Prime Ring Problem(DFS)

Prime Ring Problem

Time Limit : 4000/2000ms (Java/Other) Memory Limit : 65536/32768K (Java/Other)
Total Submission(s) : 5 Accepted Submission(s) : 4

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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
[code]#include<iostream>
#include<string.h>
using namespace std;
int n,f[21];
int prime[50];
int DFS(int x[21],int s[21],int l)
{
	if(l==n) 
	{
		if(prime[1+s[l]]==0)
		{
		cout<<"1";
		for(int i=2;i<=n;i++)
			cout<<" "<<s[i];
		cout<<endl;
		}
		return 0;
	}
	else
	{
		for(int j=2;j<=n;j++)
			if(x[j]==0&&prime[j+s[l]]==0) 
			{
				s[l+1]=j,x[j]=1;
				DFS(x,s,l+1);
				if(j<=n) x[j]=0;
			}
	}
	return 0;

}
int main()
{
	int s[21],x[21],l,sum;
	sum=0;
	memset(prime,0,sizeof(prime));
	for(int i=2;i<=25;i++)
		for(int j=2;j*i<=50;j++)
			prime[j*i]=1;
	while(cin>>n)
	{
		sum++;
	memset(x,0,sizeof(x));
	cout<<"Case "<<sum<<":"<<endl;
	s[1]=1;l=1;
	DFS(x,s,l);
	cout<<endl;
	}
	return 0;

}

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