# C++ Program to Implement the Alexander Bogomolny’s UnOrdered Permutation Algorithm for Elements From 1 to N

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This is a C++ program to implement the Alexander Bogomolny’s UnOrdered Permutation Algorithm for elements from 1 to N

## Algorithms

Begin
function AlexanderBogomolny() to implement the Algorithms
Arguments:
Val[] = an array
N = number of elements taken as input.
K = level
Body of the function:
intialize l = -1
l = l+1
Val[k] = l
if (l == N)
Call function display(Val, N)
else
for i = 0 to N-1
if (Val[i] == 0)
Call AlexanderBogomolny(Val, N, i)
l = l - 1
Val[k] = 0
End

## Example

#include<iostream>
#include<iomanip>
using namespace std;
void display(const int *n, const int size) //to display the permutation
{
int i;
if (n != 0) {
for ( i = 0; i < size; i++) {
cout<<setw(4)<<n[i];
}
cout<<"\n";
}
}
void AlexanderBogomolny(int *Val, int N, int k) {
static int l = -1;
int i;
//At start,Assign level to 0.
l = l+1;
Val[k] = l;
if (l == N)
display(Val, N);
else
for (i = 0; i < N; i++)
//Assign values to the array if it is zero.
if (Val[i] == 0)
AlexanderBogomolny(Val, N, i);
//Decrement the level after all possible permutation after that level.
l = l-1;
Val[k] = 0;
}
int main() {
int i, N, cnt = 1;
cout<<"Enter the value to permute first N natural numbers: ";
cin>>N;
int Val[N];
for (i = 0; i < N; i++) {
Val[i] = 0;
cnt *= (i+1);
}
cout<<"\nThe number of permutations possible is: "<<cnt;
cout<<"\n\nPermutation using Alexander Bogomolyn's Algorithms \n";
AlexanderBogomolny(Val, N, 0);
return 0;
}

## Output

Enter the value to permute first N natural numbers: 5
The number of permutations possible is: 120
Permutation using Alexander Bogomolyn's Algorithms
1 2 3 4 5
1 2 3 5 4
1 2 4 3 5
1 2 5 3 4
1 2 4 5 3
1 2 5 4 3
1 3 2 4 5
1 3 2 5 4
1 4 2 3 5
1 5 2 3 4
1 4 2 5 3
1 5 2 4 3
1 3 4 2 5
1 3 5 2 4
1 4 3 2 5
1 5 3 2 4
1 4 5 2 3
1 5 4 2 3
1 3 4 5 2
1 3 5 4 2
1 4 3 5 2
1 5 3 4 2
1 4 5 3 2
1 5 4 3 2
2 1 3 4 5
2 1 3 5 4
2 1 4 3 5
2 1 5 3 4
2 1 4 5 3
2 1 5 4 3
3 1 2 4 5
3 1 2 5 4
4 1 2 3 5
5 1 2 3 4
4 1 2 5 3
5 1 2 4 3
3 1 4 2 5
3 1 5 2 4
4 1 3 2 5
5 1 3 2 4
4 1 5 2 3
5 1 4 2 3
3 1 4 5 2
3 1 5 4 2
4 1 3 5 2
5 1 3 4 2
4 1 5 3 2
5 1 4 3 2
2 3 1 4 5
2 3 1 5 4
2 4 1 3 5
2 5 1 3 4
2 4 1 5 3
2 5 1 4 3
3 2 1 4 5
3 2 1 5 4
4 2 1 3 5
5 2 1 3 4
4 2 1 5 3
5 2 1 4 3
3 4 1 2 5
3 5 1 2 4
4 3 1 2 5
5 3 1 2 4
4 5 1 2 3
5 4 1 2 3
3 4 1 5 2
3 5 1 4 2
4 3 1 5 2
5 3 1 4 2
4 5 1 3 2
5 4 1 3 2
2 3 4 1 5
2 3 5 1 4
2 4 3 1 5
2 5 3 1 4
2 4 5 1 3
2 5 4 1 3
3 2 4 1 5
3 2 5 1 4
4 2 3 1 5
5 2 3 1 4
4 2 5 1 3
5 2 4 1 3
3 4 2 1 5
3 5 2 1 4
4 3 2 1 5
5 3 2 1 4
4 5 2 1 3
5 4 2 1 3
3 4 5 1 2
3 5 4 1 2
4 3 5 1 2
5 3 4 1 2
4 5 3 1 2
5 4 3 1 2
2 3 4 5 1
2 3 5 4 1
2 4 3 5 1
2 5 3 4 1
2 4 5 3 1
2 5 4 3 1
3 2 4 5 1
3 2 5 4 1
4 2 3 5 1
5 2 3 4 1
4 2 5 3 1
5 2 4 3 1
3 4 2 5 1
3 5 2 4 1
4 3 2 5 1
5 3 2 4 1
4 5 2 3 1
5 4 2 3 1
3 4 5 2 1
3 5 4 2 1
4 3 5 2 1
5 3 4 2 1
4 5 3 2 1
5 4 3 2 1
Updated on 30-Jul-2019 22:30:26