hdu 1016 Prime Ring Problem（DFS）

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

 

题意：很容易理解，就是让你输出满足相邻的相加是素数的序列（注意不要重复）

解题思路：用DFS去遍历它，然后判断是否满足。

#include <stdio.h>

int a[20],b[20],n;

int judge(int m)
{	int k;
	if(m == 2)
		return 1;
	for(k = 2; k < m; k++)
	{
		if(m%k == 0)
		{
			break;
		}
	}
	if(k == m)
		return 1;
	else
		return 0;
}
void dfs(int j)
{
	int i;
	if(j == n && judge(a[n]+1))
	{
		for(i = 1;i<n;i++)
			printf("%d ",a[i]);
		printf("%d\n",a[n]);
	}
	for(i = 2;i<=n;i++)
	{
		if(b[i]!=0 && judge(a[j]+i))
		{
			a[j+1]=i;
			b[i]=0;
			dfs(j+1);
			b[i]=i;
		}
	}
}
int main()
{
    int k;

	a[1]=1;
    
	for(k=1;k<=20;k++)
		b[k]=k;

    
    
	for(k=1;scanf("%d",&n)!=EOF;k++)
    {	
		printf("Case %d:\n",k);  
		
		if(n%2 == 0)
			dfs(1);

		printf("\n");
    }
    return 0;
}