hdu 1016 Prime Ring Problem [素数环]

最新推荐文章于 2019-07-09 01:02:49 发布

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本文介绍了一个经典的组合数学问题——Prime Ring Problem，并提供了一种使用深度优先搜索（DFS）和素数判断算法来解决该问题的方法。通过递归地尝试在环形结构中填充数字，并确保相邻数字之和为素数，最终输出所有可能的解决方案。

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Prime Ring Problem

hdu 1016 题目链接

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

程序代码：

#include <stdio.h>
#include <string.h>
#include <math.h>
int a[30],book[30],n;
 
int prime(int n)
{
	int i,k;
	if(n<2)
		return 0;
	k=(int)sqrt(n);
	for(i=2;i<=k;i++)
		if(n%i==0)
			return 0;
	return 1;
}
void dfs(int step)
{
	int i;
	/*for(i=1;i<n;i++)
		printf("%d ",a[i]);
	  printf("%d\n",a[n]);*/
	if(step==n+1)
	{
		if(prime(a[1]+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(book[i]==0&&prime(a[step-1]+i)==1)
		{
			book[i]=1;
			a[step]=i;
			dfs(step+1);
			book[i]=0;
		}
	}
	return ;
}
int main()
{
	int t=0;
	while(scanf("%d",&n)!=EOF)
	{
		t++;
		printf("Case %d:\n",t);
		memset(book,0,sizeof(book));
		a[1]=1;
		book[1]=1;
		dfs(2);
		printf("\n");
	}
	return 0;
}