mmrz's library

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:warning: verify/yosupo/bipertitematching.cpp

Depends on

Code

# define PROBLEM "https://judge.yosupo.jp/problem/bipertitematching"

#include "./../../template/template.hpp"
#include "./../../graph/bipartite_matching.hpp"

void mmrz::solve(){
	int l, r, m;
	cin >> l >> r >> m;
	vector<pair<int, int>> es;
	while(m--){
		int a, b;
		cin >> a >> b;
		es.emplace_back(a, b);
	}

	auto bm = bipartite_matching(l, r, es);

	cout << ssize(bm) << '\n';
	for(auto [l_v, r_v] : bm){
		cout << l_v << ' ' << r_v << '\n';
	}
}
#line 1 "verify/yosupo/bipertitematching.cpp"
# define PROBLEM "https://judge.yosupo.jp/problem/bipertitematching"

#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "graph/bipartite_matching.hpp"

#line 2 "graph/dinic.hpp"

#line 6 "graph/dinic.hpp"

template<typename T>
struct dinic {

	struct edge{
		int to;
		T cap;
		T rev;
		T init_cap;
	};
		
	int n;
	std::vector<std::vector<edge>> G;
	std::vector<int> level;
	std::vector<int> iter;

	std::vector<int> from_idx, to_idx;
	int edge_idx;

	dinic(int _v) : n(_v), G(n), level(n), iter(n), edge_idx(0) {}

	int add_edge(int from, int to, T cap){
		G[from].push_back((edge){to, cap, (T)G[to].size(), cap});
		G[to].push_back((edge){from, 0, (T)(G[from].size() - 1), 0});
		from_idx.emplace_back(from);
		to_idx.emplace_back((int)G[from].size()-1);
		
		return edge_idx++;
	}

	void bfs(int s){
		for(int i = 0;i < n;i++)level[i] = -1;
		std::queue<int> que;
		level[s] = 0;
		que.push(s);
		while(!que.empty()){
			int v = que.front();
			que.pop();
			for(int i = 0;i < (int)G[v].size();i++){
				edge &e = G[v][i];
				if(e.cap > 0 && level[e.to] < 0){
					level[e.to] = level[v] + 1;
					que.push(e.to);
				}
			}
		}
	}

	T dfs(int v, int t, T f){
		if(v == t)return f;
		for(int &i = iter[v];i < (int)G[v].size();i++){
			edge &e = G[v][i];
			if(e.cap > 0 && level[v] < level[e.to]){
				T d = dfs(e.to, t, min(f, e.cap));
				if(d > 0){
					e.cap -= d;
					G[e.to][e.rev].cap += d;
					return d;
				}
			}
		}
		return 0;
	}

	T calc(int s, int t){
		T flow = 0;
		for(;;){
			bfs(s);
			if(level[t] < 0)return flow;
			for(int i = 0;i < n;i++)iter[i] = 0;
			T f;
			while((f = dfs(s, t, std::numeric_limits<T>::max())) > 0) {
				flow += f;
			}
		}
	}

	T get_flow(int idx){
		return G[from_idx[idx]][to_idx[idx]].init_cap - G[from_idx[idx]][to_idx[idx]].cap;
	}
};
#line 4 "graph/bipartite_matching.hpp"

#line 6 "graph/bipartite_matching.hpp"
#include<ranges>

vector<pair<int, int>> bipartite_matching(const int &l, const int &r, const vector<pair<int, int>> &es) {

	dinic<int> matching(l+r+2);
	const int S = l+r+0;
	const int T = l+r+1;

	for(int i = 0;i < l;i++)matching.add_edge(S, i, 1);
	for(int i = 0;i < r;i++)matching.add_edge(l+i, T, 1);
	for(auto [u, v] : es){
		matching.add_edge(u, l+v, 1);
	}

	matching.calc(S, T);

	std::vector<pair<int, int>> ret;
	
	// C++23
	// for(auto [idx, edge] : es | std::views::enumerate) {
	for(int idx = 0;idx < ssize(es);idx++){
		auto &edge = es[idx];
		if(matching.get_flow(l+r+idx) == 1){
			ret.emplace_back(edge);
		}
	}

	return ret;
}
#line 5 "verify/yosupo/bipertitematching.cpp"

void mmrz::solve(){
	int l, r, m;
	cin >> l >> r >> m;
	vector<pair<int, int>> es;
	while(m--){
		int a, b;
		cin >> a >> b;
		es.emplace_back(a, b);
	}

	auto bm = bipartite_matching(l, r, es);

	cout << ssize(bm) << '\n';
	for(auto [l_v, r_v] : bm){
		cout << l_v << ' ' << r_v << '\n';
	}
}
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