hdu 1016 Prime Ring Problem

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 17618    Accepted Submission(s): 7937

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
  
  
  
  

   
    
  
  
  
  

   
   生成素数环，用dfs
  
  
  
  

   
    
  
  
  
  

   
   AC代码：
  
  
  
  

   
   
#include <iostream>
#include <cstring>
#include <cmath>

using namespace std;
int vis[25],a[25],vis_p[60],n;

void dfs(int cur)
{
    if(cur==n&&!vis_p[a[0]+a[n-1]])
    {
      for(int i=0;i<n-1;i++)
      cout<<a[i]<<" ";            //最后一个数后面不能输出空格
      cout<<a[n-1];
      cout<<endl;
    }
    else
    for(int i=2;i<=n;i++)
    {
        if(!vis[i]&&!vis_p[i+a[cur-1]])
        {
            a[cur]=i;
            vis[i]=1;
            dfs(cur+1);
            vis[i]=0;
        }
    }
}
int main()
{

    int m = sqrt(50);
    memset(vis_p,0,sizeof(vis_p));
     for(int i=2;i<m;i++)
     if(!vis_p[i])
      for(int j=i*i;j<=50;j+=i) vis_p[j]=1;
     int c=0;
     a[0]=1;
     while(cin>>n)
     {
         memset(vis,0,sizeof(vis));
         c++;
         cout<<"Case "<<c<<":"<<endl;
         dfs(1);
         cout<<endl;

     }
     return 0;

}