Prime Ring Problem

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

Total Submission(s): 41154    Accepted Submission(s): 18221

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

直接暴力搜索，我估计是需要剪枝，因为开始没有剪枝，然后测试了一下n=20，半天没有出结果。

于是想了一下剪枝：

1 开始的数字不是1的时候，说明所有的组合都找出来了，剩余的就是旋转这个圈得到的结果

2 如果当前的数字和它前一个相加不是素数的话，就不用继续往下找了。

 

#include
        
         #include
         
          using namespace std;int n;int num[25];bool vis[25];int prime[30];void dfs(int a){    if(a>n+1) return;    if(num[1]!=1) return;    if(a==n+1)    {        for(int i=1; i
          
           1)            {                if (!prime[num[a%n]+num[(a-1)%n]])                continue;            }            //cout<
           
            <<"  "<
           
          
         
        

 

 

 

Source

  

 

直接暴力搜索9