Prime Ring Problem HDU - 1016

最新推荐文章于 2021-03-09 20:07:10 发布

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最新推荐文章于 2021-03-09 20:07:10 发布

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本文介绍了一种基于数字的环形谜题解决方案，通过放置自然数于环形结构中，确保相邻数字之和为素数。使用递归深度优先搜索算法实现，输出所有可能的组合，并按字典序排列。

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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.   

  
Inputn (0 < n < 20).  
OutputThe 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 Input6
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

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
#define inf 0x3f3f3f3f
using namespace std;

int book[22];
int a[22];

int is_prime(int x)
{
    for(int i=2;i<=sqrt(x);i++)
    {
        if(x%i==0)
            return 0;
    }
    return 1;
}

void dfs(int n,int k)
{
    if(k>n)
    {
        if(is_prime(a[k-1]+a[1])==0)
            return ;
    }
    int i;
    if(k>n)
    {
        printf("%d",a[1]);
        for(i=2;i<=n;i++)
        {
            printf(" %d",a[i]);
        }
        printf("\n");
        return ;
    }
    for(i=2;i<=n;i++)
    {
        if(book[i]==0&&is_prime(i+a[k-1])==1)
        {
            a[k]=i;
            book[i]=1;
            dfs(n,k+1);
            book[i]=0;
        }
    }
}

int main()
{
    int n,num=0;
    while(~scanf("%d",&n))
    {
        memset(book,0,sizeof(book));
        num++;
        a[1]=1;book[1]=1;
        printf("Case %d:\n",num);
        dfs(n,2);
        printf("\n");
    }
    return 0;
}