7.31 B - Prime Ring Problem

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本文介绍了一个名为B-PrimeRing的问题，该问题要求将1至n的自然数放置于n个圆环中，使得相邻两圆环内的数字之和为质数。文章提供了一段C语言代码，用于解决此问题，并展示了如何通过递归深度优先搜索来找出所有可能的解决方案。

B - Prime Ring Problem

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<stdio.h>
#include<string.h>
int m,n;
int a[5000],book[5000];
int p[100]={0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,
1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1};

void dsf(int x,int y)
{
	int i,flag=0,t;
	for(i=2;i<=y;i++)
	{
		if(book[i]==0&&p[i+a[x-1]]==1)
		{
			a[x]=i;
			book[i]=1;
			dsf(x+1,y);
			book[i]=0;
		}
		
	}
	if(x==y)
	{
		if(x==y&&p[a[0]+a[y-1]]==1)
		{
			printf("%d",a[0]);
			for(i=1;i<y;i++)
			{
				printf(" %d",a[i]);
			}
			printf("\n");
		}
		return ;		
	}
	return ;
}


int main()
{
	int i,j,k,t;
	t=1;
	while(scanf("%d",&n)!=EOF)
	{
		printf("Case %d:\n",t++);
		memset(book,0,sizeof(book));
		a[0]=1;
		dsf(1,n);
		printf("\n");
	}
	return 0;
}