Maximum product subarray

Time: O(N); Space: O(1); medium

Given an integer array nums, find the contiguous subarray within an array (containing at least one number) which has the largest product.

Example 1:

Input: A = [2,3,-2,4]

Output: 6

Explanation:

  • [2,3] has the largest product 6.

Example 2:

Input: A = [-2,0,-1]

Output: 0

Explanation:

  • The result cannot be 2, because [-2,-1] is not a subarray.

[1]:

class Solution1(object):
    """
    Time: O(N)
    Space: O(1)
    """
    def maxProduct(self, A):
        """
        :type  A: List[int]
        :rtype: int
        """
        global_max, local_max, local_min = float("-inf"), 1, 1
        for x in A:
            local_max, local_min = max(x, local_max * x, local_min * x), min(x, local_max * x, local_min * x)
            global_max = max(global_max, local_max)

        return global_max

[2]:

s = Solution1()

A = [2,3,-2,4]
assert s.maxProduct(A) == 6

A = [-2,0,-1]
assert s.maxProduct(A) == 0

[3]:

class Solution2(object):
    def maxProduct(self, A):
        """
        :type  A: List[int]
        :rtype: int
        """
        global_max, local_max, local_min = float("-inf"), 1, 1
        for x in A:
            local_max = max(1, local_max)
            if x > 0:
                local_max, local_min = local_max * x, local_min * x
            else:
                local_max, local_min = local_min * x, local_max * x
            global_max = max(global_max, local_max)

        return global_max

[4]:

s = Solution2()

A = [2,3,-2,4]
assert s.maxProduct(A) == 6

A = [-2,0,-1]
assert s.maxProduct(A) == 0