Description

Given a set of n≧1 elements, the problem is to print all possible permutations of this set. For example, if the set is (1,2,3), then the set of permutations is {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,2,1), (3,1,2)}.

 

<Hint1>

Looking at the case of four elements (1,2,3,4). The answer can be constructed by writing

1. ‘1’ followed by all the permutations of (2,3,4)
2. ‘2’ followed by all the permutations of (1,3,4)
3. ‘3’ followed by all the permutations of (1,2,4)
4. ‘4’ followed by all the permutations of (1,2,3)

 

<Hint2>

A recursive method to implement the above idea is as follows:

Consider the case of (1,2,3,4), that is, n=4.

1. Place the set elements in a global array, and set the position index “k” as 0.
2. Use a for-loop to “swap” (or exchange) the 1st element with the 1st element, the 2nd element, the 3rd element, and the 4thelement, respectively.
   • In each loop-iteration:
     1. increment the position index “k” by 1 (for considering only the remaining elements in the following recursive call);
     2. use the updated k to recursively call your permutation function;
     3. note that because you use a global array, remember to swap back the two elements after the iteration.
3. In a recursive-call path, when k reaches n, it means that you get a possible permutation.

You will be provided with the following sample code, and asked to implement function "Swap" and "Perm.

 

#include <stdio.h>

char list[10];

void show(int n)
{
    int i;
    printf("(%c", list[0]);
    for (i=1; i<n; i++) {
        printf(",%c", list[i]);
    }
    printf(")\n");
}

void Swap(int k, int i)
{
    /*your code*/
}

void Perm(int k, int n)
{
    /*your code*/
}

int main(void)
{
    int num, i;

    scanf("%d", &num);

    for(i=0; i<num; i++)
        list[i] = '1'+i;
    Perm(0, num);

    return 0;
}

Input

The decimal number n that represents the number of elements in the set.

(1≦n≦5)

Output

In the output you should print all the permutations.

Be sure to add a newline character '\n' at the end of each line.

Sample Input  Download

Sample Output  Download

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