C Program to print all permutations of a given string
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
// 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.