# Alexander Bogomolny’s UnOrdered Permutation Algorithm

The Alexander Bogomolyn’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.

1. It initializes the value of current level and permutes the remaining values to the higher levels.
2. As the assigning action of the values reaches to the highest level, it prints the permutation obtained.
3. This approach is recursively implemented to obtain all possible permutations.

## C++

 `// CPP program to implement Alexander ` `// Bogomolny’s UnOrdered Permutation Algorithm ` `#include ` `using` `namespace` `std; ` ` `  `// A function to print the permutation. ` `void` `print(``int` `perm[], ``int` `N) ` `{ ` `    ``for` `(``int` `i = 0; i < N; i++) ` `        ``cout << ``" "` `<< perm[i]; ` `    ``cout << ``"\n"``; ` `} ` ` `  `// A function implementing Alexander Bogomolyn  ` `// algorithm. ` `void` `AlexanderBogomolyn(``int` `perm[], ``int` `N, ``int` `k) ` `{ ` `    ``static` `int` `level = -1; ` ` `  `    ``// 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 Function ` `int` `main() ` `{ ` `    ``int` `i, N = 3; ` `    ``int` `perm[N] = { 0 }; ` `    ``AlexanderBogomolyn(perm, N, 0); ` `    ``return` `0; ` `} `

## Java

 `// Java program to implement  ` `// Alexander Bogomolny UnOrdered  ` `// Permutation Algorithm ` `import` `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 Bogomolyn 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 Code ` `public` `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. `

## C#

 `// C# program to implement  ` `// Alexander Bogomolny UnOrdered  ` `// Permutation Algorithm ` `using` `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 Bogomolyn 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 Code ` `public` `static` `void` `Main () ` `{ ` `    ``int` `N = 3; ` `    ``int` `[]perm = ``new` `int``[N]; ` `    ``AlexanderBogomolyn(perm, N, 0); ` `} ` `} ` ` `  `// This code is contributed  ` `// by anuj_67. `

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 contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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