## Editorial for Fast Maximum Matching

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

#### Code mẫu của flashmt

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;

struct HopcroftKarp
{
vector <int> leftMatch, rightMatch, dist, cur;
vector < vector <int> > a;
int m, n;

HopcroftKarp() {}
HopcroftKarp(int _m, int _n)
{
m = _m; n = _n;
a = vector < vector <int> >(m);
leftMatch = vector <int>(n, -1);
rightMatch = vector <int>(m, -1);
dist = vector <int>(m, -1);
cur = vector <int>(m, -1);
}

{
a[x].push_back(y);
}

int bfs()
{
int found = 0;
queue <int> q;
for (int i = 0; i < m; i++)
if (rightMatch[i] < 0) dist[i] = 0, q.push(i);
else dist[i] = -1;

while (!q.empty())
{
int x = q.front(); q.pop();
for (int i = 0; i < int(a[x].size()); i++)
{
int y = a[x][i];
if (leftMatch[y] < 0) found = 1;
else
if (dist[leftMatch[y]] < 0)
dist[leftMatch[y]] = dist[x] + 1, q.push(leftMatch[y]);
}
}

return found;
}

int dfs(int x)
{
for (; cur[x] < int(a[x].size()); cur[x]++)
{
int y = a[x][cur[x]];
if (leftMatch[y] < 0 || (dist[leftMatch[y]] == dist[x] + 1 && dfs(leftMatch[y])))
{
leftMatch[y] = x; rightMatch[x] = y;
return 1;
}
}
return 0;
}

int maxMatching()
{
int match = 0;
while (bfs())
{
for (int i = 0; i < m; i++) cur[i] = 0;
for (int i = 0; i < m; i++)
if (rightMatch[i] < 0) match += dfs(i);
}
return match;
}
};

int main()
{
int m, n, edge, x, y;
cin >> m >> n >> edge;
HopcroftKarp u(m, n);
while (edge--) scanf("%d%d", &x, &y), u.addEdge(--x, --y);
cout << u.maxMatching() << endl;
}


#### Code mẫu của happyboy99x

#include<bits/stdc++.h>
using namespace std;

const int N = 50000, INF = 1e9;
int mx[N], my[N], d[N], nx, ny;
vector<int> g[N];

void enter() {
int m; cin >> nx >> ny >> m;
for(int i = 0; i < m; ++i) {
int u, v; cin >> u >> v;
g[u-1].push_back(v-1);
}
}

bool dfs(int u, int mind) {
for (int v : g[u]) if(my[v] == -1 ? d[u] == mind : d[my[v]] == d[u]+1 && dfs(my[v], mind)) return mx[u] = v, my[v] = u, true;
d[u] = INF;
return false;
}

int maxMatch() {
int matching = 0;
fill(mx, mx + nx, -1); fill(my, my + ny, -1);
while(true) {
fill(d, d + nx, INF); queue<int> q;
for(int u = 0; u < nx; ++u) if(mx[u] == -1) d[u] = 0, q.push(u);
int mind = INF;
while(!q.empty()) {
int u = q.front(); q.pop();
for (int v : g[u]) if(my[v] == -1) mind = min(mind, d[u]);
else if(d[my[v]] == INF) d[my[v]] = d[u]+1, q.push(my[v]);
}
if(mind == INF) break;
for(int u = 0; u < nx; ++u) if(d[u] > mind) d[u] = INF;
for(int u = 0; u < nx; ++u)
if(mx[u] == -1 && dfs(u, mind)) ++matching;
}
return matching;
}

int main() {
ios::sync_with_stdio(false);
enter();
cout << maxMatch() << endl;
return 0;
}


#include <bits/stdc++.h>

using namespace std;

struct BipartiteGraph {
vector<vector<int> > E;
vector<vector<pair<int, int> > > a;
vector<int> match;
vector<int> edgeMatch;
vector<bool> was;
int m, n;

BipartiteGraph(int m, int n) {
this->m = m; this->n = n;
E.clear();
a.clear();
a.resize(m);
match.assign(n, -1);
edgeMatch.assign(n, -1);
was.assign(n, false);
}

void addEdge(int u, int v, vector<int> expression) {
int index = E.size();
a[u].push_back(make_pair(v, index));
E.push_back(expression);
}

bool dfs(int u) {
for (int i = 0; i < a[u].size(); ++i) {
int v = a[u][i].first;
if (was[v]) continue;
was[v] = true;
if (match[v] == -1 || dfs(match[v])) {
match[v] = u;
edgeMatch[v] = a[u][i].second;
return true;
}
}
return false;
}

int fastMatch() {
vector<int> buffer;
for (int i = 0; i < m; ++i) buffer.push_back(i);
bool stop = false;
int ans = 0;
do {
stop = true;
for (int i = 0; i < n; ++i) was[i] = false;
for (int i = (int)buffer.size() - 1; i >= 0; --i) {
int u = buffer[i];
if (dfs(u)) {
++ans;
stop = false;
buffer[i] = buffer.back();
buffer.pop_back();
}
}
} while (!stop);
return ans;
}
};

int main() {
ios::sync_with_stdio(false);
int n, m, p; cin >> m >> n >> p;
BipartiteGraph G(m, n);
int u, v;
while (p--) {
cin >> u >> v;
}
cout << G.fastMatch() << endl;
return 0;
}


#### Code mẫu của RR

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <complex>
#include <iostream>
#include <algorithm>

#include <ctime>
#include <deque>
#include <bitset>
#include <cctype>
#include <utility>
#include <cassert>

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))
using namespace std;

// Index from 1
const int inf = 1000111;
struct Matching {
int n;
vector<int> matchL, matchR, dist;
vector<bool> seen;
vector< vector<int> > ke;

Matching(int n) : n(n), matchL(n+1), matchR(n+1), dist(n+1), seen(n+1, false), ke(n+1) {}

void addEdge(int u, int v) {
ke[u].push_back(v);
}

bool bfs() {
queue<int> qu;
FOR(u,1,n) if (!matchL[u]) {
dist[u] = 0;
qu.push(u);
} else dist[u] = inf;
dist[0] = inf;

while (!qu.empty()) {
int u = qu.front(); qu.pop();
for(__typeof(ke[u].begin()) v = ke[u].begin(); v != ke[u].end(); ++v) {
if (dist[matchR[*v]] == inf) {
dist[matchR[*v]] = dist[u] + 1;
qu.push(matchR[*v]);
}
}
}
return dist[0] != inf;
}

bool dfs(int u) {
if (u) {
for(__typeof(ke[u].begin()) v = ke[u].begin(); v != ke[u].end(); ++v)
if (dist[matchR[*v]] == dist[u] + 1 && dfs(matchR[*v])) {
matchL[u] = *v;
matchR[*v] = u;
return true;
}
dist[u] = inf;
return false;
}
return true;
}

int match() {
int res = 0;
while (bfs()) {
FOR(u,1,n)
if (!matchL[u])
if (dfs(u)) ++res;
}
return res;
}
};

int main() {
ios :: sync_with_stdio(false); cin.tie(NULL);
int m, n, p;
while (cin >> m >> n >> p) {
Matching match(max(m, n));
while (p--) {
int u, v; cin >> u >> v;
}
cout << match.match() << endl;
}
}


#### Code mẫu của hieult

#include<cstdio>
#include<cmath>
#include<math.h>
#include<cstring>
#include<cstdlib>
#include<cassert>
#include<ctime>
#include<algorithm>
#include<iterator>
#include<iostream>
#include<cctype>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<list>
#define fi first
#define se second
#define PB push_back
#define MP make_pair
#define ep 0.00001
#define oo 111111111
#define mod 1000000007
#define TR(c, it) for(typeof((c).begin()) it=(c).begin(); it!=(c).end(); it++)
#define rep(i, n) for(int i = 0; i < n; i++)
#define FOR(i, a, b) for(int i = a; i <= b; i++)
#define FORD(i, a, b) for(int i = a; i >= b; i--)
//#define g 9.81
double const PI=4*atan(1.0);

using namespace std;

typedef pair<int, int> II;
typedef vector<int> VI;
typedef vector<II> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
typedef long long ll;

void OPEN(){
freopen("A.in","r",stdin);
freopen("A.out","w",stdout);
}
// Dinic

#define maxn 50011
#define maxe 150111

struct HopcroftKarp{
int nx, ny, E, adj[maxe], next[maxe], last[maxn],
matx[maxn], maty[maxn], que[maxn], level[maxn], run[maxn];

void init(int _nx, int _ny){
nx = _nx; ny = _ny; E = 0;
FOR(x, 1, nx) last[x] = -1, matx[x] = -1;
FOR(y, 1, ny) maty[y] = -1;
}

adj[E] = y; next[E] = last[x]; last[x] = E++;
}

bool bfs(){
bool found = false;
int size = 0;
FOR(x, 1, nx){
if(matx[x] != -1) level[x] = -1;
else{
level[x] = 0;
que[size++] = x;
}
}

rep(i, size){
for(int x = que[i], e = last[x]; e != -1; e = next[e]){
if(maty[y] == -1) found = true;
else if(level[maty[y]] == -1){
level[maty[y]] = level[x] + 1;
que[size++] = maty[y];
}
}
}

return found;
}

int dfs(int x){
for(int &e = run[x]; e != -1; e = next[e]){
if(maty[y] == -1 || (level[maty[y]] == level[x] + 1 && dfs(maty[y]))){
maty[y] = x;
matx[x] = y;
return 1;
}
}
return 0;
}

int maxMatching(){
int total = 0;
while(bfs()){
FOR(x, 1, nx) run[x] = last[x];
FOR(x, 1, nx) if(matx[x] == -1) total += dfs(x);
}
}
} hopkarp;

int main(){
// OPEN();
int n, m, k, u, v;
scanf("%d %d %d", &n, &m, &k);
hopkarp.init(n, m);
rep(i, k){
scanf("%d %d", &u, &v);
}
printf("%d", hopkarp.maxMatching());
}


#### Code mẫu của skyvn97

#include<cstdio>
#include<vector>
#include<queue>
#define MAX   50505
using namespace std;
const int INF=(int)1e7;
vector<int> g[MAX];
int matx[MAX];
int maty[MAX];
int d[MAX];
int m,n,p;
scanf("%d",&m);
scanf("%d",&n);
scanf("%d",&p);
int i,u,v;
for (i=1;i<=p;i=i+1) {
scanf("%d",&u);
scanf("%d",&v);
g[u].push_back(v);
}
}
bool BFS(void) {
queue<int> q;
while (!q.empty()) q.pop();
int i,u,v;
for (i=1;i<=m;i=i+1) {
if (matx[i]==0) {
d[i]=0;
q.push(i);
}
else d[i]=INF;
}
d[0]=INF;
while (!q.empty()) {
u=q.front();q.pop();
if (d[u]<d[0])
for (i=0;i<g[u].size();i=i+1) {
v=g[u][i];
if (d[maty[v]]>=INF) {
d[maty[v]]=d[u]+1;
q.push(maty[v]);
}
}
}
return (d[0]<INF);
}
bool DFS(const int &u) {
if (u==0) return (true);
int i,v;
for (i=0;i<g[u].size();i=i+1) {
v=g[u][i];
if (d[maty[v]]==d[u]+1)
if (DFS(maty[v])) {
matx[u]=v;
maty[v]=u;
return (true);
}
}
d[u]=INF;
return (false);
}
void fastmatching(void) {
int i;
for (i=1;i<=m;i=i+1) matx[i]=0;
for (i=1;i<=n;i=i+1) maty[i]=0;
int res=0;
while (BFS()) {
//  printf("ok\n");
for (i=1;i<=m;i=i+1)
if (matx[i]==0)
if (DFS(i)) res++;
//printf("%d\n",res);
}
printf("%d",res);
}
int main(void) {
#ifndef ONLINE_JUDGE
freopen("tmp.txt","r",stdin);
#endif
fastmatching();
return 0;
}


#### Code mẫu của khuc_tuan

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

struct List {
int i;
List * next;
};

List cont[400000];
int ncont1, ncont2;

List * ke[50050];
List * keY[50050];

int M, N, nE;
int X[50050], Y[50050], Q[50050], levelX[50050], levelY[50050];
bool vs[50050];
int L, R, maxLevel, socap;

inline void addList( List * & p, int i, int & cn) {
List * q = cont + ++cn;
q->i = i;
q->next = p;
p = q;
}

bool bfs() {
L = 1;
R = 0;
memset( levelX, 0, sizeof(levelX));
memset( levelY, 0, sizeof(levelY));
ncont2 = 155000;
memset( keY, 0, sizeof(keY));

for(int i=1;i<=M;++i) if(X[i]==0) Q[++R] = i, levelX[i] = 1;
maxLevel = 1000000;
while(L<=R) {
int u = Q[L++];
if(levelX[u] > maxLevel) break;
for(List * p = ke[u]; p!=NULL; p = p->next) {
int v = p->i;
if(levelY[v]==0) {
levelY[v] = levelX[u] + 1;
if(Y[v]==0)
maxLevel = levelY[v];
else
if(levelX[Y[v]]==0) {
levelX[Y[v]] = levelY[v] + 1;
Q[++R] = Y[v];
}
}
if(levelY[v] == levelX[u] + 1) addList( keY[v], u, ncont2);
}
}
return maxLevel < 1000000;
}

bool dfs(int j) {
for(List * p = keY[j]; p!=NULL; p = p->next) {
int i = p->i;
if(!vs[i]) {
vs[i] = true;
if(levelX[i]==1 || dfs(X[i])) {
X[i] = j;
Y[j] = i;
return true;
}
}
}
return false;
}

void tang() {
memset( vs, 0, sizeof(vs));
for(int i=1;i<=N;++i)
if(levelY[i]==maxLevel && Y[i]==0)
if(dfs(i)) ++socap;
}

int main() {
scanf("%d%d%d", &M, &N, &nE);
for(int i=0;i<nE;++i) {
int u, v;
scanf("%d%d", &u, &v);
if(X[u]==0 && Y[v]==0) {
X[u] = v;
Y[v] = u;
++socap;
}