Prime Ring Problem

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 17642    Accepted Submission(s): 7945

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)

 

Recommend

JGShining

 

 

DFS水过

#include<iostream>
using namespace std; 
int n,vi[23];
int a[23],j;
bool isprime(int b,int c){
 int m=b+c;
 for(int i=2;i<=m/2;i++)
  if(m%i==0)
   return false;
  
 return true;
}

void DFS(int k){
 if(k>n) 
  return ;
 if(j==n){
  if(isprime(a[j-1],1)){
   for(int l=0;l<j-1;l++)
    cout<<a[l]<<" ";
   cout<<a[j-1]<<endl;
  }
  return ;
 }
 int i;

 for(i=1;i<=n;i++)
 {
  if(!vi[i]&&isprime(k,i)){
   a[j++]=i;
   vi[i]=1;
   DFS(i);
   vi[i]=0;
   j--;
  }

 }
}

int main()
{

 int count=0,s=0;
 while(cin>>n){
  
  cout<<"Case "<<++count<<":"<<endl;
  j=0;
  memset(vi,0,sizeof(vi));
  vi[1]=1;
  a[j++]=1;
  DFS(1);
  cout<<endl;
 }
 return 0;
}