学步园

题意：给定一些学生和课程的关系，问是否每一门课程能唯一对应一个学生。

解法：每一条边对应一个选择关系，问题就是求一个完备匹配是否存在。

代码如下：

#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;

int P, N;
char G[105][305], vis[305];
int match[305];

bool path(int u) {
    for (int i = 1; i <= N; ++i) {
        if (!G[u][i] || vis[i]) continue;
        vis[i] = 1;
        if (!match[i] || path(match[i])) {
            match[i] = u;
            return true;    
        }
    }
    return false;
}

bool query() {
    int ret = 0;
    memset(match, 0, sizeof (match));
    for (int i = 1; i <= P; ++i) {
        memset(vis, 0, sizeof (vis));
        ret += path(i);    
    }
    return ret == P;
}

int main() {
    int T, num, c;
    scanf("%d", &T);
    while (T--) {
        memset(G, 0, sizeof (G));
        scanf("%d %d", &P, &N);
        for (int i = 1; i <= P; ++i) {
            scanf("%d", &num);
            for (int j = 1; j <= num; ++j) {
                scanf("%d", &c);
                G[i][c] = 1;
            }    
        }
        printf(query() ? "YES\n" : "NO\n");
    }
    return 0;    
}