hdu 1016

Problem Description

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

 

#include <stdio.h>
int a[39],b[21],c[21];
int n;
void dfs(int j)
{
     int i;
     if(j==n&&a[1+c[n]])
      { 
            for(i=1;i<n;i++)
            printf("%d ",c[i]);
            printf("%d",c[n]);
            printf("\n");
      }
       for(i=2;i<=n;i++)
           if(b[i]!=0&&a[c[j]+i]==1)
           {
                  c[j+1]=i;
                  b[i]=0;
                  dfs(j+1);
                  b[i]=i;
           }    
}
int main()
{
    int k;
    a[2]=a[3]=a[5]=a[7]=a[11]=a[13]=a[17]=a[17]=a[19]=a[23]=a[29]=a[31]=a[33]=a[37]=a[39]=1;
    c[1]=1;
    for(k=1;k<=20;k++)
        b[k]=k;
    k=1;
    while(scanf("%d",&n)!=EOF)
    {
         printf("Case %d:\n",k++);  
         dfs(1);
         printf("\n");                                           
    }
    return 0;
}