matching-2.cpp

#include"iomanip"
#include"iostream"
#include"limits"
#include"cmath"
#include"vector"
#include"algorithm"
#include"list"
#include"queue"
#include"stack"
#include"set"
#include"unordered_set"
#include"map"
#include"unordered_map"
#include"string"
#include"cstring"
#include"assert.h"
using namespace std;
#define ff first
#define ss second
#define all(v) v.begin(),v.end()
#define mp make_pair
#define pb push_back
#define mset(a,b) memset(a,b,sizeof(a))
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef long long LL;

struct Edge {
  int u, v;
  LL cap, flow;
  Edge() {}
  Edge(int u, int v, LL cap): u(u), v(v), cap(cap), flow(0) {}
};

struct Dinic {
  int N;
  vector<Edge> E;
  vector<vector<int>> g;
  vector<int> d, pt;
  
  Dinic(int N): N(N), E(0), g(N), d(N), pt(N) {}

  void AddEdge(int u, int v, LL cap) {
    if (u != v) {
      E.emplace_back(u, v, cap);
      g[u].emplace_back(E.size() - 1);
      E.emplace_back(v, u, 0);
      g[v].emplace_back(E.size() - 1);
    }
  }

  bool BFS(int S, int T) {
    queue<int> q({S});
    fill(d.begin(), d.end(), N + 1);
    d[S] = 0;
    while(!q.empty()) {
      int u = q.front(); q.pop();
      if (u == T) break;
      for (int k: g[u]) {
        Edge &e = E[k];
        if (e.flow < e.cap && d[e.v] > d[e.u] + 1) {
          d[e.v] = d[e.u] + 1;
          q.emplace(e.v);
        }
      }
    }
    return d[T] != N + 1;
  }

  LL DFS(int u, int T, LL flow = -1) {
    if (u == T || flow == 0) return flow;
    for (int &i = pt[u]; i < g[u].size(); ++i) {
      Edge &e = E[g[u][i]];
      Edge &oe = E[g[u][i]^1];
      if (d[e.v] == d[e.u] + 1) {
        LL amt = e.cap - e.flow;
        if (flow != -1 && amt > flow) amt = flow;
        if (LL pushed = DFS(e.v, T, amt)) {
          e.flow += pushed;
          oe.flow -= pushed;
          return pushed;
        }
      }
    }
    return 0;
  }

  LL MaxFlow(int S, int T) {
    LL total = 0;
    while (BFS(S, T)) {
      fill(pt.begin(), pt.end(), 0);
      while (LL flow = DFS(S, T))
        total += flow;
    }
    return total;
  }
};


int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n,m,p;
    cin>>n>>m>>p;
    Dinic ob(n+m+2);
    for(int i=0;i<p;++i)
    {
        int x,y;
        cin>>x>>y;
        ob.AddEdge(x,n+y,1);
    }
    for(int i=1;i<=n;++i)
    {
        ob.AddEdge(0,i,1);
    }
    for(int i=1;i<=m;++i)
    {
        ob.AddEdge(n+i,n+m+1,1);
    }
    ll ans = ob.MaxFlow(0,n+m+1);
    cout<<ans<<'\n';
}