Prime Ring Problem HDU - 1016

A ring is compose of n circles as shown in diagram. Put natural number 1, 2, ..., n into each circle separately, and the sum of numbers in two adjacent circles should be a prime.   Note: the number of first circle should always be 1.     
Input
n (0 < n < 20).  
Output
The output format is shown as sample below. Each row represents a series of circle numbers in the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements. Print solutions in lexicographical order.  You are to write a program that completes above process.  Print a blank line after each case.  
Sample Input
68
Sample Output
Case 1:1 4 3 2 5 61 6 5 2 3 4Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 8 3 21 6 7 4 3 8 5 2
#include <iostream>#include <algorithm>#include <cstdio>#include <cstring>#include <cmath>#define inf 0x3f3f3f3fusing namespace std;int book[22];int a[22];int is_prime(int x){    for(int i=2;i<=sqrt(x);i++)    {        if(x%i==0)            return 0;    }    return 1;}void dfs(int n,int k){    if(k>n)    {        if(is_prime(a[k-1]+a[1])==0)            return ;    }    int i;    if(k>n)    {        printf("%d",a[1]);        for(i=2;i<=n;i++)        {            printf(" %d",a[i]);        }        printf("\n");        return ;    }    for(i=2;i<=n;i++)    {        if(book[i]==0&&is_prime(i+a[k-1])==1)        {            a[k]=i;            book[i]=1;            dfs(n,k+1);            book[i]=0;        }    }}int main(){    int n,num=0;    while(~scanf("%d",&n))    {        memset(book,0,sizeof(book));        num++;        a[1]=1;book[1]=1;        printf("Case %d:\n",num);        dfs(n,2);        printf("\n");    }    return 0;}

                                             
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