HUAS Summer Trainning #3 C

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Description

 

A ring is composed of n (even number) circles as shown in diagram. Put natural numbers  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 <= 16)

 

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.

 

You are to write a program that completes above process.

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

題目大意：使1~n這些數組成環，並且兩兩相加要是素數，輸出所有的解。

解題思路:第一個數總是1，直接用DFS從第二數開始遍曆，遍曆到底部不滿足，回溯到上一個個節點，知道遍曆完所有的可行解。

代碼：

 1 #include<iostream> 2 #include<cstring> 3 using namespace std; 4 const int maxn=50+5; 5 int a[maxn],b[maxn],d[maxn],n,i,j; 6 int sushu(int x) 7 { 8     for(i=2;i*i<=x;i++) 9         if(x%i==0)10             return 0;11     return 1;12 }13 void dfs(int cur)14 {15     if(cur==n&&d[a[0]+a[cur-1]])16     {17         cout<<a[0];18         for(int  i=1;i<n;i++)19             cout<<" "<<a[i];20         cout<<endl;21     }22     else23     {24         for(int i=2;i<=n;i++)25         {26             if(!b[i]&&d[i+a[cur-1]])27             {28                 a[cur]=i;29                 b[i]=1;30                 dfs(cur+1);31                 b[i]=0;32             }33         }34     }35 }36 int main()37 {38     int p=0,t=0;39     while(cin>>n&&n)40     {41         if(p++)42             cout<<endl;    43         cout<<"Case "<<++t<<":"<<endl;44     45       memset(a,0,sizeof(a));46       memset(d,0,sizeof(d));47       for(j=2;j<n*2;j++)48           d[j]=sushu(j);49       memset(b,0,sizeof(b));50       a[0]=1;51       dfs(1);52     }53     return 0;54 }

 

HUAS Summer Trainning #3 C