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

 1 #include <stdio.h>

 2 #include <math.h>

 3 #define MAX 20

 4 int a[MAX],b[MAX],N;

 5 int Is_Prime(int num)

 6 {

 7    for(int i=2;i<=(int)sqrt((double)num);i++)

 8       if(num%i==0)

 9          return 0;

10    return 1;

11 }

12 void Dfs(int n)

13 {

14    int i,j;

15    if(n==N && Is_Prime(a[n-1]+a[0]))

16       {

17          for(i=0;i<N;i++)

18             printf(i==N-1?"%d":"%d ",a[i]);//草蛋的格式 

19          printf("\n"); 

20       }

21    else

22       {

23          for(i=1;i<N;i++)

24             {

25                if(b[i]!=0 && Is_Prime(a[n-1]+b[i]))

26                   {

27                      a[n++]=b[i];

28                      b[i]=0;

29                      Dfs(n);

30                      b[i]=i+1;

31                      n--;

32                   }  

33             }

34       }

35 }

36 int main()

37 {

38    int i,j,k,num=1;

39    while(scanf("%d",&N)!=EOF)

40       {

41          a[0]=1;

42          for(i=0;i<N;i++)

43             b[i]=i+1;

44          printf("Case %d:\n",num++);

45          Dfs(1);

46          printf("\n");

47       }   

48 }