许诺 • 9天前
#include <iostream>
#include <vector>
#include <queue>
#include <cstring>
using namespace std;
const int INF = 1e9; const int MAXN = 40010; // n + m + 2
struct Edge {
int to, cap, rev;
};
vector graph[MAXN]; int level[MAXN], iter[MAXN];
void add_edge(int from, int to, int cap) {
graph[from].push_back({to, cap, (int)graph[to].size()});
graph[to].push_back({from, 0, (int)graph[from].size() - 1});
}
void bfs(int s) {
memset(level, -1, sizeof(level));
queue<int> q;
level[s] = 0;
q.push(s);
while (!q.empty()) {
int v = q.front(); q.pop();
for (auto &e : graph[v]) {
if (e.cap > 0 && level[e.to] < 0) {
level[e.to] = level[v] + 1;
q.push(e.to);
}
}
}
}
int dfs(int v, int t, int f) {
if (v == t) return f;
for (int &i = iter[v]; i < graph[v].size(); i++) {
Edge &e = graph[v][i];
if (e.cap > 0 && level[v] < level[e.to]) {
int d = dfs(e.to, t, min(f, e.cap));
if (d > 0) {
e.cap -= d;
graph[e.to][e.rev].cap += d;
return d;
}
}
}
return 0;
}
int max_flow(int s, int t) {
int flow = 0;
while (true) {
bfs(s);
if (level[t] < 0) return flow;
memset(iter, 0, sizeof(iter));
int f;
while ((f = dfs(s, t, INF)) > 0) {
flow += f;
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
while (T--) {
int m, n;
cin >> m >> n; // m个教室,n个学生
// 初始化图
for (int i = 0; i <= n + m + 2; i++) {
graph[i].clear();
}
int S = 0, T = n + m + 1;
// 源点连接到所有学生
for (int i = 1; i <= n; i++) {
add_edge(S, i, 1);
}
// 所有教室连接到汇点
for (int i = 1; i <= m; i++) {
add_edge(n + i, T, 1);
}
// 读入每个教室可以上课的学生
for (int i = 1; i <= m; i++) {
int k;
cin >> k;
for (int j = 0; j < k; j++) {
int student;
cin >> student;
// 学生连接到教室
add_edge(student, n + i, 1);
}
}
int flow = max_flow(S, T);
if (flow == m) {
cout << "YES\n";
} else {
cout << "NO\n";
}
}
return 0;
}
评论:
请先登录,才能进行评论