152 Maximum Product Subarray

Given an integer array nums, find a subarray (A subarray is a contiguous non-empty sequence of elements within an array.) that has the largest product, and return the product.

The test cases are generated so that the answer will fit in a 32-bit integer.

Example 1:

Input: nums = [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.

Example 2:

Input: nums = [-2,0,-1]
Output: 0
Explanation: The result cannot be 2, because [-2,-1] is not a subarray.

Constraints:

• 1 <= nums.length <= 2 * 104
• -10 <= nums[i] <= 10
• The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

Record both "max" and "min" up to the number i in DP.

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class Solution:
    def maxProduct(self, nums: List[int]) -> int:
        dp_max = [nums[0]]
        dp_min = [nums[0]]
        for i in range(1, len(nums)):
            args = (
                dp_max[-1] * nums[i],
                dp_min[-1] * nums[i],
                nums[i]
            )
            dp_max.append(max(*args))
            dp_min.append(min(*args))
        return max(dp_max)