hdu 1016 Prime Ring Problem

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

先弄一张素数表；
然后进行深搜；

#include<iostream>
#include<string>
#include<algorithm>
#include<cstdio>
#include<cmath>
#include<cstring>
using namespace std;
bool flag[21]={0};
int ans[21]={1};
int isprime[]={3,5,7,11,13,17,19,23,29,31,37};
bool find_p(int n)
{
for(int i=0;i<11;++i)
{
if(n==isprime[i]) return true;
}
return false;
}
void dfs(int n,int i)
{
if(i==n&&find_p(ans[0]+ans[n-1]))
{
cout<<ans[0];
for(int i=1;i<n;++i)
cout<<" "<<ans[i];
cout<<endl;
}
else
{
for(int j=2;j<=n;++j)
{
if(flag[j]!=1&&find_p(j+ans[i-1]))
{
ans[i]=j;
flag[j]=1;
dfs(n,i+1);
flag[j]=0;
}
}
}
}
int main()
{
int n,kase=0;
while(scanf("%d",&n)!=EOF)
{
++kase;
memset(flag,0,sizeof(flag));
printf("Case %d:\n",kase);
dfs(n,1);
cout<<endl;
}
return 0;
}