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Maximum Product of Three Numbers

Difficulty: Easy

Problem Description

Given an integer array nums, find three numbers whose product is maximum and return the maximum product.

Key Insights

The maximum product of three numbers can be obtained either from the three largest numbers or from the two smallest (most negative) numbers and the largest number.
Sorting the array allows us to easily access the largest and smallest numbers.
Negative numbers can yield a higher product when multiplied together, thus we need to consider both maximum and minimum values.

Space and Time Complexity

Time Complexity: O(n log n) - due to the sorting of the array.
Space Complexity: O(1) - only a constant amount of extra space is used.

Solution

To find the maximum product of three numbers, we can sort the input array. Once sorted, the potential maximum products can be found by either:

Multiplying the three largest numbers (the last three elements in the sorted array).
Multiplying the two smallest numbers (which could be negative) with the largest number (the last element in the sorted array). By comparing these two products, we can determine the maximum product.

Code Solutions

def maximumProduct(nums):
    # Sort the array
    nums.sort()
    # Calculate the maximum product by comparing two scenarios:
    # 1. Product of the three largest numbers
    product1 = nums[-1] * nums[-2] * nums[-3]
    # 2. Product of the two smallest numbers and the largest number
    product2 = nums[0] * nums[1] * nums[-1]
    # Return the maximum of the two products
    return max(product1, product2)

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