hdu1016 Prime Ring Problem（）

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

68

Sample Output

Case 1:1 4 3 2 5 61 6 5 2 3 4Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 8 3 21 6 7 4 3 8 5 2

#include <iostream>#include <cmath>#include <cstring>using namespace std;  const int maxn=100;int prime[maxn];int ans[maxn];int n;void ini(){int m=sqrt(maxn+0.5);memset(prime,0,sizeof(prime));for(int i=2;i<=m;i++)if(!prime[i])for(int j=i*i;j<=maxn;j+=i)prime[j]=1;}void dfs(int cur){if(cur>n){cout<<ans[1];for(int i=2;i<=n;i++)cout<<" "<<ans[i];cout<<endl;}if(cur==1){ans[cur]=1;dfs(cur+1);}elsefor(int i=1;i<=n;i++){int flag=1;for(int j=1;j<cur;j++){if(ans[j]==i){flag=0;break;}}if(cur!=n)if(prime[i+ans[cur-1]]==0&&flag){ans[cur]=i;dfs(cur+1);}if(cur==n){if(prime[i+ans[cur-1]]==0&&prime[i+ans[1]]==0&&flag){ans[cur]=i;dfs(cur+1);}}}}int main()  {int ncase=1;ini();while(cin>>n){cout<<"Case "<<ncase++<<":"<<endl;dfs(1);cout<<endl;}return 0; }