HDU1016 Prime Ring Problem（素数环）

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 66883 Accepted Submission(s): 28675

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

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

clockwisely 顺时针地

anticlockwisely 逆时针地

lexicographical 字典序地

比较典型的dfs。注意格式要求，每一组的最后一个数据后面没有空格。

AC代码：

 1 #include<iostream>
 2 #include<sstream>
 3 #include<algorithm>
 4 #include<string>
 5 #include<cstring>
 6 #include<iomanip>
 7 #include<vector>
 8 #include<cmath>
 9 #include<ctime>
10 #include<stack>
11 using namespace std;
12 int N,a[21],book[21];
13 bool isprime(int n)//n是否为素数 
14 {
15     if(n==2||n==3) return 1;
16     if(n%6!=1&&n%6!=5) return 0;
17     int b=sqrt(n);
18     for(int i=5;i<=b;i+=6)
19         if(n%i==0||n%(i+2)==0) return 0;
20     return 1;
21 }
22 void dfs(int step)
23 {
24     if(step==N+1)
25     {
26         if(isprime(a[1]+a[N]))
27         {
28             for(int j=1;j<=N;j++)
29             if(j!=N) cout<<a[j]<<' ';
30             else cout<<a[j];
31             cout<<endl;
32         }
33                 return;
34     }
35     for(int i=2;i<=N;i++)
36     {
37         if(book[i]) continue;
38         if(isprime(i+a[step-1])) 
39         {
40             book[i]=true;
41             a[step]=i;
42             dfs(step+1);
43             book[i]=false;//回溯 
44         }
45     }
46 }
47 int main()
48 {
49     int count=1;
50     while(cin>>N)
51     {
52         memset(book,0,sizeof(0));
53         a[1]=1;
54         cout<<"Case "<<count++<<":
";
55         dfs(2);
56                 cout<<endl;
57     }
58 }
59

View Code