m1une's library

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:heavy_check_mark: verify/graph/flow/max_flow.test.cpp

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Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/GRL_6_A"

#include "../../../graph/flow/max_flow.hpp"
#include "../../../utilities/fast_io.hpp"

int main() {
    m1une::utilities::FastInput input;
    m1une::utilities::FastOutput output;

    int vertex_count, edge_count;
    input >> vertex_count >> edge_count;
    m1une::flow::MaxFlow<long long> flow(vertex_count);
    flow.reserve_edges(edge_count);
    for (int edge = 0; edge < edge_count; edge++) {
        int from, to;
        long long capacity;
        input >> from >> to >> capacity;
        flow.add_edge(from, to, capacity);
    }
    output << flow.max_flow(0, vertex_count - 1) << '\n';
}
#line 1 "verify/graph/flow/max_flow.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/GRL_6_A"

#line 1 "graph/flow/max_flow.hpp"



#include <algorithm>
#include <cassert>
#include <cstddef>
#include <limits>
#include <vector>

namespace m1une {
namespace flow {

template <class Cap>
struct MaxFlow {
    struct Edge {
        int from;
        int to;
        Cap cap;
        Cap flow;
    };

   private:
    struct InternalEdge {
        int to;
        int rev;
        Cap cap;
    };

    struct Position {
        int from;
        int edge;
    };

    int _n;
    std::vector<Position> _pos;
    std::vector<std::vector<InternalEdge>> _g;

    Cap highest_label_preflow_push(int s, int t) {
        const int dead = 2 * _n;
        const int unreachable = _n + 1;
        std::vector<Cap> excess(_n, Cap(0));
        std::vector<int> state(8 * std::size_t(_n) + 2);
        int* height = state.data();
        int* height_count = height + _n;
        int* current = height_count + dead + 1;
        int* queue = current + _n;
        int* next = queue + _n;
        int* bucket_head = next + _n;
        std::vector<char> active(_n, false);
        int highest = -1;
        long long work = 0;
        const long long arc_count =
            2LL * static_cast<long long>(_pos.size());
        const long long work_limit = std::max(1LL, 4 * arc_count + _n);

        auto activate = [&](int v) {
            if (v == s || v == t || active[v] || excess[v] == Cap(0) ||
                height[v] >= dead) {
                return;
            }
            active[v] = true;
            next[v] = bucket_head[height[v]];
            bucket_head[height[v]] = v;
            highest = std::max(highest, height[v]);
        };

        auto rebuild_buckets = [&]() {
            std::fill(bucket_head, bucket_head + dead + 1, -1);
            std::fill(active.begin(), active.end(), false);
            highest = -1;
            for (int v = 0; v < _n; v++) activate(v);
        };

        auto global_relabel = [&]() {
            std::fill(height, height + _n, unreachable);
            std::fill(height_count, height_count + dead + 1, 0);
            std::fill(current, current + _n, 0);
            int head = 0;
            int tail = 0;
            height[t] = 0;
            height[s] = _n;
            queue[tail++] = t;
            while (head != tail) {
                int v = queue[head++];
                for (const auto& e : _g[v]) {
                    if (e.to == s || height[e.to] != unreachable) continue;
                    const auto& reverse = _g[e.to][e.rev];
                    if (reverse.cap == Cap(0)) continue;
                    height[e.to] = height[v] + 1;
                    queue[tail++] = e.to;
                }
            }
            for (int v = 0; v < _n; v++) height_count[height[v]]++;
            rebuild_buckets();
            work = 0;
        };

        auto gap = [&](int empty_height) {
            for (int v = 0; v < _n; v++) {
                if (v == s || v == t || height[v] <= empty_height ||
                    height[v] >= _n) {
                    continue;
                }
                height_count[height[v]]--;
                height[v] = unreachable;
                height_count[height[v]]++;
                current[v] = 0;
            }
            rebuild_buckets();
        };

        auto relabel = [&](int v) -> bool {
            int old_height = height[v];
            int new_height = dead;
            work += int(_g[v].size());
            for (const auto& e : _g[v]) {
                if (e.cap != Cap(0)) {
                    new_height = std::min(new_height, height[e.to] + 1);
                }
            }
            height_count[old_height]--;
            height[v] = std::min(new_height, dead);
            height_count[height[v]]++;
            current[v] = 0;
            if (old_height < _n && height_count[old_height] == 0) {
                gap(old_height);
                return true;
            }
            return false;
        };

        auto push = [&](int v, InternalEdge& e) {
            Cap sent = std::min(excess[v], e.cap);
            bool was_zero = excess[e.to] == Cap(0);
            e.cap -= sent;
            _g[e.to][e.rev].cap += sent;
            excess[v] -= sent;
            excess[e.to] += sent;
            if (was_zero) activate(e.to);
        };

        auto discharge = [&](int v) {
            while (excess[v] != Cap(0) && height[v] < dead) {
                if (current[v] == int(_g[v].size())) {
                    if (relabel(v)) return;
                    continue;
                }
                auto& e = _g[v][current[v]];
                work++;
                if (e.cap != Cap(0) && height[v] == height[e.to] + 1) {
                    push(v, e);
                } else {
                    current[v]++;
                }
            }
            activate(v);
        };

        for (auto& e : _g[s]) {
            if (e.to == s || e.cap == Cap(0)) continue;
            Cap sent = e.cap;
            e.cap = Cap(0);
            _g[e.to][e.rev].cap += sent;
            excess[e.to] += sent;
        }
        global_relabel();

        while (highest >= 0) {
            if (bucket_head[highest] == -1) {
                highest--;
                continue;
            }
            int v = bucket_head[highest];
            bucket_head[highest] = next[v];
            if (!active[v] || height[v] != highest) continue;
            active[v] = false;
            discharge(v);
            if (work >= work_limit) global_relabel();
        }
        return excess[t];
    }

   public:
    MaxFlow() : MaxFlow(0) {}

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

    int size() const {
        return _n;
    }

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

    void reserve_edges(int edge_count) {
        assert(0 <= edge_count);
        _pos.reserve(edge_count);
        if (_n == 0 || edge_count == 0 ||
            2 * std::size_t(edge_count) < std::size_t(_n)) {
            return;
        }
        const std::size_t average_degree =
            (3 * std::size_t(edge_count) + std::size_t(_n) - 1)
            / std::size_t(_n);
        for (auto& edges : _g) edges.reserve(average_degree);
    }

    void reserve_edges(int edge_count, const std::vector<int>& degrees) {
        assert(0 <= edge_count);
        assert(int(degrees.size()) == _n);
        _pos.reserve(edge_count);
        for (int v = 0; v < _n; v++) {
            assert(0 <= degrees[v]);
            _g[v].reserve(degrees[v]);
        }
    }

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(Cap(0) <= cap);
        int id = int(_pos.size());
        int from_id = int(_g[from].size());
        int to_id = int(_g[to].size());
        if (from == to) to_id++;
        _pos.push_back(Position{from, from_id});
        _g[from].push_back(InternalEdge{to, to_id, cap});
        _g[to].push_back(InternalEdge{from, from_id, Cap(0)});
        return id;
    }

    int add_undirected_edge(int first, int second, Cap cap) {
        static_assert(std::numeric_limits<Cap>::is_signed);
        assert(0 <= first && first < _n);
        assert(0 <= second && second < _n);
        assert(Cap(0) <= cap);
        assert(cap <= std::numeric_limits<Cap>::max() / Cap(2));
        int id = int(_pos.size());
        int first_id = int(_g[first].size());
        int second_id = int(_g[second].size());
        if (first == second) second_id++;
        _pos.push_back(Position{first, ~first_id});
        _g[first].push_back(InternalEdge{second, second_id, cap});
        _g[second].push_back(InternalEdge{first, first_id, cap});
        return id;
    }

    Edge get_edge(int i) const {
        assert(0 <= i && i < int(_pos.size()));
        const auto& position = _pos[i];
        int from = position.from;
        bool undirected = position.edge < 0;
        int idx = undirected ? ~position.edge : position.edge;
        const auto& e = _g[from][idx];
        const auto& re = _g[e.to][e.rev];
        if (undirected) {
            return Edge{
                from,
                e.to,
                (e.cap + re.cap) / Cap(2),
                (re.cap - e.cap) / Cap(2)
            };
        }
        return Edge{from, e.to, e.cap + re.cap, re.cap};
    }

    std::vector<Edge> edges() const {
        std::vector<Edge> result;
        result.reserve(_pos.size());
        for (int i = 0; i < int(_pos.size()); i++) result.push_back(get_edge(i));
        return result;
    }

    void change_edge(int i, Cap new_cap, Cap new_flow) {
        assert(0 <= i && i < int(_pos.size()));
        assert(Cap(0) <= new_cap);
        auto& position = _pos[i];
        int from = position.from;
        bool undirected = position.edge < 0;
        int idx = undirected ? ~position.edge : position.edge;
        auto& e = _g[from][idx];
        auto& re = _g[e.to][e.rev];
        if (undirected) {
            assert(new_cap <= std::numeric_limits<Cap>::max() / Cap(2));
            assert(-new_cap <= new_flow && new_flow <= new_cap);
            e.cap = new_cap - new_flow;
            re.cap = new_cap + new_flow;
        } else {
            assert(Cap(0) <= new_flow && new_flow <= new_cap);
            e.cap = new_cap - new_flow;
            re.cap = new_flow;
        }
    }

    Cap max_flow(int s, int t) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
        return highest_label_preflow_push(s, t);
    }

    Cap max_flow_push_relabel(int s, int t) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
        return highest_label_preflow_push(s, t);
    }

    Cap max_flow_dinic(int s, int t) {
        return max_flow(s, t, std::numeric_limits<Cap>::max());
    }

    Cap max_flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        std::vector<int> work(3 * std::size_t(_n));
        int* level = work.data();
        int* iter = level + _n;
        int* queue = iter + _n;
        auto bfs = [&]() -> bool {
            std::fill(level, level + _n, -1);
            int head = 0;
            int tail = 0;
            level[s] = 0;
            queue[tail++] = s;
            while (head != tail) {
                int v = queue[head++];
                for (const auto& e : _g[v]) {
                    if (level[e.to] != -1 || e.cap == Cap(0)) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return true;
                    queue[tail++] = e.to;
                }
            }
            return level[t] != -1;
        };

        auto dfs = [&](auto&& self, int v, Cap up) -> Cap {
            if (v == s) return up;
            Cap result = Cap(0);
            const int current_level = level[v];
            auto& edges = _g[v];
            const int edge_count = int(edges.size());
            for (int& i = iter[v]; i < edge_count; i++) {
                auto& e = edges[i];
                if (level[e.to] + 1 != current_level) continue;
                auto& reverse = _g[e.to][e.rev];
                if (reverse.cap == Cap(0)) continue;
                Cap d = self(
                    self,
                    e.to,
                    std::min(up - result, reverse.cap)
                );
                if (d == Cap(0)) continue;
                e.cap += d;
                reverse.cap -= d;
                result += d;
                if (result == up) return result;
            }
            level[v] = _n;
            return result;
        };

        Cap flow = 0;
        while (flow < flow_limit && bfs()) {
            std::fill(iter, iter + _n, 0);
            flow += dfs(dfs, t, flow_limit - flow);
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) const {
        assert(0 <= s && s < _n);
        std::vector<bool> visited(_n, false);
        std::vector<int> queue(_n);
        int head = 0;
        int tail = 0;
        visited[s] = true;
        queue[tail++] = s;
        while (head != tail) {
            int v = queue[head++];
            for (const auto& e : _g[v]) {
                if (e.cap == Cap(0) || visited[e.to]) continue;
                visited[e.to] = true;
                queue[tail++] = e.to;
            }
        }
        return visited;
    }
};

}  // namespace flow
}  // namespace m1une


#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#include <utility>
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

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 5 "verify/graph/flow/max_flow.test.cpp"

int main() {
    m1une::utilities::FastInput input;
    m1une::utilities::FastOutput output;

    int vertex_count, edge_count;
    input >> vertex_count >> edge_count;
    m1une::flow::MaxFlow<long long> flow(vertex_count);
    flow.reserve_edges(edge_count);
    for (int edge = 0; edge < edge_count; edge++) {
        int from, to;
        long long capacity;
        input >> from >> to >> capacity;
        flow.add_edge(from, to, capacity);
    }
    output << flow.max_flow(0, vertex_count - 1) << '\n';
}
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