Subsets II

Problem Description

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.

Key Insights

• The problem requires generating all possible subsets of a given array.
• Duplicates in the input array can lead to duplicate subsets in the output.
• A backtracking approach is suitable to explore all possible combinations of elements.
• Sorting the input array helps in efficiently skipping over duplicates during subset generation.

Space and Time Complexity

Time Complexity: O(2^n), where n is the number of elements in the input array. Each element can either be included or excluded from a subset.

Space Complexity: O(n), for storing the current subset and the output list of subsets.

Solution

To solve the problem, we can use a backtracking algorithm. The approach involves the following steps:

1. Sort the Input: Start by sorting the input array. This helps in easily identifying duplicates and skipping them.
2. Backtracking Function: Create a recursive function that takes the current index and the current subset as arguments. In each call:
   • Add the current subset to the result list.
   • Iterate through the elements starting from the current index.
   • For each element, if it's a duplicate (i.e., the element is the same as the previous element), skip it to avoid duplicate subsets.
   • Include the current element in the subset and call the function recursively.
   • After the recursive call, backtrack by removing the last element added to the subset.
3. Return Results: Finally, return the list of all unique subsets.

Code Solutions