L2 · Working engineerRecursion~10 min · 4 tests#53

Generate All Subsets (Power Set)

Generate every subset of a list with recursion or iterative doubling in O(n·2ⁿ). Classic backtracking question with order-insensitive tests.

The problem

Return every subset of nums (values are distinct), including the empty set. Order of subsets, and inside each subset, does not matter.

Examples

Example 1

Input

subsets([1, 2, 3])

Expected output

[[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]

Example 2
Input
```
subsets([0])
```
Expected output
```
[[], [0]]
```

+ 2 hidden tests on Submit.

Edge cases to ask about

Empty input
Single element

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · subsets

def subsets(nums):
    """All subsets of nums, including []."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and read why.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Include/exclude recursion	O(n · 2ⁿ)	O(n · 2ⁿ)	Each element doubles the number of subsets.
Iterative doubling	O(n · 2ⁿ)	O(n · 2ⁿ)	Start with [[]]; for each x, add x to every subset so far.
bestBitmasks 0..2ⁿ−1	O(n · 2ⁿ)	O(n · 2ⁿ)	Bit i set ⇒ include nums[i].

Walkthrough of the optimal approach (try it yourself first)

Start with [[]]. For each x, every existing subset spawns a twin with x appended, doubling the list. After n elements there are 2ⁿ subsets.

Building [s + [x] for s in result] before the += matters — iterating over result while appending to it would loop forever.

Complexity: O(n · 2ⁿ) time, O(n · 2ⁿ) space. There are 2ⁿ subsets, each up to n long.

Reveal the reference solution

def subsets(nums):
    result = [[]]
    for x in nums:
        result += [s + [x] for s in result]
    return result

Follow-ups interviewers ask

Input has duplicates — no duplicate subsets.
Only subsets of size k (combinations).

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Generate All Subsets (Power Set) in Python?

The optimal solution runs in O(n · 2ⁿ) time and O(n · 2ⁿ) auxiliary space. There are 2ⁿ subsets, each up to n long.

What is the brute-force approach, and how do you optimise it?

Include/exclude recursion: O(n · 2ⁿ) time, O(n · 2ⁿ) space. Each element doubles the number of subsets. Iterative doubling: O(n · 2ⁿ) time, O(n · 2ⁿ) space. Start with [[]]; for each x, add x to every subset so far. Bitmasks 0..2ⁿ−1: O(n · 2ⁿ) time, O(n · 2ⁿ) space. Bit i set ⇒ include nums[i].

What follow-up questions do interviewers ask about Generate All Subsets (Power Set)?

Input has duplicates — no duplicate subsets. Only subsets of size k (combinations).