What is the optimal time complexity of solving Subsets?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Subsets?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Subsets?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Subsets?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Subsets

Learn how to solve the 'Subsets' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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.

Implement a function subsets(nums: list) -> list.

Constraints

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

Examples

Example 1

Input

[1,2,3]

Output

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

Explanation

All 2^3 = 8 subsets of [1,2,3] are generated, including the empty set and the full set.

Example 2

Input

[0]

Output

[[],[0]]

Explanation

The two subsets of [0] are the empty set [] and [0].

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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