HDU 1016 DFS

Prime Ring Problem

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

素数环...1-n组成的环，每相邻两个数之和都是素数....

 

#include <iostream>using namespace std;/*将从1到n这n个整数围成一个圆环，若其中任意2个相邻的数字相加，结果均为素数，那么这个环就成为素数环。*/int n;int start[20],result[20]={0,1};//start记录该数字是否用过，result判断是否素数int prim[39]={0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0};void dfs(int num,int count)//count计数{if(count==n&&prim[result[n]+1])//最后一个与1的和为素数{printf("1");for(int i=2;i<=n;i++)printf(" %d",result[i]);printf("\n");return;}for(int k=2;k<=n;k++){if(prim[num+k]&&start[k]==0)//num与其相邻的数相邻且{                        //这个相邻的数没有被用过result[count+1]=k;start[k]=1;dfs(k,count+1);start[k]=0;//查找后需将其初始化（多次查找）}}}int main(){int Case=1;while(cin>>n){memset(start,0,sizeof(start));printf("Case %d:\n",Case++);dfs(1,1);cout<<endl;}return 0;}