A permutation, also called an “arrangement number” or “order,” is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. A string of length n has n! permutation.

Below are the permutations of string ABC.

ABC, ACB, BAC, BCA, CAB, CBA

// C program to print all permutations with duplicates allowed

## include <stdio.h>

## include <string.h>

/* Function to swap values at two pointers */

```
void swap(char *x, char *y)
{
char temp;
temp = *x;
*x = *y;
*y = temp;
}
```

/* Function to print permutations of string

This function takes three parameters:

1. String

2. Starting index of the string

3. Ending index of the string. */

```
void permute(char *a, int l, int r)
{
int i;
if (l == r)
printf("%s\n", a);
else
{
for (i = l; i <= r; i++)
{
swap((a+l), (a+i));
permute(a, l+1, r);
swap((a+l), (a+i)); //backtrack
}
}
}
```

/* Driver program to test above functions */

```
int main()
{
char str[] = "ABC";
int n = strlen(str);
permute(str, 0, n-1);
return 0;
}
```

### Output:

ABC

ACB

BAC

BCA

CBA

CAB

### Algorithm Paradigm: Backtracking

Time Complexity: O(n*n!)