m1une's library

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:heavy_check_mark: verify/graph/chordal_graph_recognition.test.cpp

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Code

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

#include "../../graph/chordal_graph_recognition.hpp"

#include <cassert>
#include <cstdint>
#include "../../utilities/fast_io.hpp"
#include <vector>

namespace {

using Graph = m1une::graph::Graph<>;
using Result = m1une::graph::ChordalGraphResult;

std::vector<std::vector<char>> adjacency_matrix(const Graph& graph) {
    const int size = graph.size();
    std::vector<std::vector<char>> adjacent(size, std::vector<char>(size, false));
    for (const auto& edge : graph.edges()) {
        if (edge.from == edge.to) continue;
        adjacent[edge.from][edge.to] = true;
        adjacent[edge.to][edge.from] = true;
    }
    return adjacent;
}

void validate(const Graph& graph) {
    const int size = graph.size();
    const auto adjacent = adjacency_matrix(graph);
    Result result = m1une::graph::chordal_graph_recognition(graph);
    assert(m1une::graph::is_chordal(graph) == result.is_chordal);

    if (result.is_chordal) {
        assert(result.induced_cycle.empty());
        assert(int(result.perfect_elimination_order.size()) == size);
        std::vector<int> position(size, -1);
        for (int index = 0; index < size; index++) {
            int vertex = result.perfect_elimination_order[index];
            assert(0 <= vertex && vertex < size);
            assert(position[vertex] == -1);
            position[vertex] = index;
        }
        for (int vertex = 0; vertex < size; vertex++) {
            std::vector<int> later_neighbors;
            for (int to = 0; to < size; to++) {
                if (adjacent[vertex][to] && position[vertex] < position[to]) {
                    later_neighbors.push_back(to);
                }
            }
            for (int first : later_neighbors) {
                for (int second : later_neighbors) {
                    if (first != second) assert(adjacent[first][second]);
                }
            }
        }
        return;
    }

    assert(result.perfect_elimination_order.empty());
    const int cycle_size = int(result.induced_cycle.size());
    assert(cycle_size >= 4);
    std::vector<char> used(size, false);
    for (int index = 0; index < cycle_size; index++) {
        const int vertex = result.induced_cycle[index];
        assert(0 <= vertex && vertex < size);
        assert(!used[vertex]);
        used[vertex] = true;
        for (int other = index + 1; other < cycle_size; other++) {
            const int distance = other - index;
            const bool consecutive = distance == 1 || distance == cycle_size - 1;
            assert(bool(adjacent[vertex][result.induced_cycle[other]]) == consecutive);
        }
    }
}

void test_fixed() {
    validate(Graph());
    validate(Graph(1));

    Graph tree(8);
    for (int vertex = 1; vertex < 8; vertex++) tree.add_edge(vertex / 2, vertex);
    validate(tree);
    assert(m1une::graph::is_chordal(tree));

    Graph complete(9);
    for (int first = 0; first < 9; first++) {
        for (int second = first + 1; second < 9; second++) {
            complete.add_edge(first, second);
        }
    }
    validate(complete);

    for (int size = 4; size <= 12; size++) {
        Graph cycle(size);
        for (int vertex = 0; vertex < size; vertex++) {
            cycle.add_edge(vertex, (vertex + 1) % size);
        }
        validate(cycle);
        assert(!m1une::graph::is_chordal(cycle));
    }

    Graph parallel(4);
    parallel.add_edge(0, 1);
    parallel.add_edge(0, 1);
    parallel.add_directed_edge(1, 2);
    int inactive = parallel.add_edge(0, 2);
    parallel.erase_edge(inactive);
    parallel.add_edge(2, 3);
    validate(parallel);
}

void test_randomized() {
    std::uint64_t state = 0xd1b54a32d192ed03ULL;
    auto random = [&]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 1000; trial++) {
        const int size = int(random() % 11);
        Graph graph(size);
        for (int first = 0; first < size; first++) {
            for (int second = first + 1; second < size; second++) {
                if (random() % 3 == 0) continue;
                if (random() & 1) {
                    graph.add_edge(first, second);
                } else {
                    graph.add_directed_edge(first, second);
                }
                if (random() % 13 == 0) graph.add_edge(first, second);
            }
        }
        validate(graph);
    }
}

void test_deep_graph() {
    const int size = 50000;
    Graph graph(size);
    for (int vertex = 1; vertex < size; vertex++) graph.add_edge(vertex - 1, vertex);
    Result result = m1une::graph::chordal_graph_recognition(graph);
    assert(result.is_chordal);
    assert(int(result.perfect_elimination_order.size()) == size);
}

}  // namespace

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

    test_fixed();
    test_randomized();
    test_deep_graph();
    int size, edge_count;
    fast_input >> size >> edge_count;
    Graph graph(size);
    while (edge_count--) {
        int first, second;
        fast_input >> first >> second;
        graph.add_edge(first, second);
    }

    Result result = m1une::graph::chordal_graph_recognition(graph);
    if (result.is_chordal) {
        fast_output << "YES\n";
        for (int index = 0; index < size; index++) {
            if (index != 0) fast_output << ' ';
            fast_output << result.perfect_elimination_order[index];
        }
        fast_output << '\n';
    } else {
        fast_output << "NO\n" << result.induced_cycle.size() << '\n';
        for (int index = 0; index < int(result.induced_cycle.size()); index++) {
            if (index != 0) fast_output << ' ';
            fast_output << result.induced_cycle[index];
        }
        fast_output << '\n';
    }
}
#line 1 "verify/graph/chordal_graph_recognition.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/chordal_graph_recognition"

#line 1 "graph/chordal_graph_recognition.hpp"



#include <algorithm>
#include <cassert>
#include <queue>
#include <utility>
#include <vector>

#line 1 "graph/graph.hpp"



#include <array>
#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 11 "graph/chordal_graph_recognition.hpp"

namespace m1une {
namespace graph {

struct ChordalGraphResult {
    bool is_chordal;
    std::vector<int> perfect_elimination_order;
    std::vector<int> induced_cycle;
};

namespace internal {

class MaximumCardinalitySearch {
    std::vector<int> _head;
    std::vector<int> _next;
    std::vector<int> _previous;
    std::vector<int> _weight;

    void erase(int vertex) {
        const int weight = _weight[vertex];
        if (_previous[vertex] == -1) {
            _head[weight] = _next[vertex];
        } else {
            _next[_previous[vertex]] = _next[vertex];
        }
        if (_next[vertex] != -1) _previous[_next[vertex]] = _previous[vertex];
    }

    void insert(int vertex) {
        const int weight = _weight[vertex];
        _previous[vertex] = -1;
        _next[vertex] = _head[weight];
        if (_head[weight] != -1) _previous[_head[weight]] = vertex;
        _head[weight] = vertex;
    }

   public:
    explicit MaximumCardinalitySearch(int size)
        : _head(size + 1, -1),
          _next(size, -1),
          _previous(size, -1),
          _weight(size, 0) {
        for (int vertex = 0; vertex < size; vertex++) insert(vertex);
    }

    std::vector<int> run(const std::vector<std::vector<int>>& adjacency) {
        const int size = int(adjacency.size());
        std::vector<int> order;
        order.reserve(size);
        std::vector<char> selected(size, false);
        std::vector<int> seen_neighbor(size, -1);
        int maximum_weight = 0;

        while (int(order.size()) < size) {
            while (_head[maximum_weight] == -1) maximum_weight--;
            const int vertex = _head[maximum_weight];
            erase(vertex);
            selected[vertex] = true;
            order.push_back(vertex);

            for (int to : adjacency[vertex]) {
                if (to == vertex || selected[to] || seen_neighbor[to] == vertex) continue;
                seen_neighbor[to] = vertex;
                erase(to);
                _weight[to]++;
                insert(to);
                maximum_weight = std::max(maximum_weight, _weight[to]);
            }
        }
        return order;
    }
};

inline std::vector<int> chordless_cycle(
    const std::vector<std::vector<int>>& adjacency, int vertex, int first,
    int second
) {
    const int size = int(adjacency.size());
    std::vector<char> forbidden(size, false);
    for (int to : adjacency[vertex]) forbidden[to] = true;
    forbidden[vertex] = true;
    forbidden[first] = false;
    forbidden[second] = false;

    std::vector<int> parent(size, -1);
    std::queue<int> queue;
    parent[first] = first;
    queue.push(first);
    while (!queue.empty() && parent[second] == -1) {
        const int current = queue.front();
        queue.pop();
        for (int to : adjacency[current]) {
            if (forbidden[to] || parent[to] != -1) continue;
            parent[to] = current;
            queue.push(to);
        }
    }
    assert(parent[second] != -1);

    std::vector<int> path;
    for (int current = second; current != first; current = parent[current]) {
        path.push_back(current);
    }
    path.push_back(first);
    std::reverse(path.begin(), path.end());

    std::vector<int> cycle;
    cycle.reserve(path.size() + 1);
    cycle.push_back(vertex);
    cycle.insert(cycle.end(), path.begin(), path.end());
    return cycle;
}

}  // namespace internal

// Recognizes a chordal graph. On success, returns a perfect elimination
// ordering; on failure, returns an induced cycle of length at least four.
template <class T>
ChordalGraphResult chordal_graph_recognition(const Graph<T>& graph) {
    const int size = graph.size();
    std::vector<std::vector<int>> adjacency(size);
    for (const Edge<T>& edge : graph.edges()) {
        if (edge.from == edge.to) continue;
        adjacency[edge.from].push_back(edge.to);
        adjacency[edge.to].push_back(edge.from);
    }

    std::vector<int> order = internal::MaximumCardinalitySearch(size).run(adjacency);
    std::vector<int> position(size);
    for (int index = 0; index < size; index++) position[order[index]] = index;

    std::vector<int> parent(size, -1);
    std::vector<std::vector<int>> children(size);
    for (int vertex = 0; vertex < size; vertex++) {
        for (int to : adjacency[vertex]) {
            if (position[to] < position[vertex] &&
                (parent[vertex] == -1 || position[parent[vertex]] < position[to])) {
                parent[vertex] = to;
            }
        }
        if (parent[vertex] != -1) children[parent[vertex]].push_back(vertex);
    }

    std::vector<int> adjacent_stamp(size, -1);
    for (int center = 0; center < size; center++) {
        for (int to : adjacency[center]) adjacent_stamp[to] = center;
        for (int vertex : children[center]) {
            for (int to : adjacency[vertex]) {
                if (position[to] >= position[center] || adjacent_stamp[to] == center) continue;
                return ChordalGraphResult{
                    false,
                    {},
                    internal::chordless_cycle(adjacency, vertex, to, center),
                };
            }
        }
    }

    std::reverse(order.begin(), order.end());
    return ChordalGraphResult{true, std::move(order), {}};
}

template <class T>
bool is_chordal(const Graph<T>& graph) {
    return chordal_graph_recognition(graph).is_chordal;
}

}  // namespace graph
}  // namespace m1une


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

#line 6 "verify/graph/chordal_graph_recognition.test.cpp"
#include <cstdint>
#line 1 "utilities/fast_io.hpp"



#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#line 18 "utilities/fast_io.hpp"
#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 9 "verify/graph/chordal_graph_recognition.test.cpp"

namespace {

using Graph = m1une::graph::Graph<>;
using Result = m1une::graph::ChordalGraphResult;

std::vector<std::vector<char>> adjacency_matrix(const Graph& graph) {
    const int size = graph.size();
    std::vector<std::vector<char>> adjacent(size, std::vector<char>(size, false));
    for (const auto& edge : graph.edges()) {
        if (edge.from == edge.to) continue;
        adjacent[edge.from][edge.to] = true;
        adjacent[edge.to][edge.from] = true;
    }
    return adjacent;
}

void validate(const Graph& graph) {
    const int size = graph.size();
    const auto adjacent = adjacency_matrix(graph);
    Result result = m1une::graph::chordal_graph_recognition(graph);
    assert(m1une::graph::is_chordal(graph) == result.is_chordal);

    if (result.is_chordal) {
        assert(result.induced_cycle.empty());
        assert(int(result.perfect_elimination_order.size()) == size);
        std::vector<int> position(size, -1);
        for (int index = 0; index < size; index++) {
            int vertex = result.perfect_elimination_order[index];
            assert(0 <= vertex && vertex < size);
            assert(position[vertex] == -1);
            position[vertex] = index;
        }
        for (int vertex = 0; vertex < size; vertex++) {
            std::vector<int> later_neighbors;
            for (int to = 0; to < size; to++) {
                if (adjacent[vertex][to] && position[vertex] < position[to]) {
                    later_neighbors.push_back(to);
                }
            }
            for (int first : later_neighbors) {
                for (int second : later_neighbors) {
                    if (first != second) assert(adjacent[first][second]);
                }
            }
        }
        return;
    }

    assert(result.perfect_elimination_order.empty());
    const int cycle_size = int(result.induced_cycle.size());
    assert(cycle_size >= 4);
    std::vector<char> used(size, false);
    for (int index = 0; index < cycle_size; index++) {
        const int vertex = result.induced_cycle[index];
        assert(0 <= vertex && vertex < size);
        assert(!used[vertex]);
        used[vertex] = true;
        for (int other = index + 1; other < cycle_size; other++) {
            const int distance = other - index;
            const bool consecutive = distance == 1 || distance == cycle_size - 1;
            assert(bool(adjacent[vertex][result.induced_cycle[other]]) == consecutive);
        }
    }
}

void test_fixed() {
    validate(Graph());
    validate(Graph(1));

    Graph tree(8);
    for (int vertex = 1; vertex < 8; vertex++) tree.add_edge(vertex / 2, vertex);
    validate(tree);
    assert(m1une::graph::is_chordal(tree));

    Graph complete(9);
    for (int first = 0; first < 9; first++) {
        for (int second = first + 1; second < 9; second++) {
            complete.add_edge(first, second);
        }
    }
    validate(complete);

    for (int size = 4; size <= 12; size++) {
        Graph cycle(size);
        for (int vertex = 0; vertex < size; vertex++) {
            cycle.add_edge(vertex, (vertex + 1) % size);
        }
        validate(cycle);
        assert(!m1une::graph::is_chordal(cycle));
    }

    Graph parallel(4);
    parallel.add_edge(0, 1);
    parallel.add_edge(0, 1);
    parallel.add_directed_edge(1, 2);
    int inactive = parallel.add_edge(0, 2);
    parallel.erase_edge(inactive);
    parallel.add_edge(2, 3);
    validate(parallel);
}

void test_randomized() {
    std::uint64_t state = 0xd1b54a32d192ed03ULL;
    auto random = [&]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 1000; trial++) {
        const int size = int(random() % 11);
        Graph graph(size);
        for (int first = 0; first < size; first++) {
            for (int second = first + 1; second < size; second++) {
                if (random() % 3 == 0) continue;
                if (random() & 1) {
                    graph.add_edge(first, second);
                } else {
                    graph.add_directed_edge(first, second);
                }
                if (random() % 13 == 0) graph.add_edge(first, second);
            }
        }
        validate(graph);
    }
}

void test_deep_graph() {
    const int size = 50000;
    Graph graph(size);
    for (int vertex = 1; vertex < size; vertex++) graph.add_edge(vertex - 1, vertex);
    Result result = m1une::graph::chordal_graph_recognition(graph);
    assert(result.is_chordal);
    assert(int(result.perfect_elimination_order.size()) == size);
}

}  // namespace

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

    test_fixed();
    test_randomized();
    test_deep_graph();
    int size, edge_count;
    fast_input >> size >> edge_count;
    Graph graph(size);
    while (edge_count--) {
        int first, second;
        fast_input >> first >> second;
        graph.add_edge(first, second);
    }

    Result result = m1une::graph::chordal_graph_recognition(graph);
    if (result.is_chordal) {
        fast_output << "YES\n";
        for (int index = 0; index < size; index++) {
            if (index != 0) fast_output << ' ';
            fast_output << result.perfect_elimination_order[index];
        }
        fast_output << '\n';
    } else {
        fast_output << "NO\n" << result.induced_cycle.size() << '\n';
        for (int index = 0; index < int(result.induced_cycle.size()); index++) {
            if (index != 0) fast_output << ' ';
            fast_output << result.induced_cycle[index];
        }
        fast_output << '\n';
    }
}
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