README.md

628. Maximum Product of Three Numbers

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

Example 1:

Input: [1,2,3]
Output: 6

Example 2:

Input: [1,2,3,4]
Output: 24

Note:

1. The length of the given array will be in range [3,10⁴] and all elements are in the range [-1000, 1000].
2. Multiplication of any three numbers in the input won't exceed the range of 32-bit signed integer.

Solutions (Python)

1. Sort

class Solution:
    def maximumProduct(self, nums: List[int]) -> int:
        nums.sort()
        return nums[-1] * max(nums[-2] * nums[-3], nums[0] * nums[1])

2. Linear Scan

class Solution:
    def maximumProduct(self, nums: List[int]) -> int:
        min1, min2 = 1000, 1000
        max1, max2, max3 = -1000, -1000, -1000

        for n in nums:
            if n <= min1:
                min2 = min1
                min1 = n
            elif n < min2:
                min2 = n

            if n >= max3:
                max1 = max2
                max2 = max3
                max3 = n
            elif n >= max2:
                max1 = max2
                max2 = n
            elif n > max1:
                max1 = n

        return max3 * max(min1 * min2, max1 * max2)