# C++ Program to Implement Alexander Bogomolny’s UnOrdered Permutation Algorithm

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This is a C++ program to implement the Alexander Bogomolyn’s Unordered Permutation algorithm for elements from 1 to N.

Problem Description

1. The Alexander Bogomolyn’s algorithm is to permute first ‘N’ natural numbers.
2. The time complexity of this algorithm is O(n!).

Problem Solution

1. This algorithm takes N value.
2. It initializes the value current level and permutes the remaining values to the higher levels.
3. As the assigning action of the values reaches to the highest level, it prints the permutation obtained.
4. Exit.

Program/Source Code

C++ Program to implement the Alexander Bogomolyn’s algorithm.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

```#include<iostream>
#include<iomanip>

using namespace std;

// A function to print the permutation.
void print(const int *v, const int size)
{
int i;
// Print the array if it is non-empty.
if (v != 0)
{
for ( i = 0; i < size; i++)
{
cout<<setw(4)<<v[i];
}
cout<<"\n";
}
}

// A function implementing Alexander Bogomolyn algorithm.
void AlexanderBogomolyn(int *Value, int N, int k)
{
static int level = -1;
int i;
// Assign level to zero at start.
level = level+1;
Value[k] = level;

if (level == N)
print(Value, N);
else
for (i = 0; i < N; i++)
// Assign values to the array if it is zero.
if (Value[i] == 0)
AlexanderBogomolyn(Value, N, i);

// Decrement the level after all possible permutation after that level.
level = level-1;
Value[k] = 0;
}

int main()
{
int i, N, count = 1;
cout<<"Enter the N value to permute first N natural numbers: ";
cin>>N;
int Value[N];

for (i = 0; i < N; i++)
{
Value[i] = 0;
count *= (i+1);
}

// Print the permutation's count.
cout<<"\nThe number of permutations possible is: "<<count;

// Print the permutation.
cout<<"\n\nPermutation using Alexander Bogomolyn's algorithm: \n";
AlexanderBogomolyn(Value, N, 0);

return 0;
}```
Program Explanation

1. Take the N value from the user.
2. Compute the factorial which will be the total number of permutation for that N value.
3. Call AlexanderBogomolyn(), with array V[], N and K be the current index of the array.
4. Inside the function, a static integer variable level will be defining the array level to be modified to generate the permutation.
5. As the level value reaches the highest value ‘N’ then print the array as the generated permutation.
6. Likewise, print all the permutation.
7. Exit.

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Runtime Test Cases
```Enter the N value to permute first N natural numbers: 3

The number of permutations possible is: 6

Permutation using Alexander Bogomolyn's algorithm:
1   2   3
1   3   2
2   1   3
3   1   2
2   3   1
3   2   1

Case 2:
Enter the N value to permute first N natural numbers: 4

The number of permutations possible is: 24

Permutation using Alexander Bogomolyn's algorithm:
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```

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