Prime Ring Problem HDU - 1016

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. 


 

Inputn (0 < n < 20). 

OutputThe 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

题目大意：就是给定几个数，然后必须以1开头，相邻两个数之和必须是素数。

思路；因为最大只有20个数，所以可以用回溯法，注意下递归的边界就可以了，另外判断是不是素数，因为这里的数比较下，可以自己写个函数判断，但是因为之前刚学了筛数法，所以我尝试直接打表素数。

下面是ac代码

#include<cstdio>

#include<string.h>

int vis[20],n,ss[50],a[25];

void sushudabiao()

{

    ss[1]=0;

    for(int i=2;i<=40;i++)

    {

        if(!ss[i])

        {

            for(int j=i*2;j<=40;j+=i)

            {

                ss[j]=1;

            }

        }

    }

}

void dfs(int x)

{

    if(x>n)

    {

        if(!ss[a[x-1]+1])

        {

        for(int j=1;j<=n;j++)

        {

            printf("%d%c",a[j],j==n?'\n':' ');

        }

        }

        return;

    }

    for(int i=2;i<=n;i++)

    {

        a[x]=i;

        if(!ss[a[x]+a[x-1]]&&!vis[i])

        {

            vis[i]=1;

            dfs(x+1);

            vis[i]=0;

        }

    }

}

int main()

{

    int t=1;

    sushudabiao();

    while(~scanf("%d",&n))

    {

        printf("Case %d:\n",t++);

        a[1]=1;

            memset(vis,0,sizeof(vis));

            dfs(2);

            printf("\n");

    }

    return 0;

}