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
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 a[] = new int[n]; //初始数组1-n int color[] = new int[n]; //判断数字是否已经存在 int prant[] = new int[n]; //输出数据排序 int count =0;//计数器 for(int i=0;i<n;i++){ a[i]=i+1; color[i] = -1; }//初始化数据 Case++; System.out.println("Case "+(Case)+":"); dfs(a,color,prant,count,0); System.out.println(); } } private static void dfs(int[] a, int[] color, int[] prant, int count,int m) { //System.out.println(count); count++;//计数器加1 if(count == a.length&&p(prant[0],a[m])){ //注意第一个数和最后一个数相加的和也必须为素数 prant[count-1]=a[m]; for(int i=0;i<a.length-1;i++){ System.out.print(prant[i]+" "); } System.out.println(prant[a.length-1]); //return ; } for(int i=0;i<a.length;i++){ color[m] =1; if(p(a[m],a[i])&&color[i]==-1){ color[i]=1; prant[count-1]=a[m]; dfs(a,color,prant,count,i); color[i]=-1; } } } //判断是不是素数 private static boolean p(int i, int j) { int sum = i+j; for(int a=2;a*a<=sum;a++){ if(sum%a==0){ return false; } } return true; } }
