HDOJ 1016 Prime Ring Problem素数环【深搜】

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;    }}

C语言：

#include <iostream>#include <stdio.h>#include <string.h>using namespace std;int n;int df[21];int t=1;int m[21];int mi;bool pn(int x,int y){//判断素数    for(int i=2;i*i<=x+y;i++){        if((x+y)%i==0){            return false;        }    }    return true;}void dfs(int x){    if(mi==n&&pn(m[1],m[n])){        for(int i=1;i<n;i++){            printf("%d ",m[i]);        }        printf("%d\n",m[n]);        return;    }    for(int i=2;i<=n;i++){        if(df[i]==0&&pn(x,i)){            df[x]=1;            mi++;//当前小球数            m[mi]=i;            dfs(i);            df[x]=0;            mi--;//必须减一        }    }}int main(){    while(~scanf("%d",&n)){        printf("Case %d:\n",t);        t++;        memset(df,0,sizeof(df));        mi=1;        m[mi]=1;        dfs(1);        printf("\n");    }    return 0;}