#line 1 "test/yj_bipartitematching.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bipartitematching"
#include <cstdio>
#include <vector>
#line 1 "Graph/capacitated_adjacency_list.cpp"
/**
* @brief 容量つきグラフの隣接リスト
* @author えびちゃん
*/
#include <cstddef>
#line 1 "Graph/adjacency_list.cpp"
/**
* @brief 重みつきグラフの隣接リスト
* @author えびちゃん
*/
#line 10 "Graph/adjacency_list.cpp"
#include <algorithm>
#include <type_traits>
#line 13 "Graph/adjacency_list.cpp"
template <typename WeightType>
class weighted_edge {
public:
using size_type = size_t;
using weight_type = WeightType;
protected:
size_type M_src, M_dst;
weight_type M_weight;
public:
weighted_edge() = default;
weighted_edge(weighted_edge const&) = default;
weighted_edge(weighted_edge&&) = default;
weighted_edge(size_type s, size_type d, weight_type w):
M_src(s), M_dst(d), M_weight(w)
{}
weighted_edge& operator =(weighted_edge const&) = default;
weighted_edge& operator =(weighted_edge&&) = default;
bool operator <(weighted_edge const& other) const {
if (M_weight < other.M_weight) return true;
if (other.M_weight < M_weight) return false;
if (M_src != other.M_src) return M_src < other.M_src;
return M_dst < other.M_dst;
}
size_type source() const { return M_src; }
size_type target() const { return M_dst; }
weight_type weight() const { return M_weight; }
};
struct directed_tag {};
struct undirected_tag {};
template <typename Edge, typename Directedness>
class adjacency_list {
public:
using size_type = size_t;
using edge_type = Edge;
using weight_type = typename Edge::weight_type;
private:
std::vector<std::vector<edge_type>> M_g;
public:
adjacency_list() = default;
adjacency_list(adjacency_list const&) = default;
adjacency_list(adjacency_list&&) = default;
explicit adjacency_list(size_type n): M_g(n) {}
template <typename... Args>
void emplace(size_type src, size_type dst, Args... args) {
M_g[src].emplace_back(src, dst, args...);
if (std::is_same<Directedness, undirected_tag>::value)
M_g[dst].emplace_back(dst, src, args...);
}
void sort_by_index() {
auto cmp = [](auto const& e1, auto const& e2) {
return e1.target() < e2.target();
};
for (auto v: M_g) std::sort(v.begin(), v.end(), cmp);
}
size_type size() const { return M_g.size(); }
auto const& operator [](size_type i) const { return M_g[i]; }
};
#line 12 "Graph/capacitated_adjacency_list.cpp"
template <typename WeightType>
class capacitated_edge {
public:
using size_type = size_t;
using weight_type = WeightType;
protected:
size_type M_src, M_dst;
weight_type M_capacity;
size_type M_rev;
public:
capacitated_edge() = default;
capacitated_edge(capacitated_edge const&) = default;
capacitated_edge(capacitated_edge&&) = default;
capacitated_edge(size_type s, size_type d, weight_type c, size_type r):
M_src(s), M_dst(d), M_capacity(c), M_rev(r)
{}
capacitated_edge& operator =(capacitated_edge const&) = default;
capacitated_edge& operator =(capacitated_edge&&) = default;
bool operator <(capacitated_edge const& other) const {
if (M_capacity < other.M_capacity) return true;
if (other.M_capacity < M_capacity) return false;
if (M_src != other.M_src) return M_src < other.M_src;
return M_dst < other.M_dst;
}
size_type source() const { return M_src; }
size_type target() const { return M_dst; }
weight_type capacity() const { return M_capacity; }
weight_type& capacity() { return M_capacity; }
size_type reversed() const { return M_rev; }
};
template <typename WeightType, typename Directedness>
class adjacency_list<capacitated_edge<WeightType>, Directedness> {
public:
using size_type = size_t;
using edge_type = capacitated_edge<WeightType>;
using weight_type = WeightType;
private:
std::vector<std::vector<edge_type>> M_g;
public:
adjacency_list() = default;
adjacency_list(adjacency_list const&) = default;
adjacency_list(adjacency_list&&) = default;
explicit adjacency_list(size_type n): M_g(n) {}
template <typename... Args>
void emplace(size_type src, size_type dst, weight_type cap) {
M_g[src].emplace_back(src, dst, cap, M_g[dst].size());
if (std::is_same<Directedness, directed_tag>::value) {
M_g[dst].emplace_back(dst, src, weight_type{0}, M_g[src].size()-1);
} else if (std::is_same<Directedness, undirected_tag>::value) {
M_g[dst].emplace_back(dst, src, cap, M_g[src].size()-1);
}
}
size_type size() const { return M_g.size(); }
auto const& operator [](size_type i) const { return M_g[i]; }
auto& operator [](size_type i) { return M_g[i]; }
};
#line 1 "Graph/dinitz.cpp"
/**
* @brief 最大流 (Dinitz 法)
* @author えびちゃん
*/
#include <queue>
#line 11 "Graph/dinitz.cpp"
#line 1 "utility/literals.cpp"
/**
* @brief ユーザ定義リテラル
* @author えびちゃん
*/
#line 10 "utility/literals.cpp"
#include <cstdint>
constexpr intmax_t operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }
constexpr int8_t operator ""_i8(unsigned long long n) { return n; }
constexpr int16_t operator ""_i16(unsigned long long n) { return n; }
constexpr int32_t operator ""_i32(unsigned long long n) { return n; }
constexpr int64_t operator ""_i64(unsigned long long n) { return n; }
constexpr uint8_t operator ""_u8(unsigned long long n) { return n; }
constexpr uint16_t operator ""_u16(unsigned long long n) { return n; }
constexpr uint32_t operator ""_u32(unsigned long long n) { return n; }
constexpr uint64_t operator ""_u64(unsigned long long n) { return n; }
#line 1 "utility/limits.cpp"
/**
* @brief 型依存の定数
* @author えびちゃん
*/
#include <limits>
#include <utility>
template <typename Tp>
class limits: public std::numeric_limits<Tp> {};
template <typename T1, typename T2>
class limits<std::pair<T1, T2>> {
public:
static constexpr auto min() {
return std::make_pair(limits<T1>::min(), limits<T2>::min());
}
static constexpr auto max() {
return std::make_pair(limits<T1>::max(), limits<T2>::max());
}
};
#line 1 "utility/make/fix_point.cpp"
/**
* @brief ラムダ式の再帰
* @author えびちゃん
*/
#ifndef H_make_fix_point
#define H_make_fix_point
#line 10 "utility/make/fix_point.cpp"
template <typename Fn>
class fix_point: Fn {
public:
explicit constexpr fix_point(Fn&& f) noexcept: Fn(std::forward<Fn>(f)) {}
template <typename... Args>
constexpr decltype(auto) operator ()(Args&&... args) const {
return Fn::operator ()(*this, std::forward<Args>(args)...);
}
};
template <typename Fn>
static inline constexpr decltype(auto) make_fix_point(Fn&& f) noexcept {
return fix_point<Fn>{std::forward<Fn>(f)};
}
#endif /* !defined(H_make_fix_point) */
#line 15 "Graph/dinitz.cpp"
struct dinitz_tag {} dinitz;
template <typename AdjacencyList>
auto max_flow(AdjacencyList& g, size_t s, size_t t,
typename AdjacencyList::weight_type fl, dinitz_tag) {
using size_type = typename AdjacencyList::size_type;
using weight_type = typename AdjacencyList::weight_type;
size_type n = g.size();
std::vector<size_type> level(n), iter(n);
auto bfs = [&](size_type s) -> void {
level.assign(n, -1_zu);
std::queue<size_type> q;
level[s] = 0;
q.push(s);
while (!q.empty()) {
size_type v = q.front();
q.pop();
for (auto const& e: g[v]) {
if (e.capacity() > weight_type(0) && level[e.target()] == -1_zu) {
level[e.target()] = level[e.source()] + 1;
q.push(e.target());
}
}
}
};
auto dfs = make_fix_point([&](auto dfs_, size_type v, weight_type f) -> weight_type {
if (v == t) return f;
for (size_type& i = iter[v]; i < g[v].size(); ++i) {
auto& e = g[v][i];
if (e.capacity() > weight_type(0) && level[v] < level[e.target()]) {
weight_type f0 = dfs_(e.target(), std::min(f, e.capacity()));
if (f0 > weight_type(0)) {
e.capacity() -= f0;
g[e.target()][e.reversed()].capacity() += f0;
return f0;
}
}
}
return weight_type(0);
});
weight_type res{0};
while (true) {
bfs(s);
if (level[t] == -1_zu) return res;
iter.assign(n, 0);
weight_type f;
while ((f = dfs(s, fl)) > weight_type(0)) {
res += f;
fl -= f;
if (fl == weight_type(0)) return res;
}
}
}
template <typename AdjacencyList>
auto max_flow(AdjacencyList& g, size_t s, size_t t, dinitz_tag) {
auto fl = limits<typename AdjacencyList::weight_type>::max();
return max_flow(g, s, t, fl, dinitz);
}
#line 8 "test/yj_bipartitematching.test.cpp"
int main() {
size_t l, r, m;
scanf("%zu %zu %zu", &l, &r, &m);
adjacency_list<capacitated_edge<int>, directed_tag> g(l+r+2);
size_t source = l+r;
size_t sink = source+1;
for (size_t i = 0; i < m; ++i) {
size_t a, b;
scanf("%zu %zu", &a, &b);
g.emplace(a, l+b, 1);
}
for (size_t i = 0; i < l; ++i) g.emplace(source, i, 1);
for (size_t i = 0; i < r; ++i) g.emplace(l+i, sink, 1);
printf("%d\n", max_flow(g, source, sink, dinitz));
for (size_t i = 0; i < l; ++i) {
for (auto const& e: g[i]) {
size_t j = e.target();
if (j == source) continue;
if (e.capacity() == 0) printf("%zu %zu\n", i, j-l);
}
}
}
test/yj_bipartitematching.test.cpp