Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 37703    Accepted Submission(s): 16659

 

 

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

 

 

Source

 

 

 

1 #include 
     
       2 #include 
      
        3 #include 
       
         4 using namespace std; 5 bool vis[20]; 6 int a[20]; 7 int n; 8 bool prime(int m) 9 {10     if(m==1) return false;11     if(m==2) return true;12     for(int i=2;i*i<=m;i++)13         if(m%i==0) return false;14     return true;15 }16 void dfs(int m)17 {18     if(m==n&&prime(a[m-1]+a[0])){19         for(int i=0;i
        
         >n){43         cout<<"Case "<<++j<<":"<