Prime Ring Problem

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 Asia 1996, Shanghai (Mainland China)

题外话：

省赛的失利也不能阻挡我前进的脚步，经历过就是一件好事，正如老师所说的，结果谁也没法预测，但这个过程是实实在在的，自己可以在其中收获很多东西。人生中需要经历很多事情，有些事情，只有亲身经历过才会懂。

解题思路：

素数环要求任何相邻的两个数相加的和必须为素数。用DFs，从一年前期末考试两个多小时也没做出来这个题到现在的一次Ac，自己真的进步了。

代码：

#include 
  
   
#include 
   
     #include 
    
      #include 
     
       using namespace std; const int maxn=25; bool visit[maxn]; int num[maxn]; int n; bool prime(int n) { if(n==1) return false; if(n==2) return true; if(n%2==0) return false; for(int i=3;i<=(int)sqrt(n);i+=2) if(n%i==0) return false; return true; } void dfs(int step) { if(step>n&&prime(num[n]+num[1])) { for(int i=1;i<=n-1;i++) cout<
      
       >n) { cout<<"Case "<

[ACM] 1016 Prime Ring Problem （深度优先搜索）

Prime Ring Problem