Permutations II

Problem Description

Given a collection of numbers, nums, that might contain duplicates, return all possible unique permutations in any order.

Key Insights

• The problem requires generating all unique permutations of an array that may contain duplicates.
• Using a backtracking approach allows us to explore all possible arrangements while avoiding duplicates.
• Sorting the input array helps in easily skipping over duplicates during the permutation generation process.

Space and Time Complexity

Time Complexity: O(n! * n), where n is the length of the input array. The n! factor comes from generating all permutations, and the n factor comes from copying the current permutation to the result. Space Complexity: O(n), for storing the current permutation and the result list.

Solution

To solve the problem, we use a backtracking approach with the following steps:

1. Sort the input array to facilitate handling duplicates.
2. Create a recursive function that builds permutations.
3. Use a boolean array to track which elements are included in the current permutation.
4. Skip duplicates by checking adjacent elements during the recursive calls.
5. When a valid permutation is found, add it to the result list.

Code Solutions