[Python] How to efficiently solve the Maximum Product Subarray problem in Python?

I’m trying to solve the Maximum Product Subarray problem, which is described as follows:

Given an array of integers (positive, negative, or zero), find the maximum product of any contiguous subarray.

Example: Input: [-2, 6, -3, -10, 0, 2] Output: 180 Explanation: The subarray [6, -3, -10] gives the product 6 * -3 * -10 = 180.

I’ve tried iterating through the array while keeping track of the current maximum and minimum products, but I’m getting confused about how to handle cases where a negative number or zero appears.

def maxProduct(arr):
max_ending_here = 0
min_ending_here = 0
max_so_far = 0

Not sure how to update max_ending_here and min_ending_here for negative numbers


for num in arr:
pass # Implementation goes here

return max_so_far


`

`Questions:

1. How should I handle the transition when encountering a negative number or zero in the array?
2. Is there a better way to handle this problem without considering all possible subarrays explicitly (which would take O(n²) or more)?
3. What is the optimal time complexity of solving this problem, and how can I ensure my approach achieves it?

Any guidance or suggestions would be greatly appreciated. Thank you!`

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