> For the complete documentation index, see [llms.txt](https://coding-9.gitbook.io/untitled/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://coding-9.gitbook.io/untitled/recursion-and-backtracking/46.-permutations.md).

# 46. Permutations

## Problem Statement

<br>

Given an array `nums` of distinct integers, return *all the possible permutations*. You can return the answer in **any order**.

&#x20;

**Example 1:**

<pre><code><strong>Input: nums = [1,2,3]
</strong><strong>Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
</strong></code></pre>

**Example 2:**

<pre><code><strong>Input: nums = [0,1]
</strong><strong>Output: [[0,1],[1,0]]
</strong></code></pre>

**Example 3:**

<pre><code><strong>Input: nums = [1]
</strong><strong>Output: [[1]]
</strong></code></pre>

&#x20;

**Constraints:**

* `1 <= nums.length <= 6`
* `-10 <= nums[i] <= 10`
* All the integers of `nums` are **unique**.<br>

<br>

## Intuition

```
Take an element at every position

Approach 1 :
MAintain a map for marking which element is taken and push the elements accordingly

Approach 2: Eliminate the extra map space

Basically, Swap elemnts such that all elemets gets a chance at all position

Once swapped, swap other elements of remaining array
```

### Links

<https://leetcode.com/problems/permutations/description/>

### Video Links

<https://www.youtube.com/watch?v=YK78FU5Ffjw&ab_channel=takeUforward>\
\
<https://www.youtube.com/watch?v=f2ic2Rsc9pU&ab_channel=takeUforward>

### Approach 1:

```
Taking map
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    vector<vector<int>> find_ans(vector<vector<int>> &ans, vector<int> &nums, 
            vector<int> &temp, unordered_map<int, bool> &mp){

        if(temp.size() == nums.size()){
            ans.push_back(temp);
            return ans;
        }
        
        /*
            Pushing and marking the element in the map
            When we return unmark the array and proceed
        */

        for(int i=0; i<nums.size(); i++){
            if(mp.find(i) == mp.end()){
                temp.push_back(nums[i]);
                mp[i] = true;

                find_ans(ans, nums, temp, mp);

                temp.pop_back();
                mp.erase(i);
            }
        }
        
        return ans;
    }

    vector<vector<int>> permute(vector<int>& nums) {
        vector<vector<int>> ans;
        unordered_map<int, bool> mp;
        vector<int> temp;
        
        return find_ans(ans, nums, temp, mp);
    }
};
```

{% endcode %}

### Approach 2:

```
Elimination of map
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    vector<vector<int>> find_ans(vector<vector<int>> &ans, vector<int> &nums, int index){
        if(index == nums.size()){
            ans.push_back(nums);
            return ans;
        }

        for(int i=index; i<nums.size(); i++){
            swap(nums[index], nums[i]);
            find_ans(ans, nums, index+1);
            swap(nums[index], nums[i]);
        }

        return ans;
    }

    vector<vector<int>> permute(vector<int>& nums) {
        vector<vector<int>> ans;
        return find_ans(ans, nums,  0);
    }
};
```

{% endcode %}

### Approach 3:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 4:

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

###