素数环

Prime Ring Problem

 

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
#include <stdio.h>#include <string.h>#include <math.h>int a[30],book[30],n;int prime(int n){int i,k;if(n<2)return 0;k=(int)sqrt(n);for(i=2;i<=k;i++)if(n%i==0)return 0;return 1;}void dfs(int step){int i;/*for(i=1;i<n;i++)printf("%d ",a[i]);  printf("%d\n",a[n]);*/if(step==n+1){if(prime(a[1]+a[n])==1){for(i=1;i<n;i++)printf("%d ",a[i]);printf("%d\n",a[n]);}}for(i=2;i<=n;i++){if(book[i]==0&&prime(a[step-1]+i)==1){book[i]=1;a[step]=i;dfs(step+1);book[i]=0;}}return ;}int main(){int t=0;while(scanf("%d",&n)!=EOF){t++;printf("Case %d:\n",t);memset(book,0,sizeof(book));a[1]=1;book[1]=1;dfs(2);printf("\n");}return 0;}