USE C++ LANGUAGE PERMUTATIONS! As you know from Discrete Math, a permutation is
ID: 3819313 • Letter: U
Question
USE C++ LANGUAGE
PERMUTATIONS! As you know from Discrete Math, a permutation is any possible ordering of the distinct items of a set S. If SI n, there are n! permutations. This means that for large sets, it is computationally infeasible to generate all possible permutations. One well-known algorithm for generating set permutations (at least for small sets) is presented below: ALGORITHM Johnson-Trotter (r) Input: a positive integer n Output: A list of all permutations of 1,2, n initialize the first permutation as 12 n with directions pointing left while the last permutation has a mobile element find its largest mobile element k swap k and the element to which k is directed reverse the direction of all elements that are larger than k add the new permutation to the list Note: an element is mobile if its direction points to a smaller adjacent element. Example: 1 2 3 1 3 2 3 1 2 3 2 1 2 3 1 2 1 3 REQUIREMENTS Design and implement a program to generate all permutations of the set of least n positive integers. INPUT an integer n with 1 S n S 25. OUTPUT: The tag "There are x permutations of the set {1, 2 n where x n! a list of all permutations of the set f1, 2, H, one per line EXAMPLE OUTPUT There are 6 permutations of the set 1, 2, 3Explanation / Answer
#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 Johnson-Trotter(char *a, int l, int r)
{
int i;
if (l == r)
printf("%s ", a);
else
{
for (i = l; i <= r; i++)
{
swap((a+l), (a+i));
Johnson-Trotter(a, l+1, r);
swap((a+l), (a+i)); //backtrack
}
}
}
/* Driver program to test above functions */
int main()
{
char str[] = "ABC"; // Replace ABC with your given String for which you want to calculate permutation.
int n = strlen(str);
Johnson-Trotter(str, 0, n-1);
return 0;
}
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