HDOJ Prime Ring Problem （深度优先搜索）

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 11488    Accepted Submission(s): 5194

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
   
   
   
   

 

Source

Asia 1996, Shanghai (Mainland China)

 

#include <iostream>
#include <cstring>

using namespace std;

int n,j,k=1,visit[20],a[20]={1};
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 m)
{
	if(m==n && prime[1+a[n-1]])
	{
		for(int i=0;i<n-1;i++)
			cout<<a[i]<<" ";
		cout<<a[n-1]<<endl;	
	}
	
	else
	{
		for(int i=2;i<=n;i++)
		{
			if(prime[i+a[m-1]] && !visit[i])
			{
				a[m]=i;
				visit[i]=1;
				DFS(m+1);
				visit[i]=0;	
			}	
		}	
	}	
}

int main()
{	
	while(cin>>n)
	{
		memset(visit,0,sizeof(visit));
		cout<<"Case "<<k++<<":"<<endl;
		DFS(1);
		cout<<endl;
	}
	
	return 0;	
}