Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 76951 Accepted Submission(s): 32586

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

Source

Asia 1996, Shanghai (Mainland China)&source=1&searchmode=source)

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Accepted Code

package cn.edu.hdu.acm;

import java.util.*;

public class Main1016 {
    public static int n;
    public static boolean[] prime = new boolean[50];   //标记数字是否是素数
    public static boolean[] vis = new boolean[25];     //标记数字是否填过
    public static int[] ans = new int[25];      //纪录路径
    public static boolean p ;
    public static void get_prime(){           //写素数筛
        Arrays.fill(prime, false);
        prime[2]=true;
        for(int i=2;i<50;i++){
            boolean flog = true;
            for(int j=2;j*j<=i;j++){
                if(i%j==0){
                    flog = false;
                    break;
                }
            }
            if(flog){
                prime[i] = true; 
            }
        }
    }

    public static void main(String[] args){
        int cnt=0;
        Scanner sc = new Scanner(System.in);
        get_prime();
        while(sc.hasNext()){
            cnt++;
            n = sc.nextInt();
            Arrays.fill(vis, false);
            Arrays.fill(ans, 0);
            ans[1] = 1;
            p = false;
            System.out.println("Case "+cnt+":");
            DFS(2);
            System.out.println();
        }
    }

    public static void DFS(int dig){
        if(dig>n){
            if(prime[ans[dig-1]+1]){
                for(int i=1;i<=n;i++){
                    if(i<n){
                        System.out.print(ans[i]+" ");
                    }else{
                        System.out.println(ans[i]);
                    }
                }
            }
            return ;
        }
        for(int i=2;i<=n;i++){
            if(!vis[i] && prime[i+ans[dig-1]]){
                vis[i] = true;
                ans[dig] = i;
                DFS(dig+1);
                vis[i] = false;
            }
        }
    }
}