Problem description:

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

Example 1:

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Input: nums = [1,1,2]
Output:
[[1,1,2],
 [1,2,1],
 [2,1,1]]

Example 2:

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Input: nums = [1,2,3]
Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

Solution:

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class Solution:
    def _permute(self, nums, s, k):
        if len(s) == k:
            print("---")
            self.permutations.append(s[:])
        
        for i in range(len(nums)):
            if i > 0 and nums[i] == nums[i-1]:
                continue
            
            s.append(nums[i])
            print(s)
            self._permute(nums[:i] + nums[i+1:], s, k) # remove nums[i] from nums
            s.pop()
            
    def permuteUnique(self, nums: List[int]) -> List[List[int]]:
        self.permutations = []
        self._permute(sorted(nums), [], len(nums))
        return self.permutations

output of the code:

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

time complexity: $O()$
space complexity: $O()$
reference:
related problem: