hdu 1016 Prime Ring Problem

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

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

Source

Asia 1996, Shanghai (Mainland China)

思路：使用深搜遍历。

代码：

#include   
#include   
#include   
using namespace std;  
int prim[40]= {0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0};  
int n,vis[21];  
void dfs(int num,int dij[])  
{  
    if(num>n&&prim[dij[n]+dij[1]])  
    {  
        printf("%d",dij[1]);  
        for(int i=2; i<=n; i++)  
            printf(" %d",dij[i]);  
        printf("\n");  
    }  
    else  
        for(int i=2; i<=n; i++)  
            if(!vis[i]&&prim[i+dij[num-1]])  
            {  
                vis[i]=1;  
                dij[num]=i;  
                dfs(num+1,dij);  
                vis[i]=0;  
            }  
}  
  
  
int main()  
{  
    int t=1,dij[25];  
    while(~scanf("%d",&n))  
    {  
        memset(dij,0,sizeof(dij));  
        memset(vis,0,sizeof(vis));  
        dij[1]=1;  
        vis[1]=1;  
        printf("Case %d:\n",t++);  
        dfs(2,dij);  
        printf("\n");  
    }  
    return 0;  
}