Prime Ring Problem
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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.
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.
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)
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;
}
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