P3386 【模板】二分图最大匹配

https://www.luogu.com.cn/record/91953452

Luogu/P3386/P3386.cpp

@@ -1,45 +1,108 @@
 #include <iostream>
-#include <array>
-#include <vector>
+#include <algorithm>
+#include <queue>
 
 using std::cin;
 using std::cout;
 const char endl = '\n';
 
-const int N = 505;
+const int N = 505,
+          M = 5e4 + 5;
+const int INF = 0x3f3f3f3f;
 
-int n, m, e, tag[N], match[N], ans;
-std::array<std::vector<int>, N> g;
+int n, m, e, s, t, flow, ans;
+int idx, head[N << 1], ver[M << 2], edge[M << 2], next[M << 2];
+int d[N << 1], cur[N << 1];
 
-bool dfs(int u, int t) {
-    if (tag[u] == t) return false;
+void add(int u, int v, int w) {
+    next[idx] = head[u];
+    ver[idx] = v;
+    edge[idx] = w;
+    head[u] = idx++;
+}
 
-    tag[u] = t;
+bool bfs() {
+    std::fill_n(d, N << 1, 0);
 
-    for (int v : g[u]) {
-        if (!match[v] || dfs(match[v], t)) {
-            match[v] = u;
-            return true;
+    std::queue<int> q;
+
+    q.emplace(s);
+    d[s] = 1;
+    cur[s] = head[s];
+
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+
+        for (int i = head[u]; ~i; i = next[i]) {
+            int v = ver[i],
+                w = edge[i];
+
+            if (w && !d[v]) {
+                d[v] = d[u] + 1;
+                cur[v] = head[v];
+                if (v == t) return true;
+                q.emplace(v);
+            }
         }
     }
 
     return false;
 }
 
+int dinic(int u, int limit) {
+    if (u == t) return limit;
+
+    int flow = 0;
+    for (int i = cur[u]; ~i && flow < limit; i = next[i]) {
+        cur[u] = i;
+
+        int v = ver[i],
+            w = edge[i];
+
+        if (w && d[v] == d[u] + 1) {
+            int k = dinic(v, std::min(limit - flow, w));
+
+            if (!k) d[v] = 0;
+
+            edge[i] -= k;
+            edge[i ^ 1] += k;
+            flow += k;
+        }
+    }
+
+    return flow;
+}
+
 int main() {
     std::ios::sync_with_stdio(false);
     cin.tie(nullptr);
 
+    std::fill_n(head, N << 1, -1);
+
     cin >> n >> m >> e;
 
+    s = 0, t = n + m + 1;
+
+    for (int i = 1; i <= n; i++) {
+        add(s, i, 1);
+        add(i, s, 0);
+    }
+
+    for (int i = 1; i <= m; i++) {
+        add(n + i, t, 1);
+        add(t, n + i, 0);
+    }
+
     for (int i = 1, u, v; i <= e; i++) {
         cin >> u >> v;
 
-        g[u].emplace_back(v);
+        add(u, n + v, 1);
+        add(n + v, u, 0);
     }
 
-    for (int i = 1; i <= n; i++) {
-        if (dfs(i, i)) ans++;
+    while (bfs()) {
+        while (flow = dinic(s, INF)) ans += flow;
     }
 
     cout << ans << endl;