Prime Ring Problem

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

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 <iostream>#include <cstdio>#include<algorithm>#include<cmath>using namespace std;int a[25];bool vis[25];int n;bool prime(int k){int i;for(i =2 ; i * i < k+1 ; i++){if(!(k%i))return false;}return true;}void dfs(int cur)//深度搜索；{if(cur == n && prime(a[n-1]+a[0])){for(int i = 0 ; i < n; i++)printf("%d ",a[i]);printf("\n");}for(int j = 2  ;j <= n ; j++){if(!vis[j]){if(prime(a[cur-1]+j)){vis[j] = true;a[cur] =j;dfs(cur+1);vis[j] = false;}}}}int sum = 1;int main(){while(scanf("%d",&n)!=EOF){a[0] = 1;printf("Case %d:\n",sum++);dfs(1);printf("\n");}return 0;}