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.

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

68

Sample Output

Case 1:1 4 3 2 5 61 6 5 2 3 4Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 8 3 21 6 7 4 3 8 5 2

题意:给你一个数n,将1到n这些数排成环,要求相邻两数之和为素数。按要求输出即可,行末无多余空格。

采用dfs即可,一开始用STL做的还没做出来,后来用c语言很简单的思路写了一下就过了,个人认为题目没有什么难易之分。

以下是AC代码

#include <algorithm>

#include <cstring>
#include <iostream>
using namespace std;
int prime[50],book[50];
int ans[50],n;
void pri()//筛选素数 还有更快的改进版本,有兴趣可以百度
{
 prime[0]=prime[1]=0; prime[2]=1;
 for(int i=2;i<=50;i++)
     {
         for(int j=i*i;j<=50;j+=i)
    prime[j]=0; 
 } 
}
void dfs(int in)
{
 if(in==n&&prime[ans[0]+ans[n-1]])
    {
     for(int i=0;i<n-1;i++)
         printf("%d ",ans[i]);
      printf("%d\n",ans[n-1]);   
      return ;
    }else 
         {
   for(int i=1;i<=n;i++)
      if(!book[i]&&prime[i+ans[in-1]])
         {
      book[i]=1;
      ans[in]=i;
      dfs(in+1); 
      book[i]=0;
      
   }
   
 } 
} 
int main()
{
  int cnt=1;
 fill(prime,prime+50,1);
 pri();
 while(cin>>n)
 { 
    memset(ans,0,sizeof(ans));
    memset(book,0,sizeof(book));
 ans[0]=1; 
 book[1]=1;
 printf("Case %d:\n",cnt++);
 dfs(1);
 printf("\n");
 }
 return 0;
}            

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