Prime Ring Problem

L - Prime Ring Problem

Time Limit:2000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

Submit  Status

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<iostream>
#include<cstring>
#include<math.h>
using namespace std;
int path[22];
bool visited[22];
int n,num=1;
bool isprime(int x){
     for(int i=2;i<=(int)sqrt(x);i++)
         if(x%i==0)
             return false;
     return true;
}
void dfs(int v,int cnt){
     if(cnt==n){        
          for(int i=0;i<n-1;i++)
             cout<<path[i]<<" ";
          cout<<path[n-1]<<endl;
     }
     if(cnt>n)
        return ;
     for(int i=2;i<=n;i++){
          if(!visited[i] && isprime(i+v) ){
              if(cnt==n-1){
                  if(!isprime(i+path[0]))
                      continue;
              }
               path[cnt]=i;
               visited[i]=true;
               dfs(i,cnt+1);
               visited[i]=false;
          }      
     }   
}
int main(){
    while(cin>>n){
          memset(visited,false,sizeof(visited));  
          path[0]=1;   
          visited[1]=true;     
          cout<<"Case "<<num++<<":"<<endl;  
          dfs(1,1);        
          cout<<endl;     
    }
//system("pause");
return 0;
}