Problem Statement

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

Example 1:

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

Example 2:

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

Constraints:

• 1 <= nums.length <= 8
• 10 <= nums[i] <= 10

Problem Link

Permutations II - LeetCode

Recursion Tree

Code

class Solution {
public:
   
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        
        int n = nums.size();
        vector<vector<int>> res;
        
        perm(nums,0,n-1,res);
            return res;
        
        
    }
    
    void perm(vector<int> &nums,int l,int r,vector<vector<int>> &res)
    {
        if(l==r)
            res.push_back(nums);
        
        unordered_set <int> st;
        for(int i=l;i<=r;i++)
        {
            if(st.find(nums[i])!=st.end())
                continue;
            
            st.insert(nums[i]);
            
            swap(nums[i],nums[l]);
            
            perm(nums,l+1,r,res);
             
            swap(nums[i],nums[l]);
            
        }
    }
};

Complexity Analysis:

Time Complexity: In worst case O(n*n!)

Note that there are n! permutations and it requires O(n) time to print a permutation.