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.

输入

n (0 < n < 20).

输出

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.

样例输入

68

样例输出

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>#define mem(a,b) memset(a,b,sizeof(a))int prime[100]= {1,1};int a[50],md[50],n;void sushu(){    int i,j;    for(i=2; i<=10; i++)        if(prime[i]==0)            for(j=2*i; j<=50; j+=i)                prime[j]=1;}void dfs(int step){    int i,j;    if(step==n+1&&prime[a[n]+a[1]]==0)    {        for(i=1; i<n; i++)            printf("%d ",a[i]);        printf("%d\n",a[n]);        return;    }    for(i=2; i<=n; i++)    {        if(md[i]==0&&prime[i+a[step-1]]==0)        {            a[step]=i;            md[i]=1;            dfs(step+1);            md[i]=0;        }    }    return;}int main(){    int num=1;    a[1]=1;    sushu();    while(~scanf("%d",&n))    {        mem(md,0);        printf("Case %d:\n",num++);        dfs(2);        printf("\n");    }    return 0;}