46. Permutations

Problem Statement

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

Example 1:

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

Example 2:

Input: nums = [0,1]
Output: [[0,1],[1,0]]

Example 3:

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

Constraints:

• 1 <= nums.length <= 6

• -10 <= nums[i] <= 10

• All the integers of nums are unique.

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

C++

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);
    }
};

Approach 2:

Elimination of map

C++

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);
    }
};

Approach 3:

C++

Approach 4:

C++

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