HDU 1016

Prime Ring Problem

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 37484    Accepted Submission(s): 16554

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

 

解题思路：

　　简单的DFS即可

#include <iostream>
#include <cmath>
#include <string.h>
int n;
int ans[20],used[20];
using namespace std;
bool isprime(int m)
{
    for(int i=2;i<=sqrt(m*1.0);i++)
    {
        if(m%i==0)  return 0;
    }
    return 1;
}
void dfs(int x)
{
    if(x==n+1 && isprime(ans[1]+ans[n]))
    {
        for(int i=1;i<n;i++)
        {
            cout<<ans[i]<<' ';
        }
        cout<<ans[n]<<endl;
    }
    else
    {
        for(int j=2;j<=n;j++)
        {
            if(used[j]==0 && isprime(j+ans[x-1]))
            {
                ans[x]=j;
                used[j]=1;
                dfs(x+1);
                used[j]=0;
            }
        }
    }
}
int main()
{
    int k=1;
    while(cin>>n)
    {
        memset(used,0,sizeof(used));
        printf("Case %d:
",k);
        k++;
        ans[1]=1;
        used[1]=1;
        dfs(2);
        cout<<endl;
    }
}