HDU_1016——素环问题DFS

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>
#define MAX 20
int a[MAX],b[MAX],N;
int Is_Prime(int num)
{
   for(int i=2;i<=(int)sqrt((double)num);i++)
      if(num%i==0)
         return 0;
   return 1;
}
void Dfs(int n)
{
   int i,j;
   if(n==N && Is_Prime(a[n-1]+a[0]))
      {
         for(i=0;i<N;i++)
            printf(i==N-1?"%d":"%d ",a[i]);//草蛋的格式 
         printf("\n"); 
      }
   else
      {
         for(i=1;i<N;i++)
            {
               if(b[i]!=0 && Is_Prime(a[n-1]+b[i]))
                  {
                     a[n++]=b[i];
                     b[i]=0;
                     Dfs(n);
                     b[i]=i+1;
                     n--;
                  }  
            }
      }
}
int main()
{
   int i,j,k,num=1;
   while(scanf("%d",&N)!=EOF)
      {
         a[0]=1;
         for(i=0;i<N;i++)
            b[i]=i+1;
         printf("Case %d:\n",num++);
         Dfs(1);
         printf("\n");
      }   
}