# 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.

 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 `````` ``````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)``````