Question

I have written a program to print all the permutations of the string using backtracking method.

# include <stdio.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 i, int n) 
{
   int j; 
   if (i == n)
     printf("%s\n", a);
   else
   {
        for (j = i; j <= n; j++)
       {
              swap((a+i), (a+j));
              permute(a, i+1, n);
              swap((a+i), (a+j)); //backtrack
           }
   }
} 

/* Driver program to test above functions */
int main()
{
   char a[] = "ABC";  
   permute(a, 0, 2);
   getchar();
   return 0;
}

What would be time complexity here.Isn’t it o(n²).How to check the time complexity in case of recursion? Correct me if I am wrong.

Thanks.

Answer 1

The complexity is O(N*N!), You have N! permutations, and you get all of them.

In addition, each permutation requires you to print it, which is O(N) – so totaling in O(N*N!)