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<cstdio>
#include<string.h>
using namespace std;
int n,cnt=1;
int vis[21];int A[21];
int prime[38]= {0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1};
void dfs(int cur)
{
if(cur==n&&prime[A[0]+A[n-1]])
{
cout<<A[0];
for(int i=1;i<n;i++)
cout<<" "<<A[i];
cout<<endl;
}
else for(int i=2;i<=n;i++)
if(!vis[i]&&prime[i+A[cur-1]])
{
A[cur] = i;
vis[i]=1;
dfs(cur+1);
vis[i]=0;
}
}
int main(){
A[0]=1;
while(cin>>n)
{
memset(vis,0,sizeof(vis));
cout<<"Case "<<cnt++<<":"<<endl;
dfs(1);
// cout<<endl;
}
return 0;
}