Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 21151 Accepted Submission(s): 9465

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

Source

Asia 1996, Shanghai (Mainland China)

深度搜索....无压力；；

代码：

 1 #include<stdio.h>
 2 #include<stdlib.h>
 3 #include<string.h>
 4 int str[]={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20};
 5 int ans[21]={1};
 6 int n,cnt;  /*代表搜索的深度*/  
 7 bool flag;
 8  /*可能需要剪枝*/
 9 void  dfs(int step)
10 {
11     int i,j,temp; 
12    if(step==n)   /*说明搜索到底了！*/
13    {
14         flag=true;
15          temp=ans[0]+ans[n-1];   //开头和结尾也要判断
16            for(j=2;j*j<=temp;j++)
17            {
18             if(temp%j==0)
19             {
20                flag=false;
21                break;
22             }
23            }
24        if(flag)
25        {
26           printf("%d",ans[0]);
27           for( i=1;i<n;i++)
28           {
29            printf(" %d",ans[i]);
30           }
31            puts("");
32        }
33    }
34     else
35     {
36       for(i=1;i<n;i++)
37       {
38           if(str[i])
39           {
40              flag=true;     
41              temp=ans[cnt-1]+str[i];
42               for(j=2;j*j<=temp;j++)
43               {
44                   if(temp%j==0)
45                   {
46                      flag=false;
47                       break;
48                   }
49               }
50             if(flag)
51             {
52              ans[cnt++]=str[i];
53              str[i]=0;
54              dfs(step+1);
55              str[i]=ans[--cnt];
56              ans[cnt]=0;
57             }
58           }
59       }
60     }
61 }
62 
63 int main()
64 {
65     int count=1;
66     while(scanf("%d",&n)!=EOF)
67     {
68         cnt=1;
69         printf("Case %d:n",count++);
70         dfs(1);
71         puts("");
72     }
73     return 0;
74 }

HDUOJ----(1016)Prime Ring Problem

Prime Ring Problem