HDU 1016 Prime Ring Problem(搜索，素数环)

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本文介绍了一个名为PrimeRing的问题，该问题是关于在一个由n个圆圈组成的环中放置1到n的自然数，并确保相邻两个圆圈内的数字之和为质数。文章提供了一个C++实现示例，通过深度优先搜索算法寻找所有符合条件的排列方案。

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 60423 Accepted Submission(s): 26107

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

#include<stdio.h>
#include<math.h>
#include<string.h> 
using namespace std;
int n;
int a[25];
int vis[25];
int prim(int x)
{
	int i;
	for(i=2;i<=sqrt(x);i++)
	if(x%i==0) return 0;
	return 1;
}
void dfs(int k){
	if(k==n&&prim(a[n]+1)){
		for(int i=1;i<n;i++)
			printf("%d ",a[i]);
		printf("%d\n",a[n]);
		return;
	}
	for(int i=2;i<=n;i++){
		if(!vis[i]&&prim(a[k]+i)){
			a[k+1]=i;
			vis[i]=1;
			dfs(k+1);
			vis[i]=0;
		}
	}
}
int main()
{
	int ans=0;
	while(~scanf("%d",&n))
	{
		memset(vis,0,sizeof(vis));
		printf("Case %d:\n",++ans);
		vis[1]=1;
		a[1]=1;
		if(n==1||n%2==0)
		dfs(1);
		printf("\n");
	}
}