[HDOJ1016]Prime Ring Problem

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1016

原题：

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.

输入N个数字，求1到N这N个数字连成环以后两两相加均为素数的所有情况。

非常经典的DFS题。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
int n;
int cir[21];
int prime[41];
int vis[21];
int isPrime(int x)
{
    int i;
    int sqx = sqrt((float)x);
    for(i = 2; i <= sqx; i++)
    {
        if(x % i == 0)
        {    
            return 0;
        }
    }
    return 1;
}

void dfs(int x)
{
    int i;
    if(x == n && prime[cir[1]+cir[n]])    //make a circle
    {
        for(i = 1; i < n; i++)
        {
            printf("%d ", cir[i]);
        }
        printf("%d
", cir[n]);
        return ;
    }
    for(i = 2; i <= n; i++)
    {
        if(vis[i] == 0 && prime[cir[x]+i])
        {
            cir[x+1] = i;
            vis[i] = 1;
            dfs(x+1);
            vis[i] = 0;    //reset
        }
    }
}

int main()
{
    int i, Case = 1;
    for(i = 1; i < 41; i++)    //list primes.
    {
        if(isPrime(i))
        {
            prime[i] = 1;
        }
    }

    while(scanf("%d", &n) != EOF && n)
    {
        printf("Case %d:
", Case++);
        memset(vis, 0, sizeof(vis));
        cir[1] = 1;
        vis[1] = 1;
        dfs(1);
        printf("
");
    }
    return 0;
}