1020

题意：n的环组成圆圈。把自然数1,2,……、n分别到每个圆和数字的总和在两个相邻的圈子里是一个质数

思路：从头开始，然后去找下一个加上一是质数的数，进行递归，到最后一个数的时候，也是如此，如果出现无法dfs下去的情况，就开始下一次dfs

#include<iostream>
#include<cstring>
using namespace std;

int n, cnt = 1;
int visit[21], ansList[21];
int Prime[38] = { 0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1 };
void dfs(int cur)
{
    if (cur == n && Prime[ansList[0] + ansList[n - 1]])
    {
        cout << ansList[0];
        for (int i = 1; i < n; ++i)
            cout << " " << ansList[i];
        cout << endl;
    }
    else
    {
        for (int i = 2; i <= n; ++i)
            if (!visit[i] && Prime[i + ansList[cur - 1]])
           {
                ansList[cur] = i;
               visit[i] = 1;
                dfs(cur + 1);
                visit[i] = 0;
            }
    }
}
int main()
{
    ansList[0] = 1;
    while (cin >> n)
    {          memset(visit, 0, sizeof(visit));
        cout << "Case " << cnt++ << ":\n";
        dfs(1);
        cout << endl;
    }
    return 0;
}