HDU 1016 Prime Ring Problem （深搜）

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<cstring>
using namespace std;
int a[10005],vis[10005];
int n;
bool isprime(int x){//判断是不是素数 
	if(x==1||x==0)
	    return 0;
	for(int i=2;i<=x/2;i++){
		if(x%i==0)
		    return 0;
	}
	return 1;
}
void dfs(int step){
	if(step==n+1){//满足条件 
		for(int i=1;i<=n;i++){
			if(i!=1)
			    cout<<" ";
			cout<<a[i];
		}
		cout<<endl;
		return ; //跳出 
	}
	for(int i=1;i<=n;i++){//从1到n开始试 
		if(vis[i]==1)//用过了 
		    continue;
		if(isprime(a[step-1]+i)){//两个数的和，是素数 
			if(step==n){
				if(!isprime(i+1))//最后一个圈里的，他的下一个是1 
				    continue;
			}
			a[step]=i;//存进去 
			vis[i]=1;//标记 
			dfs(step+1);//下一步 
			vis[i]=0;//取消标记 
		}
	}
}
int main(){
	int count=1;
	while(~scanf("%d",&n)){
		memset(a,0,sizeof(a));
		memset(vis,0,sizeof(vis));//初始化 
		a[1]=1;//第一个必须是1 
		vis[1]=1;//标记 
		cout<<"Case "<<count++<<":"<<endl;
		dfs(2);//从2 开始 
		cout<<endl;
	}
}