What is the optimal time complexity of solving Generate 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 Generate subsets?

The space complexity is O(1) 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 Generate 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 Generate 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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Python BasicsEasy

Generate subsets

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

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Problem Statement

Easy

Write a function generate_subsets(arr) that takes a list of distinct integers and returns all possible subsets (the power set). Return the result as a sorted list of sorted lists. Include the empty subset. Sort each individual subset, then sort the list of subsets by length first, then lexicographically.

Constraints

•0 <= len(arr) <= 10
•All elements in arr are distinct
•-100 <= arr[i] <= 100

Examples

Example 1

Input

arr = [1, 2, 3]

Output

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

Explanation

An array of 3 elements has 2^3 = 8 subsets, including the empty set and the full set.

Example 2

Input

arr = [1, 2]

Output

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

Explanation

2^2 = 4 subsets.

Example 3

Input

arr = [5]

Output

[[], [5]]

Explanation

2^1 = 2 subsets: the empty set and [5].

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

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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