HDU 1016-Prime Ring Problem

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 53521    Accepted Submission(s): 23677

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
素数环问题，这里用的是深搜
#include<iostream>#include<algorithm>#include<string.h>using namespace std;int n,num[21],vis[21],ring[21],mark;int prime(int t)//判断t是否是素数{if(t==1) return 0;if(t==2) return 1;for(int i=2;i<t;i++){if(t%i==0){return 0;break;}}return 1;}void print()//用来输出素数环序列的{for(int i=1;i<=n;i++){i==n ? cout<<ring[i]:cout<<ring[i]<<' ';}cout<<endl;}void dfs(int t){vis[t]=1;ring[mark++]=t;if(mark==n+1&&prime(ring[n]+1)) print();//这里要注意这是一个素数环，环，环，所以尾和头还要判断for(int i=1;i<=n;i++){if(!vis[i]&&prime(t+i)){dfs(i);}}vis[t]=0;mark--;}int main(){int count=0;while(cin>>n){count++;mark=1;memset(vis,0,sizeof(vis));for(int i=1;i<=n;i++)//这个num完全没必要，我强迫症...num[i]=i;cout<<"Case "<<count<<':'<<endl;dfs(1);cout<<endl;}return 0;}