What is the optimal time complexity of solving Subsets II?

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 II?

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 II?

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 II?

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 II

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

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Problem Statement

Easy

Given an integer array nums that may contain duplicates, return all possible subsets (the power set).

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

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

Constraints

•1 <= nums.length <= 10
•-10 <= nums[i] <= 10

Examples

Example 1

Input

[1,2,2]

Output

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

Explanation

Unlike the basic subsets problem, [1,2,2] has duplicate 2's. We skip duplicate subsets like having two copies of [2].

Example 2

Input

[0]

Output

[[],[0]]

Explanation

Same as basic subsets for a single element.

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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