HDOJ Prime Ring Problem （深度优先搜索）

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 11488    Accepted Submission(s): 5194

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

 

Source

Asia 1996, Shanghai (Mainland China)

 

#include <iostream>#include <cstring>using namespace std;int n,j,k=1,visit[20],a[20]={1};int prime[38]={0,0,1,1,0,1,0,1,0,0,       0,1,0,1,0,0,0,1,0,1,       0,0,0,1,0,0,0,0,0,1,       0,1,0,0,0,0,0,1};    void DFS(int m){if(m==n && prime[1+a[n-1]]){for(int i=0;i<n-1;i++)cout<<a[i]<<" ";cout<<a[n-1]<<endl;}else{for(int i=2;i<=n;i++){if(prime[i+a[m-1]] && !visit[i]){a[m]=i;visit[i]=1;DFS(m+1);visit[i]=0;}}}}int main(){while(cin>>n){memset(visit,0,sizeof(visit));cout<<"Case "<<k++<<":"<<endl;DFS(1);cout<<endl;}return 0;}