verify/graph/library_checker_general_matching.test.cpp

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Last update: 2026-10-06 01:57:24+09:00
Problem: https://judge.yosupo.jp/problem/general_matching

Depends on

Code

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

#include "../../utilities/fast_io.hpp"

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

#include "../../graph/graph.hpp"
#include "../../graph/general_matching.hpp"

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    int N, M;
    fast_input >> N >> M;
    m1une::graph::GeneralMatching gm(N);
    while (M--) {
        int u, v;
        fast_input >> u >> v;
        gm.add_edge(u, v);
    }
    fast_output << gm.max_matching() << '\n';
    for (auto p : gm.matching()) {
        fast_output << p.from << ' ' << p.to << '\n';
    }
}

#line 1 "verify/graph/library_checker_general_matching.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/general_matching"

#line 1 "utilities/fast_io.hpp"



#include <algorithm>
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#include <utility>
#include <unistd.h>
#include <vector>

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 4 "verify/graph/library_checker_general_matching.test.cpp"

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

#line 1 "graph/graph.hpp"



#line 8 "graph/graph.hpp"

namespace m1une {
namespace graph {

template <class T = int>
struct Edge {
    using cost_type = T;

    int from;
    int to;
    T cost;
    int id;
    bool alive;

    Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
    Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
        : from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}

    int other(int v) const {
        assert(v == from || v == to);
        return from ^ to ^ v;
    }
};

template <class T = int>
struct Graph {
    using edge_type = Edge<T>;
    using cost_type = T;

   private:
    struct EdgePositions {
        std::array<std::pair<int, int>, 2> value{};
        int size = 0;

        void push_back(std::pair<int, int> position) {
            assert(size < 2);
            value[size++] = position;
        }
    };

    int _n;
    int _edge_count;
    std::vector<std::vector<edge_type>> _g;
    std::vector<EdgePositions> _edge_positions;

   public:
    Graph() : _n(0), _edge_count(0) {}
    explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    int edge_count() const {
        return _edge_count;
    }

    int add_vertex() {
        _g.emplace_back();
        return _n++;
    }

    int add_directed_edge(int from, int to, T cost = T(1)) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int id = _edge_count++;
        int idx = int(_g[from].size());
        _g[from].push_back(edge_type(from, to, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({from, idx});
        return id;
    }

    int add_edge(int u, int v, T cost = T(1)) {
        assert(0 <= u && u < _n);
        assert(0 <= v && v < _n);
        int id = _edge_count++;
        int u_idx = int(_g[u].size());
        _g[u].push_back(edge_type(u, v, cost, id));
        int v_idx = int(_g[v].size());
        _g[v].push_back(edge_type(v, u, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({u, u_idx});
        _edge_positions.back().push_back({v, v_idx});
        return id;
    }

    void set_edge_alive(int id, bool alive) {
        assert(0 <= id && id < _edge_count);
        for (int i = 0; i < _edge_positions[id].size; ++i) {
            auto [v, idx] = _edge_positions[id].value[i];
            _g[v][idx].alive = alive;
        }
    }

    void erase_edge(int id) {
        set_edge_alive(id, false);
    }

    void revive_edge(int id) {
        set_edge_alive(id, true);
    }

    bool is_edge_alive(int id) const {
        assert(0 <= id && id < _edge_count);
        assert(_edge_positions[id].size != 0);
        auto [v, idx] = _edge_positions[id].value[0];
        return _g[v][idx].alive;
    }

    const std::vector<edge_type>& operator[](int v) const {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    std::vector<edge_type>& operator[](int v) {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    const std::vector<std::vector<edge_type>>& adjacency() const {
        return _g;
    }

    std::vector<std::vector<edge_type>>& adjacency() {
        return _g;
    }

    std::vector<edge_type> edges(bool include_inactive = false) const {
        std::vector<edge_type> result;
        result.reserve(_edge_count);
        std::vector<char> used(_edge_count, false);
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                if (!include_inactive && !e.alive) continue;
                if (0 <= e.id && e.id < _edge_count) {
                    if (used[e.id]) continue;
                    used[e.id] = true;
                }
                result.push_back(e);
            }
        }
        return result;
    }

    Graph reversed() const {
        Graph result(_n);
        result._edge_count = _edge_count;
        result._edge_positions.assign(_edge_count, {});
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                int idx = int(result._g[e.to].size());
                result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
                if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
            }
        }
        return result;
    }
};

}  // namespace graph
}  // namespace m1une


#line 1 "graph/general_matching.hpp"



#line 6 "graph/general_matching.hpp"
#include <optional>
#line 9 "graph/general_matching.hpp"

#line 11 "graph/general_matching.hpp"

namespace m1une {
namespace graph {

struct GeneralMatching {
    struct Edge {
        int from;
        int to;
        int id;
        bool alive;

        int other(int v) const {
            assert(v == from || v == to);
            return from ^ to ^ v;
        }
    };

    struct Pair {
        int from;
        int to;
        int edge_id;
    };

   private:
    int _n;
    std::vector<Edge> _edges;
    std::vector<std::vector<int>> _adj;
    std::vector<int> _mate;
    std::vector<int> _mate_edge;
    bool _calculated;

    void invalidate() {
        _calculated = false;
    }

    void ensure_matching() {
        if (!_calculated) max_matching();
    }

    bool is_matched_edge(int id) const {
        const auto& e = _edges[id];
        return _mate[e.from] == e.to && _mate_edge[e.from] == id;
    }

    enum MatchingLabel : char {
        even_label,
        odd_label,
        unlabeled
    };

    struct MutablePartition {
        std::vector<int> parent;
        std::vector<int> rank;
        std::vector<int> representative;

        MutablePartition() = default;

        explicit MutablePartition(int n) {
            reset(n);
        }

        void reset(int n) {
            parent.resize(n);
            rank.assign(n, 0);
            representative.resize(n);
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                representative[i] = i;
            }
        }

        int root(int v) {
            if (parent[v] == v) return v;
            return parent[v] = root(parent[v]);
        }

        int operator()(int v) {
            return representative[root(v)];
        }

        void unite(int a, int b) {
            int ra = root(a);
            int rb = root(b);
            if (ra == rb) return;
            if (rank[ra] < rank[rb]) std::swap(ra, rb);
            parent[rb] = ra;
            if (rank[ra] == rank[rb]) rank[ra]++;
        }

        void make_rep(int v) {
            representative[root(v)] = v;
        }
    };

    struct EdgeBucketQueue {
        std::vector<std::vector<int>> bucket;
        std::vector<int> head;

        void reset(int n) {
            bucket.assign(n + 3, {});
            head.assign(n + 3, 0);
        }

        void insert(int edge_id, int key) {
            if (key < 0 || int(bucket.size()) <= key) return;
            bucket[key].push_back(edge_id);
        }

        int pop(int key) {
            if (key < 0 || int(bucket.size()) <= key) return -1;
            if (head[key] == int(bucket[key].size())) return -1;
            return bucket[key][head[key]++];
        }
    };

    struct NewMatchingPair {
        int from;
        int to;
        int edge_id;
    };

    // General-graph shortest augmenting path phase solver.
    struct MicaliVaziraniSolver {
        GeneralMatching& graph;
        int n;
        int matching_size;
        int delta;
        int visit_token;
        int even_time_token;
        MutablePartition base;
        MutablePartition delayed_base;
        EdgeBucketQueue queue;
        std::vector<MatchingLabel> label;
        std::vector<MatchingLabel> h_label;
        std::vector<int> parent;
        std::vector<int> parent_edge;
        std::vector<int> source_bridge;
        std::vector<int> target_bridge;
        std::vector<int> bridge_edge;
        std::vector<int> lcp;
        std::vector<int> path_mark_1;
        std::vector<int> path_mark_2;
        std::vector<int> restore_vertex;
        std::vector<int> restore_value;
        std::vector<int> rep;
        std::vector<int> h_mate;
        std::vector<char> is_h_edge;
        std::vector<std::vector<int>> contracted_into;
        std::vector<int> h_parent_edge;
        std::vector<int> h_even_time;
        std::vector<int> h_bridge_edge;
        std::vector<int> h_bridge_dir;

        explicit MicaliVaziraniSolver(GeneralMatching& graph_)
            : graph(graph_),
              n(graph_._n),
              matching_size(0),
              delta(0),
              visit_token(0),
              even_time_token(0),
              base(n),
              delayed_base(n),
              label(n, unlabeled),
              h_label(n, unlabeled),
              parent(n, -1),
              parent_edge(n, -1),
              source_bridge(n, -1),
              target_bridge(n, -1),
              bridge_edge(n, -1),
              lcp(n, 0),
              path_mark_1(n, 0),
              path_mark_2(n, 0),
              rep(n, -1),
              h_mate(n, -1),
              is_h_edge(graph_._edges.size(), false),
              contracted_into(n),
              h_parent_edge(n, -1),
              h_even_time(n, 0),
              h_bridge_edge(n, -1),
              h_bridge_dir(n, 0) {}

        bool active(int edge_id) const {
            return graph._edges[edge_id].alive;
        }

        int other(int edge_id, int v) const {
            return graph._edges[edge_id].other(v);
        }

        int edge_weight(int edge_id) const {
            return graph.is_matched_edge(edge_id) ? 2 : 0;
        }

        void set_match(int edge_id) {
            const auto& e = graph._edges[edge_id];
            graph._mate[e.from] = e.to;
            graph._mate[e.to] = e.from;
            graph._mate_edge[e.from] = edge_id;
            graph._mate_edge[e.to] = edge_id;
        }

        void initialize_greedy_matching() {
            graph._mate.assign(n, -1);
            graph._mate_edge.assign(n, -1);
            matching_size = 0;
            for (const auto& e : graph._edges) {
                if (!e.alive) continue;
                if (graph._mate[e.from] != -1 || graph._mate[e.to] != -1) continue;
                set_match(e.id);
                matching_size++;
            }
        }

        void scan_edge(int edge_id, int from) {
            if (!active(edge_id)) return;
            int to = other(edge_id, from);
            if (to == from || graph._mate[to] == from || label[base(to)] == odd_label) return;
            if (label[to] == unlabeled) {
                queue.insert(edge_id, lcp[from] + 2);
            } else {
                queue.insert(edge_id, (lcp[from] + lcp[to]) / 2 + 1);
            }
        }

        void shrink_path(int blossom_base, int x, int y, int edge_id,
                         std::vector<std::pair<int, int>>& delayed_unions) {
            int v = base(x);
            while (v != blossom_base) {
                base.unite(v, blossom_base);
                delayed_unions.push_back({v, blossom_base});

                v = graph._mate[v];
                assert(v != -1);
                base.unite(v, blossom_base);
                delayed_unions.push_back({v, blossom_base});
                base.make_rep(blossom_base);

                source_bridge[v] = x;
                target_bridge[v] = y;
                bridge_edge[v] = edge_id;
                restore_vertex.push_back(v);
                restore_value.push_back(lcp[v]);
                lcp[v] = lcp[x] + lcp[y] - lcp[graph._mate[v]] + 2;

                for (int id : graph._adj[v]) scan_edge(id, v);
                assert(parent[v] != -1);
                v = base(parent[v]);
            }
            delayed_unions.push_back({blossom_base, blossom_base});
        }

        void build_phase_graph() {
            std::fill(h_mate.begin(), h_mate.end(), -1);
            std::fill(is_h_edge.begin(), is_h_edge.end(), false);
            for (auto& vertices : contracted_into) vertices.clear();

            for (int v = 0; v < n; v++) contracted_into[delayed_base(v)].push_back(v);

            for (const auto& e : graph._edges) {
                if (!e.alive) continue;
                int u = e.from;
                int v = e.to;
                int uh = delayed_base(u);
                int vh = delayed_base(v);
                if (uh == vh) continue;
                if (label[uh] == odd_label && label[vh] == odd_label) continue;

                int w = edge_weight(e.id);
                bool even_odd =
                    (label[uh] == even_label && label[vh] == odd_label && lcp[v] == lcp[u] + 1 - w) ||
                    (label[vh] == even_label && label[uh] == odd_label && lcp[u] == lcp[v] + 1 - w);
                bool unlabeled_unlabeled = label[uh] == unlabeled && label[vh] == unlabeled && w == 2;
                bool even_unlabeled =
                    (label[uh] == even_label && label[vh] == unlabeled && lcp[u] == delta - 2) ||
                    (label[vh] == even_label && label[uh] == unlabeled && lcp[v] == delta - 2);
                bool even_even = label[uh] == even_label && label[vh] == even_label;
                bool tight_even_even = even_even && lcp[u] + lcp[v] == 2 * delta + w - 2;

                if (even_odd || unlabeled_unlabeled || even_unlabeled || tight_even_even) {
                    is_h_edge[e.id] = true;
                    if (w == 2) {
                        h_mate[uh] = vh;
                        h_mate[vh] = uh;
                    }
                }
            }
        }

        bool phase_one() {
            delta = 0;
            base.reset(n);
            delayed_base.reset(n);
            queue.reset(n);
            std::fill(label.begin(), label.end(), unlabeled);
            std::fill(parent.begin(), parent.end(), -1);
            std::fill(parent_edge.begin(), parent_edge.end(), -1);
            std::fill(source_bridge.begin(), source_bridge.end(), -1);
            std::fill(target_bridge.begin(), target_bridge.end(), -1);
            std::fill(bridge_edge.begin(), bridge_edge.end(), -1);
            std::fill(lcp.begin(), lcp.end(), 0);

            for (int v = 0; v < n; v++) {
                if (graph._mate[v] == -1) label[v] = even_label;
            }
            for (int v = 0; v < n; v++) {
                if (label[v] != even_label) continue;
                for (int id : graph._adj[v]) scan_edge(id, v);
            }

            std::vector<std::pair<int, int>> delayed_unions;
            while (delta <= n + 1) {
                restore_vertex.clear();
                restore_value.clear();

                while (true) {
                    int edge_id = queue.pop(delta);
                    if (edge_id == -1) break;
                    if (!active(edge_id)) continue;

                    int x = graph._edges[edge_id].from;
                    int y = graph._edges[edge_id].to;
                    if (label[base(x)] != even_label) std::swap(x, y);
                    if (label[base(x)] != even_label) continue;
                    if (graph._mate[x] == y || base(x) == base(y) || label[base(y)] == odd_label) continue;

                    if (label[base(y)] == unlabeled) {
                        int z = graph._mate[y];
                        assert(z != -1);
                        lcp[y] = lcp[x] + 1;
                        lcp[z] = lcp[x] + 2;
                        parent[y] = x;
                        parent_edge[y] = edge_id;
                        parent[z] = y;
                        parent_edge[z] = graph._mate_edge[z];
                        label[y] = odd_label;
                        label[z] = even_label;
                        for (int id : graph._adj[z]) scan_edge(id, z);
                        continue;
                    }

                    if (label[base(y)] != even_label || lcp[x] + lcp[y] != 2 * delta - 2) continue;

                    ++visit_token;
                    int hx = base(x);
                    int hy = base(y);
                    path_mark_1[hx] = visit_token;
                    path_mark_2[hy] = visit_token;
                    while (path_mark_1[hy] != visit_token && path_mark_2[hx] != visit_token &&
                           (graph._mate[hx] != -1 || graph._mate[hy] != -1)) {
                        if (graph._mate[hx] != -1) {
                            assert(parent[graph._mate[hx]] != -1);
                            hx = base(parent[graph._mate[hx]]);
                            path_mark_1[hx] = visit_token;
                        }
                        if (graph._mate[hy] != -1) {
                            assert(parent[graph._mate[hy]] != -1);
                            hy = base(parent[graph._mate[hy]]);
                            path_mark_2[hy] = visit_token;
                        }
                    }

                    if (path_mark_1[hy] == visit_token || path_mark_2[hx] == visit_token) {
                        int blossom_base = path_mark_1[hy] == visit_token ? hy : hx;
                        shrink_path(blossom_base, x, y, edge_id, delayed_unions);
                        shrink_path(blossom_base, y, x, edge_id, delayed_unions);
                    } else {
                        for (int i = int(restore_vertex.size()) - 1; i >= 0; i--) {
                            lcp[restore_vertex[i]] = restore_value[i];
                        }
                        build_phase_graph();
                        return true;
                    }
                }

                for (auto [a, b] : delayed_unions) {
                    if (a == b) {
                        delayed_base.make_rep(a);
                    } else {
                        delayed_base.unite(a, b);
                    }
                }
                delayed_unions.clear();
                delta++;
            }
            return false;
        }

        int next_h_vertex_through_edge(int edge_id, int current_h) const {
            const auto& e = graph._edges[edge_id];
            return rep[rep[e.from] == current_h ? e.to : e.from];
        }

        int find_path_in_h(int h_vertex) {
            for (int v : contracted_into[h_vertex]) {
                for (int edge_id : graph._adj[v]) {
                    if (!is_h_edge[edge_id]) continue;
                    int uh = rep[other(edge_id, v)];
                    if (h_mate[h_vertex] == uh) continue;

                    if (h_label[uh] == unlabeled) {
                        int mate_uh = h_mate[uh];
                        h_label[uh] = odd_label;
                        h_parent_edge[uh] = edge_id;
                        if (mate_uh == -1) return uh;

                        h_label[mate_uh] = even_label;
                        h_even_time[mate_uh] = even_time_token++;
                        int found = find_path_in_h(mate_uh);
                        if (found != -1) return found;
                    } else {
                        int bh = delayed_base(h_vertex);
                        int zh = delayed_base(uh);
                        if (h_even_time[bh] >= h_even_time[zh]) continue;

                        std::vector<int> blossom_path;
                        std::vector<int> blossom_vertices;
                        while (zh != bh) {
                            blossom_vertices.push_back(zh);
                            zh = h_mate[zh];
                            assert(zh != -1);
                            blossom_vertices.push_back(zh);
                            blossom_path.push_back(zh);
                            assert(h_parent_edge[zh] != -1);
                            zh = delayed_base(next_h_vertex_through_edge(h_parent_edge[zh], zh));
                        }

                        for (int x : blossom_vertices) delayed_base.unite(x, bh);
                        delayed_base.make_rep(bh);

                        std::reverse(blossom_path.begin(), blossom_path.end());
                        for (int x : blossom_path) {
                            h_bridge_edge[x] = edge_id;
                            h_bridge_dir[x] = graph._edges[edge_id].to == v ? 1 : -1;
                        }
                        for (int x : blossom_path) {
                            int found = find_path_in_h(x);
                            if (found != -1) return found;
                        }
                    }
                }
            }
            return -1;
        }

        void collect_path_in_h(std::vector<int>& path, int from_h, int to_h) {
            if (from_h == to_h) return;
            if (h_label[from_h] == even_label) {
                int mate_from = h_mate[from_h];
                assert(mate_from != -1);
                int edge_id = h_parent_edge[mate_from];
                assert(edge_id != -1);
                path.push_back(edge_id);
                collect_path_in_h(path, next_h_vertex_through_edge(edge_id, mate_from), to_h);
            } else {
                int edge_id = h_bridge_edge[from_h];
                assert(edge_id != -1);
                const auto& e = graph._edges[edge_id];
                int first = rep[h_bridge_dir[from_h] == 1 ? e.from : e.to];
                int second = rep[h_bridge_dir[from_h] == 1 ? e.to : e.from];
                collect_path_in_h(path, first, rep[h_mate[from_h]]);
                path.push_back(edge_id);
                collect_path_in_h(path, second, to_h);
            }
        }

        void add_new_pair(std::vector<NewMatchingPair>& pairs, int from, int to, int edge_id) const {
            const auto& e = graph._edges[edge_id];
            assert(e.alive);
            assert((e.from == from && e.to == to) || (e.from == to && e.to == from));
            pairs.push_back(NewMatchingPair{from, to, edge_id});
        }

        void collect_path_in_graph(std::vector<NewMatchingPair>& pairs, int from, int to) {
            if (from == to) return;
            if (label[from] == even_label) {
                int mate_from = graph._mate[from];
                assert(mate_from != -1);
                int parent_of_mate = parent[mate_from];
                int edge_id = parent_edge[mate_from];
                assert(parent_of_mate != -1 && edge_id != -1);
                add_new_pair(pairs, mate_from, parent_of_mate, edge_id);
                collect_path_in_graph(pairs, parent_of_mate, to);
            } else {
                assert(source_bridge[from] != -1 && target_bridge[from] != -1 && bridge_edge[from] != -1);
                collect_path_in_graph(pairs, source_bridge[from], graph._mate[from]);
                add_new_pair(pairs, source_bridge[from], target_bridge[from], bridge_edge[from]);
                collect_path_in_graph(pairs, target_bridge[from], to);
            }
        }

        void augment_path(const std::vector<int>& h_path) {
            std::vector<NewMatchingPair> pairs;
            for (int edge_id : h_path) {
                const auto& e = graph._edges[edge_id];
                add_new_pair(pairs, e.from, e.to, edge_id);
                collect_path_in_graph(pairs, e.from, rep[e.from]);
                collect_path_in_graph(pairs, e.to, rep[e.to]);
            }

            for (const auto& p : pairs) {
                if (graph._mate[p.from] != -1) {
                    int old = graph._mate[p.from];
                    graph._mate[old] = -1;
                    graph._mate_edge[old] = -1;
                }
                if (graph._mate[p.to] != -1) {
                    int old = graph._mate[p.to];
                    graph._mate[old] = -1;
                    graph._mate_edge[old] = -1;
                }
                graph._mate[p.from] = graph._mate[p.to] = -1;
                graph._mate_edge[p.from] = graph._mate_edge[p.to] = -1;
            }
            for (const auto& p : pairs) {
                assert(graph._mate[p.from] == -1 && graph._mate[p.to] == -1);
                graph._mate[p.from] = p.to;
                graph._mate[p.to] = p.from;
                graph._mate_edge[p.from] = p.edge_id;
                graph._mate_edge[p.to] = p.edge_id;
            }
            matching_size++;
        }

        void phase_two() {
            std::fill(h_label.begin(), h_label.end(), unlabeled);
            std::fill(h_parent_edge.begin(), h_parent_edge.end(), -1);
            std::fill(h_bridge_edge.begin(), h_bridge_edge.end(), -1);
            std::fill(h_bridge_dir.begin(), h_bridge_dir.end(), 0);
            for (int v = 0; v < n; v++) rep[v] = delayed_base(v);

            std::vector<std::vector<int>> paths;
            for (int h_vertex = 0; h_vertex < n; h_vertex++) {
                if (rep[h_vertex] != h_vertex) continue;
                if (h_label[h_vertex] != unlabeled || h_mate[h_vertex] != -1) continue;

                h_label[h_vertex] = even_label;
                h_even_time[h_vertex] = even_time_token++;
                int free_h = find_path_in_h(h_vertex);
                if (free_h == -1) continue;

                std::vector<int> path;
                int edge_id = h_parent_edge[free_h];
                assert(edge_id != -1);
                path.push_back(edge_id);
                collect_path_in_h(path, next_h_vertex_through_edge(edge_id, free_h), h_vertex);
                paths.push_back(path);
            }

            assert(!paths.empty());
            for (const auto& path : paths) augment_path(path);
            for (auto& vertices : contracted_into) vertices.clear();
        }

        int solve() {
            initialize_greedy_matching();
            while (phase_one()) phase_two();
            return matching_size;
        }
    };

   public:
    GeneralMatching() : GeneralMatching(0) {}

    explicit GeneralMatching(int n) : _n(n), _adj(n), _mate(n, -1), _mate_edge(n, -1), _calculated(false) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    int edge_count() const {
        return int(_edges.size());
    }

    int add_edge(int from, int to) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(from != to);
        int id = int(_edges.size());
        _edges.push_back(Edge{from, to, id, true});
        _adj[from].push_back(id);
        _adj[to].push_back(id);
        invalidate();
        return id;
    }

    Edge get_edge(int i) const {
        assert(0 <= i && i < int(_edges.size()));
        return _edges[i];
    }

    std::vector<Edge> edges(bool include_inactive = false) const {
        std::vector<Edge> result;
        result.reserve(_edges.size());
        for (const auto& e : _edges) {
            if (include_inactive || e.alive) result.push_back(e);
        }
        return result;
    }

    void set_edge_alive(int id, bool alive) {
        assert(0 <= id && id < int(_edges.size()));
        _edges[id].alive = alive;
        invalidate();
    }

    void erase_edge(int id) {
        set_edge_alive(id, false);
    }

    void revive_edge(int id) {
        set_edge_alive(id, true);
    }

    bool is_edge_alive(int id) const {
        assert(0 <= id && id < int(_edges.size()));
        return _edges[id].alive;
    }

    int max_matching() {
        MicaliVaziraniSolver solver(*this);
        int result = solver.solve();

        _calculated = true;
        return result;
    }

    int matching_size() {
        ensure_matching();
        int result = 0;
        for (int v = 0; v < _n; v++) {
            if (v < _mate[v]) result++;
        }
        return result;
    }

    std::vector<int> mate() {
        ensure_matching();
        return _mate;
    }

    std::vector<int> mate_edge() {
        ensure_matching();
        return _mate_edge;
    }

    std::vector<Pair> matching() {
        ensure_matching();
        std::vector<Pair> result;
        for (int v = 0; v < _n; v++) {
            if (v < _mate[v]) result.push_back(Pair{v, _mate[v], _mate_edge[v]});
        }
        return result;
    }

    std::optional<std::vector<int>> minimum_edge_cover() {
        ensure_matching();

        std::vector<int> result;
        std::vector<char> covered(_n, false), used_edge(_edges.size(), false);

        auto use_edge = [&](int id) {
            if (used_edge[id]) return;
            used_edge[id] = true;
            result.push_back(id);
            covered[_edges[id].from] = true;
            covered[_edges[id].to] = true;
        };

        for (int v = 0; v < _n; v++) {
            if (v < _mate[v]) use_edge(_mate_edge[v]);
        }

        for (int v = 0; v < _n; v++) {
            if (covered[v]) continue;
            int id = -1;
            for (int edge_id : _adj[v]) {
                if (_edges[edge_id].alive) {
                    id = edge_id;
                    break;
                }
            }
            if (id == -1) return std::nullopt;
            use_edge(id);
        }

        return result;
    }
};

struct GeneralMatchingGraph {
    GeneralMatching matching;
    std::vector<int> original_edge_id;

    int original_edge(int edge_id) const {
        assert(0 <= edge_id && edge_id < int(original_edge_id.size()));
        return original_edge_id[edge_id];
    }
};

template <class T>
GeneralMatchingGraph make_general_matching(const Graph<T>& g) {
    GeneralMatchingGraph result;
    result.matching = GeneralMatching(g.size());
    for (const auto& e : g.edges()) {
        int id = result.matching.add_edge(e.from, e.to);
        if (int(result.original_edge_id.size()) <= id) result.original_edge_id.resize(id + 1);
        result.original_edge_id[id] = e.id;
    }
    return result;
}

}  // namespace graph
}  // namespace m1une


#line 10 "verify/graph/library_checker_general_matching.test.cpp"

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    int N, M;
    fast_input >> N >> M;
    m1une::graph::GeneralMatching gm(N);
    while (M--) {
        int u, v;
        fast_input >> u >> v;
        gm.add_edge(u, v);
    }
    fast_output << gm.max_matching() << '\n';
    for (auto p : gm.matching()) {
        fast_output << p.from << ' ' << p.to << '\n';
    }
}

m1une's library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/graph/library_checker_general_matching.test.cpp

Depends on

Code