Maximum Product of Three Numbers

Tested Python solution for LeetCode 628 with 16 pytest cases. Generate a practice environment with lcpy.

LeetCode 628, Easy. Topics: Array, Math, Sorting. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 16 parametrized pytest cases, and a playground notebook:

lcpy gen -n 628   # by problem number
lcpy gen -s maximum_product_of_three_numbers   # by problem name

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Problem

You are given an integer array nums.

Find three numbers whose product is maximum and return the maximum product.

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Examples

Input: nums = [1,2,3]
Output: 6
Explanation: The only three numbers are 1, 2, and 3, so the maximum product is 1 * 2 * 3 = 6.

Input: nums = [1,2,3,4]
Output: 24
Explanation: The largest product comes from the three greatest numbers: 2 * 3 * 4 = 24.

Input: nums = [-1,-2,-3]
Output: -6
Explanation: The only three numbers are -1, -2, and -3, so the maximum product is (-1) * (-2) * (-3) = -6.

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Constraints

• 3 <= nums.length <= 10^4
• -1000 <= nums[i] <= 1000

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(n)
    # Space: O(1)
    def maximum_product(self, nums: list[int]) -> int:
        max1 = max2 = max3 = -(10**18)
        min1 = min2 = 10**18
        for num in nums:
            if num > max1:
                max1, max2, max3 = num, max1, max2
            elif num > max2:
                max2, max3 = num, max2
            elif num > max3:
                max3 = num
            if num < min1:
                min1, min2 = num, min1
            elif num < min2:
                min2 = num
        return max(max1 * max2 * max3, max1 * min1 * min2)

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Complexity

Time	Space
O(n)	O(1)

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