How do you generate all subsets of an array?

Question presented to candidate: "Given a list of distinct integers, return every possible subset — the power set. Code it in Python, then tell me what changes if the list can contain duplicates."

What a strong answer should cover:

• Every element is either in or out, so there are 2^n subsets including the empty one; that bounds both time and output size.
• A backtracking solution (loop from a start index, choose / recurse with i + 1 / un-choose) and why the start index prevents reordered repeats.
• At least one alternative: the iterative doubling (cascade) or the bitmask from 0 to 2^n - 1.
• Complexity O(n · 2^n) time and output, O(n) extra space for the recursion, and why it cannot be beaten when every subset must be listed.
• Duplicates (Subsets II): sort, then skip a value equal to the previous one at the same level (i > start).
• Python details: record path[:] (a copy) not path; itertools.combinations gives the same sets ordered by size; 1 << n is exact for any n because Python integers do not overflow.

Clarifying questions expected:

• Can the input contain duplicates, and if so should equal subsets appear once?
• Does the order of the subsets (or inside each subset) matter?
• How large can n get? (2^n grows very fast.)

Code / implementation expected: Yes — a backtracking function in Python returning list[list[int]], plus the sort-and-skip change for duplicates.