prime ring problem（hdu 1016）

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 36885 Accepted Submission(s): 16252

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>  
#include <string.h>  
  
int hash[30];  
int arr[100];  
int n;  
  
int juge(int num)  
{  
    int i;  
    for(i=2;i<num;i++)  
        if(num%i==0)  
            return 0;  
    return 1;  
}  
  
void DFS(int order,int index)  
{  
   int i;  
  
   arr[order]=index;
   hash[index]=1;  
     
   if(order==n)  
   
   {
      if(juge(arr[order]+arr[1]))  
     {  
        printf("1");  
       for(i=2;i<=n;i++)  
        printf(" %d",arr[i]);  
       printf("\n");  
     }   
     return ;  
   }
  
   for(i=1;i<=n;i++)  
   {  
       if(!hash[i]&&juge(arr[order]+i))  
       {  
           DFS(order+1,i);  
           hash[i]=0; 
       }  
   }  
  return ;  
}  
  
int main()  
{  
    int flag=1;  
    while(~scanf("%d",&n))  
    {  
      printf("Case %d:\n",flag++);  
      DFS(1,1);  
      printf("\n");  
    }  
    return 0;  
}