# Alexander Bogomolny’s UnOrdered Permutation Algorithm in C++

Here, we are given a number N. Our task is to find unorder permutation of N using Alexander Bogomolny’s UnOrdered Permutation Algorithm.

Let’s discuss permutation first,

A permutation is the number of ways an item in a set can be uniquely ordered is called a permutation.

Example − Permutation of {4,9,2} would be {4,9,2}, {4,2,9}, {9,4,2}, {9,2,4}, {2,4,9} and {2,9,4}.

Permutations have found usage in defining switching networks in computer networking, parallel processing and also used in a variety of cryptographic algorithms.

Alexander Bogomolny's Unordered Permutation Algorithm

This algorithm computes all possible permutations of first N natural numbers. Given a number N, the permutations are computed from 1 to N.

Let’s take an example to understand the problem,

Input

N = 3

Output

1,2,3 ; 1,3,2 ; 2,1,3 ; 2,3,1 ; 3,1,2 ; 3,2,1

## Algorithm

1. Build a function with an array, number N, and an integer k as
parameters
2. Initialize the level, as level increases permute the rest of the values
3. When the recursion condition is reached all its values are printed.

## Example

Program to show the implementation of our algorithm −

Live Demo

#include <iostream>
using namespace std;
int level = -1;
void AlexanderBogomolyn(int permutations[], int N, int k) {
level = level + 1;
permutations[k] = level;
if (level == N) {
for (int i = 0; i < N; i++)
cout<<permutations[i]<<"\t";
cout<<endl;
}
else{
for (int i = 0; i < N; i++)
if (permutations[i] == 0)
AlexanderBogomolyn(permutations, N, i);
}
level = level - 1;
permutations[k] = 0;
}
int main(){
int N = 4;
int permutations[N] = { 0 };
cout<<"All permutations are :\n";
AlexanderBogomolyn(permutations, N, 0);
return 0;
}

## Output

All permutations are :
1 2 3 4
1 2 4 3
1 3 2 4
1 4 2 3
1 3 4 2
1 4 3 2
2 1 3 4
2 1 4 3
3 1 2 4
4 1 2 3
3 1 4 2
4 1 3 2
2 3 1 4
2 4 1 3
3 2 1 4
4 2 1 3
3 4 1 2
4 3 1 2
2 3 4 1
2 4 3 1
3 2 4 1
4 2 3 1
3 4 2 1
4 3 2 1

Updated on: 06-Aug-2020

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