCode #628) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: The maximum product can be achieved using either the three largest numbers or two smallest (negative) numbers and the largest number.

What is the brute force solution for Maximum Product of Three Numbers?

The brute force approach for Maximum Product of Three Numbers is Brute Force, with O(n³) time complexity and O(1) space complexity. The brute force approach involves checking every possible combination of three numbers in the array to find the maximum product. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Product of Three Numbers?

Maximum Product of Three Numbers uses the following concepts: Array, Math, Sorting. The recommended patterns to study are: Sorting, Greedy.

What are the interview tips for Maximum Product of Three Numbers?

Always clarify if negative numbers are allowed in the input. Discuss the brute force approach first to show your thought process before jumping to optimizations. Be prepared to explain your reasoning for choosing a specific approach, especially when dealing with edge cases.

What are common mistakes when solving Maximum Product of Three Numbers?

Not considering negative numbers which can yield a higher product when multiplied with other negatives. Assuming the maximum product is always from the three largest numbers without checking combinations.

#628

Maximum Product of Three Numbers

Easy

ArrayMathSortingSortingGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n³)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

The optimal solution leverages sorting to efficiently find the maximum product of three numbers. By sorting, we can easily access the largest and smallest numbers, which is crucial for handling negative numbers.

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Algorithm

4 steps

1Step 1: Sort the array in non-decreasing order.
2Step 2: Calculate the product of the three largest numbers (last three in the sorted array).
3Step 3: Calculate the product of the two smallest numbers (first two in the sorted array) and the largest number (last in the sorted array).
4Step 4: Return the maximum of the two products calculated in steps 2 and 3.

solution.py3 lines

1def maximumProduct(nums):
2    nums.sort()
3    return max(nums[-1] * nums[-2] * nums[-3], nums[0] * nums[1] * nums[-1])

ℹ

Complexity note: The time complexity is O(n log n) due to the sorting step. The space complexity is O(1) since we are not using any extra space that scales with input size.

1The maximum product can be achieved using either the three largest numbers or two smallest (negative) numbers and the largest number.
2Sorting helps in easily accessing the largest and smallest numbers.

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