How do you find the maximum product subarray?

Question presented to candidate: "Given an integer array that can contain negative numbers and zeros, find the contiguous subarray with the largest product and return that product. Walk me through your idea, then code it in Python."

What a strong answer should cover:

• Why plain Kadane (keep only the best product ending here) fails: a negative number turns the smallest product into the largest, so you must track both the maximum and the minimum product ending at each index.
• The recurrence: at each x, the new max is the largest of x, max * x and min * x (and the new min is the smallest of the same three); a zero resets both to 0, and the running best is updated every step.
• O(n) time and O(1) extra space, compared with the O(n²) brute force that tries every start and end.
• The alternative prefix/suffix scan (multiply left to right and right to left, restarting after a zero) and why it works: inside a stretch with no zero, the best product is always a prefix or a suffix of that stretch.
• Python details: int has arbitrary precision so products never overflow (they just get bigger and slower), the tuple swap hi, lo = lo, hi, and that nums[1:] copies the list.

Clarifying questions expected:

• Can the array contain zeros and negatives, and can it be empty?
• Is the answer guaranteed to fit in a 32-bit (or 64-bit) integer?
• Do you want just the product, or also the start and end indices of the subarray?

Code / implementation expected: Yes — a one-pass Python function that keeps the max and min product ending at each index.