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.
Source: Mathword(http://mathworld.wolfram.com/Permutation.html)
Below are the permutations of string ABC.
ABC ACB BAC BCA CBA CAB
Here is a solution that is used as a basis in backtracking.
// 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);
//backtrack
swap((a + l), (a + i));
}
}
} // Driver code 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!) Note that there are n! permutations and it requires O(n) time to print a permutation.
Auxiliary Space: O(r – l)
Note: The above solution prints duplicate permutations if there are repeating characters in the input string. Please see the below link for a solution that prints only distinct permutations even if there are duplicates in input.
Print all distinct permutations of a given string with duplicates.
Permutations of a given string using STL
Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.