m1une's library

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:heavy_check_mark: verify/matroid/weighted_matroid_intersection.test.cpp

Depends on

Code

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

#include <algorithm>
#include <cassert>
#include "../../utilities/fast_io.hpp"
#include <random>
#include <utility>
#include <vector>

#include "../../matroid/graphic_matroid.hpp"
#include "../../matroid/partition_matroid.hpp"
#include "../../matroid/weighted_matroid_intersection.hpp"

struct BruteResult {
    int cardinality = -1;
    std::vector<long long> minimum_weight;
    std::vector<long long> maximum_weight;
    std::vector<char> exists;
};

template <class Oracle1, class Oracle2>
BruteResult brute_force(const std::vector<long long>& weight, const Oracle1& oracle1,
                        const Oracle2& oracle2) {
    int n = int(weight.size());
    BruteResult result;
    result.minimum_weight.resize(n + 1);
    result.maximum_weight.resize(n + 1);
    result.exists.assign(n + 1, false);
    for (int mask = 0; mask < (1 << n); mask++) {
        std::vector<int> subset;
        long long sum = 0;
        for (int i = 0; i < n; i++) {
            if (mask >> i & 1) {
                subset.push_back(i);
                sum += weight[i];
            }
        }
        if (!oracle1(subset) || !oracle2(subset)) continue;
        int cardinality = int(subset.size());
        result.cardinality = std::max(result.cardinality, cardinality);
        if (!result.exists[cardinality]) {
            result.exists[cardinality] = true;
            result.minimum_weight[cardinality] = sum;
            result.maximum_weight[cardinality] = sum;
        } else {
            result.minimum_weight[cardinality] =
                std::min(result.minimum_weight[cardinality], sum);
            result.maximum_weight[cardinality] =
                std::max(result.maximum_weight[cardinality], sum);
        }
    }
    return result;
}

template <class Oracle1, class Oracle2>
void check(const std::vector<long long>& weight, const Oracle1& oracle1,
           const Oracle2& oracle2) {
    int n = int(weight.size());
    BruteResult expected = brute_force(weight, oracle1, oracle2);
    auto maximum =
        m1une::matroid::weighted_matroid_intersection_max(n, weight, oracle1, oracle2);
    auto minimum =
        m1une::matroid::weighted_matroid_intersection_min(n, weight, oracle1, oracle2);
    auto default_result =
        m1une::matroid::weighted_matroid_intersection(n, weight, oracle1, oracle2);

    std::vector<long long> maximum_by_cardinality;
    std::vector<long long> minimum_by_cardinality;
    auto streamed_maximum = m1une::matroid::weighted_matroid_intersection_max_each(
        n, weight, oracle1, oracle2,
        [&](int cardinality, const long long& total_weight,
            const std::vector<int>& elements) {
            assert(cardinality == int(maximum_by_cardinality.size()));
            assert(int(elements.size()) == cardinality);
            assert(oracle1(elements) && oracle2(elements));
            assert(std::is_sorted(elements.begin(), elements.end()));
            long long sum = 0;
            for (int element : elements) sum += weight[element];
            (void)cardinality;
            (void)sum;
            assert(sum == total_weight);
            assert(total_weight == expected.maximum_weight[cardinality]);
            maximum_by_cardinality.push_back(total_weight);
        });
    auto streamed_minimum = m1une::matroid::weighted_matroid_intersection_min_each(
        n, weight, oracle1, oracle2,
        [&](int cardinality, const long long& total_weight,
            const std::vector<int>& elements) {
            assert(cardinality == int(minimum_by_cardinality.size()));
            assert(int(elements.size()) == cardinality);
            assert(oracle1(elements) && oracle2(elements));
            assert(std::is_sorted(elements.begin(), elements.end()));
            long long sum = 0;
            for (int element : elements) sum += weight[element];
            (void)cardinality;
            (void)sum;
            assert(sum == total_weight);
            assert(total_weight == expected.minimum_weight[cardinality]);
            minimum_by_cardinality.push_back(total_weight);
        });

    assert(maximum.size() == expected.cardinality);
    assert(minimum.size() == expected.cardinality);
    assert(maximum.total_weight == expected.maximum_weight[expected.cardinality]);
    assert(minimum.total_weight == expected.minimum_weight[expected.cardinality]);
    assert(default_result.total_weight == maximum.total_weight);
    assert(default_result.elements == maximum.elements);
    assert(streamed_maximum.total_weight == maximum.total_weight);
    assert(streamed_maximum.elements == maximum.elements);
    assert(streamed_minimum.total_weight == minimum.total_weight);
    assert(streamed_minimum.elements == minimum.elements);
    assert(oracle1(maximum.elements) && oracle2(maximum.elements));
    assert(oracle1(minimum.elements) && oracle2(minimum.elements));
    assert(std::is_sorted(maximum.elements.begin(), maximum.elements.end()));
    assert(std::is_sorted(minimum.elements.begin(), minimum.elements.end()));

    assert(int(maximum_by_cardinality.size()) == expected.cardinality + 1);
    assert(int(minimum_by_cardinality.size()) == expected.cardinality + 1);
    for (int cardinality = 0; cardinality <= expected.cardinality; cardinality++) {
        assert(expected.exists[cardinality]);
        assert(maximum_by_cardinality[cardinality] == expected.maximum_weight[cardinality]);
        assert(minimum_by_cardinality[cardinality] == expected.minimum_weight[cardinality]);
    }
}

void test_weighted_exchange() {
    m1une::matroid::PartitionMatroid left(std::vector<int>{0, 0, 1});
    m1une::matroid::PartitionMatroid right(std::vector<int>{0, 1, 0});
    std::vector<long long> weight = {100, 60, 70};
    auto result = m1une::matroid::weighted_matroid_intersection_max(3, weight, left, right);
    assert((result.elements == std::vector<int>{1, 2}));
    assert(result.total_weight == 130);

    std::vector<long long> best_weight;
    auto streamed = m1une::matroid::weighted_matroid_intersection_max_each(
        3, weight, left, right,
        [&](int, const long long& total_weight, const std::vector<int>&) {
            best_weight.push_back(total_weight);
        });
    assert((best_weight == std::vector<long long>{0, 100, 130}));
    assert(streamed.elements == result.elements);
    assert(streamed.total_weight == result.total_weight);

    weight = {-1, -100, -200};
    result = m1une::matroid::weighted_matroid_intersection_max(3, weight, left, right);
    assert(result.size() == 2);
    assert(result.total_weight == -300);
}

void test_equal_weights() {
    m1une::matroid::PartitionMatroid first(std::vector<int>{0, 0, 1, 1, 2, 2});
    m1une::matroid::PartitionMatroid second(std::vector<int>{0, 1, 1, 2, 2, 0});
    check(std::vector<long long>(6, 0), first, second);
    check(std::vector<long long>(6, 7), first, second);
}

void test_random_weighted_matroids() {
    std::mt19937 random(987654321);
    for (int test = 0; test < 300; test++) {
        int n = random() % 10;
        std::vector<long long> weight(n);
        for (long long& value : weight) value = int(random() % 41) - 20;

        int group_count = 1 + random() % 5;
        std::vector<int> group(n);
        for (int& value : group) value = random() % group_count;
        m1une::matroid::PartitionMatroid partition(group);

        int vertex_count = 1 + random() % 6;
        std::vector<std::pair<int, int>> edges(n);
        for (auto& [u, v] : edges) {
            u = random() % vertex_count;
            v = random() % vertex_count;
        }
        m1une::matroid::GraphicMatroid graphic(vertex_count, edges);
        check(weight, partition, graphic);

        int second_group_count = 1 + random() % 5;
        std::vector<int> second_group(n);
        for (int& value : second_group) value = random() % second_group_count;
        m1une::matroid::PartitionMatroid second_partition(second_group);
        check(weight, partition, second_partition);
    }
}

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

    test_weighted_exchange();
    test_equal_weights();
    test_random_weighted_matroids();

    long long a, b;
    fast_input >> a >> b;
    fast_output << a + b << '\n';
}
#line 1 "verify/matroid/weighted_matroid_intersection.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include <algorithm>
#include <cassert>
#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#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 6 "verify/matroid/weighted_matroid_intersection.test.cpp"
#include <random>
#line 9 "verify/matroid/weighted_matroid_intersection.test.cpp"

#line 1 "matroid/graphic_matroid.hpp"



#line 5 "matroid/graphic_matroid.hpp"
#include <numeric>
#line 8 "matroid/graphic_matroid.hpp"

namespace m1une {
namespace matroid {

class GraphicMatroid {
   private:
    int _vertex_count;
    std::vector<std::pair<int, int>> _edges;

   public:
    GraphicMatroid() : _vertex_count(0) {}

    GraphicMatroid(int vertex_count, std::vector<std::pair<int, int>> edges)
        : _vertex_count(vertex_count), _edges(std::move(edges)) {
        assert(0 <= vertex_count);
#ifndef NDEBUG
        for (auto [u, v] : _edges) {
            assert(0 <= u && u < _vertex_count);
            assert(0 <= v && v < _vertex_count);
        }
#endif
    }

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

    int vertex_count() const {
        return _vertex_count;
    }

    const std::vector<std::pair<int, int>>& edges() const {
        return _edges;
    }

    bool independent(const std::vector<int>& subset) const {
        std::vector<int> parent_or_size(_vertex_count, -1);
        auto leader = [&](auto&& self, int v) -> int {
            if (parent_or_size[v] < 0) return v;
            return parent_or_size[v] = self(self, parent_or_size[v]);
        };

        for (int element : subset) {
            assert(0 <= element && element < int(_edges.size()));
            auto [u, v] = _edges[element];
            u = leader(leader, u);
            v = leader(leader, v);
            if (u == v) return false;
            if (-parent_or_size[u] < -parent_or_size[v]) std::swap(u, v);
            parent_or_size[u] += parent_or_size[v];
            parent_or_size[v] = u;
        }
        return true;
    }

    bool operator()(const std::vector<int>& subset) const {
        return independent(subset);
    }
};

}  // namespace matroid
}  // namespace m1une


#line 1 "matroid/partition_matroid.hpp"



#line 8 "matroid/partition_matroid.hpp"

namespace m1une {
namespace matroid {

class PartitionMatroid {
   private:
    std::vector<int> _group;
    std::vector<int> _capacity;

    void validate() const {
#ifndef NDEBUG
        for (int capacity : _capacity) assert(0 <= capacity);
        for (int group : _group) assert(0 <= group && group < int(_capacity.size()));
#endif
    }

   public:
    PartitionMatroid() = default;

    explicit PartitionMatroid(std::vector<int> group) : _group(std::move(group)) {
        int group_count = 0;
        for (int value : _group) {
            assert(0 <= value);
            group_count = std::max(group_count, value + 1);
        }
        _capacity.assign(group_count, 1);
    }

    PartitionMatroid(std::vector<int> group, std::vector<int> capacity)
        : _group(std::move(group)), _capacity(std::move(capacity)) {
        validate();
    }

    int size() const {
        return int(_group.size());
    }

    int group_count() const {
        return int(_capacity.size());
    }

    const std::vector<int>& groups() const {
        return _group;
    }

    const std::vector<int>& capacities() const {
        return _capacity;
    }

    bool independent(const std::vector<int>& subset) const {
        std::vector<int> count(_capacity.size(), 0);
        for (int element : subset) {
            assert(0 <= element && element < int(_group.size()));
            int group = _group[element];
            if (++count[group] > _capacity[group]) return false;
        }
        return true;
    }

    bool operator()(const std::vector<int>& subset) const {
        return independent(subset);
    }
};

}  // namespace matroid
}  // namespace m1une


#line 1 "matroid/weighted_matroid_intersection.hpp"



#line 6 "matroid/weighted_matroid_intersection.hpp"
#include <queue>
#line 10 "matroid/weighted_matroid_intersection.hpp"

namespace m1une {
namespace matroid {

template <class Weight>
struct WeightedMatroidIntersectionResult {
    Weight total_weight = Weight(0);
    std::vector<int> elements;

    int size() const {
        return int(elements.size());
    }

    bool empty() const {
        return elements.empty();
    }
};

namespace weighted_intersection_detail {

template <class Weight>
struct QueueGreater {
    bool operator()(const std::pair<Weight, int>& lhs,
                    const std::pair<Weight, int>& rhs) const {
        if (rhs.first < lhs.first) return true;
        if (lhs.first < rhs.first) return false;
        return lhs.second > rhs.second;
    }
};

template <bool Maximize, class Weight>
Weight objective_cost(const Weight& change) {
    if constexpr (Maximize) {
        return Weight(0) - change;
    } else {
        return change;
    }
}

template <bool Maximize, class Weight, class IndependenceOracle1, class IndependenceOracle2,
          class OnSolution>
WeightedMatroidIntersectionResult<Weight> solve(
    int ground_size, const std::vector<Weight>& weight, IndependenceOracle1 oracle1,
    IndependenceOracle2 oracle2, OnSolution on_solution) {
    static_assert(!std::is_arithmetic_v<Weight> || std::is_signed_v<Weight>,
                  "Weight must support negative intermediate values");
    assert(0 <= ground_size);
    assert(int(weight.size()) == ground_size);

    const int source_vertex = ground_size;
    const int sink_vertex = ground_size + 1;
    const int vertex_count = ground_size + 2;
    std::vector<char> selected(ground_size, false);
    std::vector<int> elements;
    std::vector<int> position(ground_size, -1);
    std::vector<Weight> potential(vertex_count, Weight(0));
    Weight total_weight = Weight(0);
    on_solution(0, total_weight, elements);

    while (true) {
        std::vector<std::vector<int>> adjacency(vertex_count);
        std::vector<int> sink_predecessors;

        for (int x = 0; x < ground_size; x++) {
            if (selected[x]) continue;
            elements.push_back(x);
            bool source = oracle1(elements);
            bool sink = oracle2(elements);
            elements.pop_back();
            if (source) adjacency[source_vertex].push_back(x);
            if (sink) {
                adjacency[x].push_back(sink_vertex);
                sink_predecessors.push_back(x);
            }
        }

        for (int y : elements) {
            int index = position[y];
            assert(index != -1 && elements[index] == y);
            for (int x = 0; x < ground_size; x++) {
                if (selected[x]) continue;
                elements[index] = x;
                if (oracle1(elements)) adjacency[y].push_back(x);
                if (oracle2(elements)) adjacency[x].push_back(y);
                elements[index] = y;
            }
        }

        if (adjacency[source_vertex].empty() || sink_predecessors.empty()) break;

        auto vertex_length = [&](int vertex) {
            if (vertex >= ground_size) return Weight(0);
            Weight change = selected[vertex] ? Weight(0) - weight[vertex] : weight[vertex];
            return objective_cost<Maximize>(change);
        };
        auto reduced_length = [&](int from, int to) {
            return vertex_length(to) - potential[to] + potential[from];
        };

        int first_source = adjacency[source_vertex].front();
        potential[source_vertex] = potential[first_source] - vertex_length(first_source);
        for (int x : adjacency[source_vertex]) {
            Weight candidate = potential[x] - vertex_length(x);
            if (potential[source_vertex] < candidate) potential[source_vertex] = candidate;
        }
        potential[sink_vertex] = potential[sink_predecessors.front()];
        for (int x : sink_predecessors) {
            if (potential[x] < potential[sink_vertex]) potential[sink_vertex] = potential[x];
        }
        Weight source_potential = potential[source_vertex];
        for (Weight& value : potential) value = value - source_potential;

#ifndef NDEBUG
        for (int from = 0; from < vertex_count; from++) {
            for (int to : adjacency[from]) assert(!(reduced_length(from, to) < Weight(0)));
        }
#endif

        // Dijkstra is performed lazily: fixed_distance is added to every
        // not-yet-fixed potential at once, then materialized when a vertex is fixed.
        using QueueEntry = std::pair<Weight, int>;
        std::priority_queue<QueueEntry, std::vector<QueueEntry>, QueueGreater<Weight>> heap;
        std::vector<char> fixed(vertex_count, false);
        std::vector<char> has_distance(vertex_count, false);
        std::vector<Weight> distance(vertex_count, Weight(0));
        std::vector<int> previous(vertex_count, -1);
        heap.push({Weight(0), source_vertex});
        has_distance[source_vertex] = true;

        Weight fixed_distance = Weight(0);
        bool reached_sink = false;
        std::vector<int> tight_stack;
        tight_stack.reserve(vertex_count);
        while (!heap.empty() && !reached_sink) {
            int start = heap.top().second;
            heap.pop();
            if (fixed[start]) continue;
            if (start != source_vertex) {
                assert(previous[start] != -1);
                fixed_distance = reduced_length(previous[start], start);
            }

            tight_stack.clear();
            fixed[start] = true;
            potential[start] = potential[start] + fixed_distance;
            tight_stack.push_back(start);

            while (!tight_stack.empty() && !reached_sink) {
                int current = tight_stack.back();
                tight_stack.pop_back();
                if (current == sink_vertex) {
                    reached_sink = true;
                    break;
                }
                for (int next : adjacency[current]) {
                    if (fixed[next]) continue;
                    Weight slack = reduced_length(current, next) - fixed_distance;
                    assert(!(slack < Weight(0)));
                    if (!(Weight(0) < slack)) {
                        previous[next] = current;
                        fixed[next] = true;
                        potential[next] = potential[next] + fixed_distance;
                        tight_stack.push_back(next);
                    } else {
                        Weight candidate = fixed_distance + slack;
                        if (!has_distance[next] || candidate < distance[next]) {
                            has_distance[next] = true;
                            distance[next] = candidate;
                            previous[next] = current;
                            heap.push({candidate, next});
                        }
                    }
                }
            }
        }

        for (int vertex = 0; vertex < vertex_count; vertex++) {
            if (!fixed[vertex]) potential[vertex] = potential[vertex] + fixed_distance;
        }
        if (!reached_sink) break;

        std::fill(previous.begin(), previous.end(), -1);
        std::vector<char> reached(vertex_count, false);
        std::vector<int> queue;
        queue.reserve(vertex_count);
        reached[source_vertex] = true;
        queue.push_back(source_vertex);
        for (int head = 0; head < int(queue.size()) && !reached[sink_vertex]; head++) {
            int current = queue[head];
            for (int next : adjacency[current]) {
                if (reached[next]) continue;
                Weight length = reduced_length(current, next);
                assert(!(length < Weight(0)));
                if (Weight(0) < length) continue;
                reached[next] = true;
                previous[next] = current;
                queue.push_back(next);
            }
        }
        assert(reached[sink_vertex]);
        if (!reached[sink_vertex]) break;

        // A shortest tight path with the fewest edges preserves the potential invariant
        // after its elements switch between the inside and outside of the solution.
        for (int v = sink_vertex; v != source_vertex; v = previous[v]) {
            assert(v != -1);
            if (v < ground_size) {
                potential[v] = potential[v] - vertex_length(v);
                if (selected[v]) {
                    total_weight = total_weight - weight[v];
                } else {
                    total_weight = total_weight + weight[v];
                }
                selected[v] = !selected[v];
            }
        }

        elements.clear();
        std::fill(position.begin(), position.end(), -1);
        for (int x = 0; x < ground_size; x++) {
            if (!selected[x]) continue;
            position[x] = int(elements.size());
            elements.push_back(x);
        }

#ifndef NDEBUG
        assert(oracle1(elements));
        assert(oracle2(elements));
#endif
        on_solution(int(elements.size()), total_weight, elements);
    }

    WeightedMatroidIntersectionResult<Weight> result;
    result.elements = elements;
    result.total_weight = total_weight;
    return result;
}

}  // namespace weighted_intersection_detail

template <class Weight, class IndependenceOracle1, class IndependenceOracle2>
WeightedMatroidIntersectionResult<Weight> weighted_matroid_intersection_max(
    int ground_size, const std::vector<Weight>& weight, IndependenceOracle1 oracle1,
    IndependenceOracle2 oracle2) {
    auto ignore = [](int, const Weight&, const std::vector<int>&) {};
    return weighted_intersection_detail::solve<true>(ground_size, weight, oracle1, oracle2,
                                                      ignore);
}

template <class Weight, class IndependenceOracle1, class IndependenceOracle2>
WeightedMatroidIntersectionResult<Weight> weighted_matroid_intersection_min(
    int ground_size, const std::vector<Weight>& weight, IndependenceOracle1 oracle1,
    IndependenceOracle2 oracle2) {
    auto ignore = [](int, const Weight&, const std::vector<int>&) {};
    return weighted_intersection_detail::solve<false>(ground_size, weight, oracle1, oracle2,
                                                       ignore);
}

template <class Weight, class IndependenceOracle1, class IndependenceOracle2, class OnSolution>
WeightedMatroidIntersectionResult<Weight> weighted_matroid_intersection_max_each(
    int ground_size, const std::vector<Weight>& weight, IndependenceOracle1 oracle1,
    IndependenceOracle2 oracle2, OnSolution on_solution) {
    return weighted_intersection_detail::solve<true>(ground_size, weight, oracle1, oracle2,
                                                      on_solution);
}

template <class Weight, class IndependenceOracle1, class IndependenceOracle2, class OnSolution>
WeightedMatroidIntersectionResult<Weight> weighted_matroid_intersection_min_each(
    int ground_size, const std::vector<Weight>& weight, IndependenceOracle1 oracle1,
    IndependenceOracle2 oracle2, OnSolution on_solution) {
    return weighted_intersection_detail::solve<false>(ground_size, weight, oracle1, oracle2,
                                                       on_solution);
}

template <class Weight, class IndependenceOracle1, class IndependenceOracle2>
WeightedMatroidIntersectionResult<Weight> weighted_matroid_intersection(
    int ground_size, const std::vector<Weight>& weight, IndependenceOracle1 oracle1,
    IndependenceOracle2 oracle2) {
    return weighted_matroid_intersection_max(ground_size, weight, oracle1, oracle2);
}

}  // namespace matroid
}  // namespace m1une


#line 13 "verify/matroid/weighted_matroid_intersection.test.cpp"

struct BruteResult {
    int cardinality = -1;
    std::vector<long long> minimum_weight;
    std::vector<long long> maximum_weight;
    std::vector<char> exists;
};

template <class Oracle1, class Oracle2>
BruteResult brute_force(const std::vector<long long>& weight, const Oracle1& oracle1,
                        const Oracle2& oracle2) {
    int n = int(weight.size());
    BruteResult result;
    result.minimum_weight.resize(n + 1);
    result.maximum_weight.resize(n + 1);
    result.exists.assign(n + 1, false);
    for (int mask = 0; mask < (1 << n); mask++) {
        std::vector<int> subset;
        long long sum = 0;
        for (int i = 0; i < n; i++) {
            if (mask >> i & 1) {
                subset.push_back(i);
                sum += weight[i];
            }
        }
        if (!oracle1(subset) || !oracle2(subset)) continue;
        int cardinality = int(subset.size());
        result.cardinality = std::max(result.cardinality, cardinality);
        if (!result.exists[cardinality]) {
            result.exists[cardinality] = true;
            result.minimum_weight[cardinality] = sum;
            result.maximum_weight[cardinality] = sum;
        } else {
            result.minimum_weight[cardinality] =
                std::min(result.minimum_weight[cardinality], sum);
            result.maximum_weight[cardinality] =
                std::max(result.maximum_weight[cardinality], sum);
        }
    }
    return result;
}

template <class Oracle1, class Oracle2>
void check(const std::vector<long long>& weight, const Oracle1& oracle1,
           const Oracle2& oracle2) {
    int n = int(weight.size());
    BruteResult expected = brute_force(weight, oracle1, oracle2);
    auto maximum =
        m1une::matroid::weighted_matroid_intersection_max(n, weight, oracle1, oracle2);
    auto minimum =
        m1une::matroid::weighted_matroid_intersection_min(n, weight, oracle1, oracle2);
    auto default_result =
        m1une::matroid::weighted_matroid_intersection(n, weight, oracle1, oracle2);

    std::vector<long long> maximum_by_cardinality;
    std::vector<long long> minimum_by_cardinality;
    auto streamed_maximum = m1une::matroid::weighted_matroid_intersection_max_each(
        n, weight, oracle1, oracle2,
        [&](int cardinality, const long long& total_weight,
            const std::vector<int>& elements) {
            assert(cardinality == int(maximum_by_cardinality.size()));
            assert(int(elements.size()) == cardinality);
            assert(oracle1(elements) && oracle2(elements));
            assert(std::is_sorted(elements.begin(), elements.end()));
            long long sum = 0;
            for (int element : elements) sum += weight[element];
            (void)cardinality;
            (void)sum;
            assert(sum == total_weight);
            assert(total_weight == expected.maximum_weight[cardinality]);
            maximum_by_cardinality.push_back(total_weight);
        });
    auto streamed_minimum = m1une::matroid::weighted_matroid_intersection_min_each(
        n, weight, oracle1, oracle2,
        [&](int cardinality, const long long& total_weight,
            const std::vector<int>& elements) {
            assert(cardinality == int(minimum_by_cardinality.size()));
            assert(int(elements.size()) == cardinality);
            assert(oracle1(elements) && oracle2(elements));
            assert(std::is_sorted(elements.begin(), elements.end()));
            long long sum = 0;
            for (int element : elements) sum += weight[element];
            (void)cardinality;
            (void)sum;
            assert(sum == total_weight);
            assert(total_weight == expected.minimum_weight[cardinality]);
            minimum_by_cardinality.push_back(total_weight);
        });

    assert(maximum.size() == expected.cardinality);
    assert(minimum.size() == expected.cardinality);
    assert(maximum.total_weight == expected.maximum_weight[expected.cardinality]);
    assert(minimum.total_weight == expected.minimum_weight[expected.cardinality]);
    assert(default_result.total_weight == maximum.total_weight);
    assert(default_result.elements == maximum.elements);
    assert(streamed_maximum.total_weight == maximum.total_weight);
    assert(streamed_maximum.elements == maximum.elements);
    assert(streamed_minimum.total_weight == minimum.total_weight);
    assert(streamed_minimum.elements == minimum.elements);
    assert(oracle1(maximum.elements) && oracle2(maximum.elements));
    assert(oracle1(minimum.elements) && oracle2(minimum.elements));
    assert(std::is_sorted(maximum.elements.begin(), maximum.elements.end()));
    assert(std::is_sorted(minimum.elements.begin(), minimum.elements.end()));

    assert(int(maximum_by_cardinality.size()) == expected.cardinality + 1);
    assert(int(minimum_by_cardinality.size()) == expected.cardinality + 1);
    for (int cardinality = 0; cardinality <= expected.cardinality; cardinality++) {
        assert(expected.exists[cardinality]);
        assert(maximum_by_cardinality[cardinality] == expected.maximum_weight[cardinality]);
        assert(minimum_by_cardinality[cardinality] == expected.minimum_weight[cardinality]);
    }
}

void test_weighted_exchange() {
    m1une::matroid::PartitionMatroid left(std::vector<int>{0, 0, 1});
    m1une::matroid::PartitionMatroid right(std::vector<int>{0, 1, 0});
    std::vector<long long> weight = {100, 60, 70};
    auto result = m1une::matroid::weighted_matroid_intersection_max(3, weight, left, right);
    assert((result.elements == std::vector<int>{1, 2}));
    assert(result.total_weight == 130);

    std::vector<long long> best_weight;
    auto streamed = m1une::matroid::weighted_matroid_intersection_max_each(
        3, weight, left, right,
        [&](int, const long long& total_weight, const std::vector<int>&) {
            best_weight.push_back(total_weight);
        });
    assert((best_weight == std::vector<long long>{0, 100, 130}));
    assert(streamed.elements == result.elements);
    assert(streamed.total_weight == result.total_weight);

    weight = {-1, -100, -200};
    result = m1une::matroid::weighted_matroid_intersection_max(3, weight, left, right);
    assert(result.size() == 2);
    assert(result.total_weight == -300);
}

void test_equal_weights() {
    m1une::matroid::PartitionMatroid first(std::vector<int>{0, 0, 1, 1, 2, 2});
    m1une::matroid::PartitionMatroid second(std::vector<int>{0, 1, 1, 2, 2, 0});
    check(std::vector<long long>(6, 0), first, second);
    check(std::vector<long long>(6, 7), first, second);
}

void test_random_weighted_matroids() {
    std::mt19937 random(987654321);
    for (int test = 0; test < 300; test++) {
        int n = random() % 10;
        std::vector<long long> weight(n);
        for (long long& value : weight) value = int(random() % 41) - 20;

        int group_count = 1 + random() % 5;
        std::vector<int> group(n);
        for (int& value : group) value = random() % group_count;
        m1une::matroid::PartitionMatroid partition(group);

        int vertex_count = 1 + random() % 6;
        std::vector<std::pair<int, int>> edges(n);
        for (auto& [u, v] : edges) {
            u = random() % vertex_count;
            v = random() % vertex_count;
        }
        m1une::matroid::GraphicMatroid graphic(vertex_count, edges);
        check(weight, partition, graphic);

        int second_group_count = 1 + random() % 5;
        std::vector<int> second_group(n);
        for (int& value : second_group) value = random() % second_group_count;
        m1une::matroid::PartitionMatroid second_partition(second_group);
        check(weight, partition, second_partition);
    }
}

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

    test_weighted_exchange();
    test_equal_weights();
    test_random_weighted_matroids();

    long long a, b;
    fast_input >> a >> b;
    fast_output << a + b << '\n';
}
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