This problem requires generating all possible subsets of a given array, which may contain duplicate elements, while ensuring that the solution set does not contain duplicate subsets. The core idea is to use backtracking to explore all possible combinations of elements, and carefully handle duplicates to avoid generating identical subsets.

We use sorting and a conditional check within the backtracking step to efficiently skip duplicate elements. This ensures that each unique subset is generated only once.

Intuition:

The backtracking algorithm can be visualized as a decision tree where at each element, we either include it in the subset or exclude it. To avoid duplicate subsets, we sort the input array and skip over duplicate elements when we're in the 'exclude' branch of the decision tree. This skipping is the key to ensuring uniqueness of the subsets.

Step-by-step thinking:

Sort the input array to group duplicate elements together.
Initialize an empty list to store the resulting subsets.
Start a backtracking function with the starting index of the array, the current subset, and the result list.
In the backtracking function, first add a copy of the current subset to the result list. This represents one possible subset.
Iterate through the remaining elements of the array, starting from the current index.
If the current element is a duplicate of the previous element, and it's not the first time we're considering this element in the current level of recursion, skip it.
Include the current element in the subset and recursively call the backtracking function with the next index.
After the recursive call returns, remove the last element from the subset to backtrack and explore other possibilities.

Time Complexity: O(2^N), where N is the number of elements in the input array. In the worst case, each element can either be included or excluded, resulting in 2^N possible subsets. The cost of the loop inside the `backtrack` method does not change the overall exponential complexity because it's bounded by the number of elements in the array.
Space Complexity: O(N), where N is the number of elements in the input array. This is primarily due to the space used by the recursion stack during the backtracking process. In addition, the space used to store the subsets is also O(2^N * N) in the worst case.

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159. Subsets II

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