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

 

*********************************************

 

 

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <vector>
using namespace std;

int n;
int vis[25];
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};
int ans[25];

void print(int m)
{
int i;
printf("%d",ans[1]);
for(i=2;i<=n;i++)
{
printf(" %d",ans[i]);
}
printf("\n");
}

void dfs(int point)
{
if(point==n && prime[ans[point]+ans[1]])
{
print(point);
}
else
{
for(int j=2;j<=n;j++)
{
if(!vis[j]&& prime[ans[point]+j])
{
ans[point+1]=j;
vis[j]=1;
dfs(point+1);
vis[j]=0;
}
}
}
}

int main()
{
int cas=0;
while(scanf("%d",&n)!=EOF)
{
cas++;
memset(vis,0,sizeof(vis));
vis[1]=1;
ans[1]=1;
printf("Case %d:\n",cas);
dfs(1);
printf("\n");
}
}