Prime Ring Problem dfs

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.

Inputn (0 < n < 20).
OutputThe 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

6
8

Sample Output

Case 1:
1 4 3 2 5 6
1 6 5 2 3 4

Case 2:
1 2 3 8 5 6 7 4
1 2 5 8 3 4 7 6
1 4 7 6 5 8 3 2
1 6 7 4 3 8 5 2


代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <map>
#include <cmath>
int n,ans[20]={1};
using namespace std;
int vis[21];
bool isnum(int x)
{
    if(x<=1)return false;
    for(int i=2;i<=sqrt(x);i++)
    {
        if(x%i==0)return false;
    }
    return true;
}
void dfs(int k,int last)
{
    if(k==n)
    {
        if(!isnum(ans[0]+ans[n-1]))return;
        printf("%d",ans[0]);
        for(int i=1;i<n;i++)
            printf(" %d",ans[i]);
        putchar('
');
        return;
    }
    for(int i=2;i<=n;i++)
    if(!vis[i]&&isnum(last+i))
    {
        vis[i]=1;
        ans[k]=i;
        dfs(k+1,i);
        vis[i]=0;
    }
}
int main()
{
    int k=0;
    while(cin>>n)
    {
        vis[1]=1;
        printf("Case %d:
",++k);
        dfs(1,1);
        putchar('
');
    }
}