Prime Ring Problem 1016 （dfs）

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 35191 Accepted Submission(s): 15563

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<stdio.h>#include<string.h>#include<math.h>int a[20],b[20],n;int f(int x){    int i;    for(i=2;i<=sqrt(x);i++)        if(x%i==0)            return 0;            return 1;}void dfs(int s){    int i,j;    if(s==n+1&&f(a[1]+a[n]))    {        for(i=1;i<n;i++)            printf("%d ",a[i]);            printf("%d\n",a[n]);            return ;    }    for(j=2;j<=n;j++)    {        if(f(j+a[s-1])&&b[j]==0)        {            b[j]=1;            a[s]=j;            dfs(s+1);            b[j]=0;        }    }}int main(){    int m=1;    while(scanf("%d",&n)!=EOF)    {        memset(b,0,sizeof(b));        a[1]=1;                printf("Case %d:\n",m++);        dfs(2);        printf("\n");    }    return 0;}