Prime number ring problem (backtracking method)

The prime number ring is a computer program problem. It refers to the n integers from 1 to n forming a ring. If any two adjacent numbers are added, the result is a prime number, then the ring becomes a prime number ring .

  Now it is required to enter an n, find the number of prime number rings in a circle of n numbers, and specify that the first number is 1.

#include<iostream>
#include<math.h>
using namespace std;
int n=0;
int a[100];       //对应环 
int visit[100];  //标记数组 0表示未用 1表示已用 
int check(int k)  //判断数字x是否为整数 
{
	int i,n;
	n=(int)sqrt(k);
	for(i=2;i<=n;i++)
		if(k%i==0) return 0;
	return 1;     		
}

void dfs(int step)
{
	if(step==n&&check(a[0]+a[n-1])==1) //全部填满而且第一个元素和最后一个元素满足就输出 
	{
		for(int i=0;i<n;i++)
			cout<<a[i]<<' ';
			cout<<endl;
			return ;
	}
	else
	{
		for(int i=2;i<=n;i++)
		{
			if(visit[i]==0&&check(i+a[step-1])==1){    //i没有被占用且与前一个元素符合 
				a[step]=i;
				visit[i]=1;
				dfs(step+1);
				visit[i]=0;
			}
		}
	}
	
}
int main(void)
{
	cin>>n;
	a[0]=1;  //因为是环所以第一个元素固定 
	visit[1]=1; //1已用 
	dfs(1);	//从第一个元素开始 
	return 0;	
} 

This kind of backtracking problem is similar to the Eight Queens Hamiltonian circuit problem.