Alexander Bogomolny’s UnOrdered Permutation Algorithm - GeeksforGeeks

25 Feb, 2022
Alexander Bogomolny’s algorithm is used to permute first N natural numbers. Given the value of N, we have to output all the permutations of numbers from 1 to N.Examples:  
Input : 2
Output : 1 2
         2 1

Input : 3
Output : 1 2 3
         1 3 2
         2 1 3
         3 1 2
         2 3 1
         3 2 1
The idea is to maintain an array to store the current permutation. A static integer level variable is used to define these permutations.  
It initializes the value of current level and permutes the remaining values to the higher levels.As the assigning action of the values reaches the highest level, it prints the permutation obtained.This approach is recursively implemented to obtain all possible permutations.
It initializes the value of current level and permutes the remaining values to the higher levels.
As the assigning action of the values reaches the highest level, it prints the permutation obtained.
This approach is recursively implemented to obtain all possible permutations.
 
 
C++
Java
Python3
C#
Javascript
#include<bits/stdc++.h>using namespace std; void solve(vector<int> &v,int n,string &s,vector<vector<int>> &vv){    if(v.size()==n)    {        vv.push_back(v);        return;    }    for(int i=0;i<n;i++)    {        if(s[i]!='1')        {            s[i]='1';            v.push_back(i+1);            solve(v,n,s,vv);            s[i]='0';            v.pop_back();        }    }     } int main(){    int n=3    vector<int> v;    vector<vector<int>> vv;    string s;    for(int i=0;i<n;i++) s+='0';    solve(v,n,s,vv);    for(int i=0;i<vv.size();i++)    {        for(int j=0;j<vv[i].size();j++)        {            cout<<vv[i][j]<<" ";        }        cout<<endl;    }}
// Java program to implement// Alexander Bogomolny UnOrdered// Permutation Algorithmimport java.io.*; class GFG{static int level = -1; // A function to print// the permutation.static void print(int perm[], int N){    for (int i = 0; i < N; i++)        System.out.print(" " + perm[i]);    System.out.println();} // A function implementing// Alexander Bogomolny algorithm.static void AlexanderBogomolyn(int perm[],                               int N, int k){     // Assign level to    // zero at start.    level = level + 1;    perm[k] = level;     if (level == N)        print(perm, N);    else        for (int i = 0; i < N; i++)             // Assign values            // to the array            // if it is zero.            if (perm[i] == 0)                AlexanderBogomolyn(perm, N, i);     // Decrement the level    // after all possible    // permutation after    // that level.    level = level - 1;         perm[k] = 0;} // Driver Codepublic static void main (String[] args){    int i, N = 3;    int perm[] = new int[N];    AlexanderBogomolyn(perm, N, 0);}} // This code is contributed by anuj_67.
# Python3 program to implement Alexander# Bogomolny’s UnOrdered Permutation Algorithm # A function to print permutation.def printn(perm, N):    for i in range(N):        print(" ",perm[i], sep = "", end = "")    print()     # A function implementing Alexander Bogomolny# algorithm.level = [-1]def AlexanderBogomolyn(perm, N, k):     # Assign level to zero at start.    level[0] = level[0] + 1    perm[k] = level[0]    if (level[0] == N):        printn(perm, N)    else:        for i in range(N):                         # Assign values to the array            # if it is zero.            if (perm[i] == 0):                AlexanderBogomolyn(perm, N, i)         # Decrement the level after all possible    # permutation after that level.    level[0] = level[0] - 1         perm[k] = 0    return # Driver codeN = 3perm = [0]*NAlexanderBogomolyn(perm, N, 0) # This code is contributed by SHUBHAMSINGH10
// C# program to implement// Alexander Bogomolny UnOrdered// Permutation Algorithmusing System; class GFG{static int level = -1; // A function to print// the permutation.static void print(int []perm,                  int N){    for (int i = 0; i < N; i++)        Console.Write(" " + perm[i]);    Console.WriteLine();} // A function implementing// Alexander Bogomolny algorithm.static void AlexanderBogomolyn(int []perm,                               int N, int k){     // Assign level to    // zero at start.    level = level + 1;    perm[k] = level;     if (level == N)        print(perm, N);    else        for (int i = 0; i < N; i++)             // Assign values            // to the array            // if it is zero.            if (perm[i] == 0)                AlexanderBogomolyn(perm, N, i);     // Decrement the level    // after all possible    // permutation after    // that level.    level = level - 1;         perm[k] = 0;} // Driver Codepublic static void Main (){    int N = 3;    int []perm = new int[N];    AlexanderBogomolyn(perm, N, 0);}} // This code is contributed// by anuj_67.
<script> // Javascript program to implement// Alexander Bogomolny UnOrdered// Permutation Algorithm let level = -1;   // A function to print// the permutation.function print(perm, N){    for (let i = 0; i < N; i++)        document.write(" " + perm[i]);    document.write("<br/>");}   // A function implementing// Alexander Bogomolny algorithm.function AlexanderBogomolyn(perm, N, k){       // Assign level to    // zero at start.    level = level + 1;    perm[k] = level;       if (level == N)        print(perm, N);    else        for (let i = 0; i < N; i++)               // Assign values            // to the array            // if it is zero.            if (perm[i] == 0)                AlexanderBogomolny(perm, N, i);       // Decrement the level    // after all possible    // permutation after    // that level.    level = level - 1;           perm[k] = 0;}// driver program     let i, N = 3;    let perm = Array.from({length: N}, (_, i) => 0);    AlexanderBogomolny(perm, N, 0);     </script>
Output:  
1 2 3
1 3 2
2 1 3
3 1 2
2 3 1
3 2 1
This article is contributed by Vineet Joshi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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