Is Subsets easy or hard?

Subsets is generally classified as a medium-level problem. The concept is straightforward, but it tests whether you recognize the power set pattern and implement recursive backtracking or bit masking correctly.

Subsets Python/Java solution

In Python or Java, the typical solution uses recursive backtracking. Start with an empty list, recursively add elements from the array, and store each intermediate subset. Both languages also support a bit manipulation approach that iterates from 0 to (1 << n) - 1 and checks bits to build subsets.

How to solve Subsets in O(n)?

Generating all subsets cannot be done in O(n) because the output itself contains 2^n subsets. The optimal algorithms—backtracking or bit manipulation—run in O(n * 2^n) time, which matches the size of the result set and is considered optimal for this problem.

What is the best approach for Subsets?

Recursive backtracking is the most common approach for the Subsets problem. It explores the decision tree where each element can be either included or excluded. The algorithm generates all 2^n subsets with O(n * 2^n) time complexity and O(n) recursion space, making it both intuitive and flexible for interview variations.

Is Subsets asked at Google/Amazon/Meta?

Subsets and related power set problems frequently appear in technical interviews at companies like Amazon, Google, Meta, and Microsoft. Interviewers use it to test recursion, backtracking, and understanding of combinatorial enumeration.

What data structure is used in Subsets?

The main data structure is an array or list to store the current subset during generation. Backtracking uses recursion with a dynamic list, while the bit manipulation approach uses integers as binary masks to represent subset membership.

What is the time complexity of Subsets?

The time complexity is O(n * 2^n). There are 2^n possible subsets for an array of size n, and building each subset can take up to O(n) time when copying elements into the result list.

Description Solution Video 8:47

78. Subsets

Q: How to solve Subsets in O(n)?

Generating all subsets cannot be done in O(n) because the output itself contains 2^n subsets. The optimal algorithms—backtracking or bit manipulation—run in O(n * 2^n) time, which matches the size of the result set and is considered optimal for this problem.

Q: What is the best approach for Subsets?

Recursive backtracking is the most common approach for the Subsets problem. It explores the decision tree where each element can be either included or excluded. The algorithm generates all 2^n subsets with O(n * 2^n) time complexity and O(n) recursion space, making it both intuitive and flexible for interview variations.

Q: Is Subsets asked at Google/Amazon/Meta?

Subsets and related power set problems frequently appear in technical interviews at companies like Amazon, Google, Meta, and Microsoft. Interviewers use it to test recursion, backtracking, and understanding of combinatorial enumeration.

Q: What data structure is used in Subsets?

The main data structure is an array or list to store the current subset during generation. Backtracking uses recursion with a dynamic list, while the bit manipulation approach uses integers as binary masks to represent subset membership.

Q: What is the time complexity of Subsets?

The time complexity is O(n * 2^n). There are 2^n possible subsets for an array of size n, and building each subset can take up to O(n) time when copying elements into the result list.

Medium82.7% acceptance21 companies

Given an integer array nums of unique elements, return all possible subsets (the power set).

The solution set must not contain duplicate subsets. Return the solution in any order.

Example 1:

Input: nums = [1,2,3]
Output: [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]

Example 2:

Input: nums = [0]
Output: [[],[0]]

Constraints:

1 <= nums.length <= 10
-10 <= nums[i] <= 10
All the numbers of nums are unique.

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78. Subsets

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