HDOJ-1016Prime Ring Problem(DFS)

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

1 6 7 4 3 8 5 2

这里是一个典型的深搜问题，这里如果用Boolean打表，调用import java.util.Arrays;在杭电上提交会超时 

import java.util.Scanner; 
  public class Main { 
      public static void main(String[] args) { 
       int Case=0; 
     Scanner sc = new Scanner(System.in); 
     while(sc.hasNext()){ 
        int n= sc.nextInt();
      int color[] = new int[n]; 
      int arr[] = new int[n]; 
      int prant[] = new int [n]; 
      int count=0; //Arrays.fill(color,false); 
      for(int i=0;i<arr.length;i++){       
             arr[i]=i+1; //初始化所有数据 
         color[i]=-1; 
      } 
      Case++; 
      System.out.println("Case "+(Case)+":"); 
      dfs(arr,color,prant,count,0); 
      System.out.println();       
      } 
    } 
    public static void dfs(int[] arr,int[] color,int[] prant,int count,int m){ 
      count++; 
      if(count==arr.length && prime(prant[0],arr[m])){ //第一个数与最后一个数相加的和也是素数 
          prant[count-1] = arr[m]; 
        for(int i=0;i<arr.length-1;i++){ 
            System.out.print(prant[i]+" "); 
        } 
        System.out.println(prant[arr.length-1]); 
      } 
      for(int i=0;i<arr.length;i++){ 
          color[m]=1; 
        if(prime(arr[m],arr[i]) && color[i]==-1){ 
            color[i]=1; prant[count-1]=arr[m]; 
          dfs(arr,color,prant,count,i); 
          color[i]=-1; 
        } 
      } 
      } 
     //判断素数
     public static boolean prime(int i,int j){ 
        int sum=i+j; 
      for(int k=2;k*k<=sum;k++){ 
      if(sum%k==0){ 
        return false; 
      } 
        } 
    return true; 
    } 
}