#line 1 "verify/graph/eulerian_trail_undirected.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_undirected"
#include <cassert>
#line 1 "utilities/fast_io.hpp"
#include <algorithm>
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#include <utility>
#include <unistd.h>
#include <vector>
namespace m1une {
namespace utilities {
struct FastOutput;
namespace internal {
// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
std::string* _capture = nullptr;
template <class T>
std::string format_cell(const T& value) {
std::string result;
struct CaptureGuard {
std::string*& target;
std::string* previous;
~CaptureGuard() { target = previous; }
} guard{_capture, _capture};
_capture = &result;
write(value);
return result;
}
template <class Matrix>
void write_aligned_matrix(const Matrix& matrix) {
std::vector<std::vector<std::string>> rows;
std::vector<std::size_t> widths;
for (const auto& row : matrix) {
auto& cells = rows.emplace_back();
std::size_t column = 0;
for (const auto& value : row) {
cells.push_back(format_cell(value));
if (column == widths.size()) widths.push_back(0);
widths[column] = std::max(widths[column], cells.back().size());
++column;
}
}
bool first = true;
for (const auto& row : rows) {
if (!first) write_char('\n');
first = false;
for (std::size_t column = 0; column < row.size(); ++column) {
if (column != 0) write_char(_range_separator);
for (std::size_t padding = row[column].size();
padding < widths[column]; ++padding) {
write_char(' ');
}
write(row[column]);
}
}
}
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {
if (_stream == stdout
&& internal::standard_output_instance == nullptr) {
internal::standard_output_instance = this;
}
}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
if (internal::standard_output_instance == this) {
internal::standard_output_instance = nullptr;
}
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_capture != nullptr) {
_capture->push_back(c);
return;
}
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
if (_capture != nullptr) {
_capture->append(s);
return;
}
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_capture == nullptr && _position > buffer_size - 64) flush();
char captured[64];
char* const begin = _capture != nullptr ? captured : _buffer + _position;
char* destination = begin;
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) *destination++ = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(destination, digits, 4);
destination += 4;
}
if (_capture != nullptr) {
_capture->append(begin, destination - begin);
} else {
_position += int(destination - begin);
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class Matrix>
void write_aligned(const Matrix& matrix) {
using Row = internal::range_stored_value_t<const Matrix>;
using Cell = internal::range_stored_value_t<const Row>;
static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
"write_aligned requires a two-dimensional range");
static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
"write_aligned requires scalar cells");
write_aligned_matrix(matrix);
}
template <class Matrix>
void println_aligned(const Matrix& matrix) {
write_aligned(matrix);
write_char('\n');
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
#line 5 "verify/graph/eulerian_trail_undirected.test.cpp"
#include <optional>
#include <random>
#line 9 "verify/graph/eulerian_trail_undirected.test.cpp"
#line 1 "graph/eulerian_trail.hpp"
#line 9 "graph/eulerian_trail.hpp"
#line 1 "graph/graph.hpp"
#line 8 "graph/graph.hpp"
namespace m1une {
namespace graph {
template <class T = int>
struct Edge {
using cost_type = T;
int from;
int to;
T cost;
int id;
bool alive;
Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
: from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}
int other(int v) const {
assert(v == from || v == to);
return from ^ to ^ v;
}
};
template <class T = int>
struct Graph {
using edge_type = Edge<T>;
using cost_type = T;
private:
struct EdgePositions {
std::array<std::pair<int, int>, 2> value{};
int size = 0;
void push_back(std::pair<int, int> position) {
assert(size < 2);
value[size++] = position;
}
};
int _n;
int _edge_count;
std::vector<std::vector<edge_type>> _g;
std::vector<EdgePositions> _edge_positions;
public:
Graph() : _n(0), _edge_count(0) {}
explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
assert(0 <= n);
}
int size() const {
return _n;
}
bool empty() const {
return _n == 0;
}
int edge_count() const {
return _edge_count;
}
int add_vertex() {
_g.emplace_back();
return _n++;
}
int add_directed_edge(int from, int to, T cost = T(1)) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
int id = _edge_count++;
int idx = int(_g[from].size());
_g[from].push_back(edge_type(from, to, cost, id));
_edge_positions.emplace_back();
_edge_positions.back().push_back({from, idx});
return id;
}
int add_edge(int u, int v, T cost = T(1)) {
assert(0 <= u && u < _n);
assert(0 <= v && v < _n);
int id = _edge_count++;
int u_idx = int(_g[u].size());
_g[u].push_back(edge_type(u, v, cost, id));
int v_idx = int(_g[v].size());
_g[v].push_back(edge_type(v, u, cost, id));
_edge_positions.emplace_back();
_edge_positions.back().push_back({u, u_idx});
_edge_positions.back().push_back({v, v_idx});
return id;
}
void set_edge_alive(int id, bool alive) {
assert(0 <= id && id < _edge_count);
for (int i = 0; i < _edge_positions[id].size; ++i) {
auto [v, idx] = _edge_positions[id].value[i];
_g[v][idx].alive = alive;
}
}
void erase_edge(int id) {
set_edge_alive(id, false);
}
void revive_edge(int id) {
set_edge_alive(id, true);
}
bool is_edge_alive(int id) const {
assert(0 <= id && id < _edge_count);
assert(_edge_positions[id].size != 0);
auto [v, idx] = _edge_positions[id].value[0];
return _g[v][idx].alive;
}
const std::vector<edge_type>& operator[](int v) const {
assert(0 <= v && v < _n);
return _g[v];
}
std::vector<edge_type>& operator[](int v) {
assert(0 <= v && v < _n);
return _g[v];
}
const std::vector<std::vector<edge_type>>& adjacency() const {
return _g;
}
std::vector<std::vector<edge_type>>& adjacency() {
return _g;
}
std::vector<edge_type> edges(bool include_inactive = false) const {
std::vector<edge_type> result;
result.reserve(_edge_count);
std::vector<char> used(_edge_count, false);
for (int v = 0; v < _n; v++) {
for (const auto& e : _g[v]) {
if (!include_inactive && !e.alive) continue;
if (0 <= e.id && e.id < _edge_count) {
if (used[e.id]) continue;
used[e.id] = true;
}
result.push_back(e);
}
}
return result;
}
Graph reversed() const {
Graph result(_n);
result._edge_count = _edge_count;
result._edge_positions.assign(_edge_count, {});
for (int v = 0; v < _n; v++) {
for (const auto& e : _g[v]) {
int idx = int(result._g[e.to].size());
result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
}
}
return result;
}
};
} // namespace graph
} // namespace m1une
#line 11 "graph/eulerian_trail.hpp"
namespace m1une {
namespace graph {
struct EulerianTrail {
std::vector<int> vertices;
std::vector<int> edge_ids;
int edge_count() const {
return int(edge_ids.size());
}
bool is_circuit() const {
return vertices.empty() || vertices.front() == vertices.back();
}
};
namespace internal {
template <class T>
std::optional<EulerianTrail> hierholzer(
const Graph<T>& graph,
int start,
int active_edge_count
) {
EulerianTrail result;
if (active_edge_count == 0) {
if (start != -1) result.vertices.push_back(start);
return result;
}
assert(0 <= start && start < graph.size());
std::vector<char> used(graph.edge_count(), false);
std::vector<int> cursor(graph.size(), 0);
std::vector<int> vertex_stack(1, start);
std::vector<int> incoming_edge_stack(1, -1);
std::vector<int> reversed_vertices;
std::vector<int> reversed_edges;
reversed_vertices.reserve(active_edge_count + 1);
reversed_edges.reserve(active_edge_count);
while (!vertex_stack.empty()) {
const int vertex = vertex_stack.back();
while (cursor[vertex] < int(graph[vertex].size())) {
const Edge<T>& edge = graph[vertex][cursor[vertex]];
if (edge.alive && !used[edge.id]) break;
cursor[vertex]++;
}
if (cursor[vertex] < int(graph[vertex].size())) {
const Edge<T>& edge = graph[vertex][cursor[vertex]++];
used[edge.id] = true;
vertex_stack.push_back(edge.to);
incoming_edge_stack.push_back(edge.id);
continue;
}
reversed_vertices.push_back(vertex);
const int incoming_edge = incoming_edge_stack.back();
if (incoming_edge != -1) reversed_edges.push_back(incoming_edge);
vertex_stack.pop_back();
incoming_edge_stack.pop_back();
}
if (int(reversed_edges.size()) != active_edge_count) return std::nullopt;
std::reverse(reversed_vertices.begin(), reversed_vertices.end());
std::reverse(reversed_edges.begin(), reversed_edges.end());
result.vertices = std::move(reversed_vertices);
result.edge_ids = std::move(reversed_edges);
return result;
}
template <class T>
std::vector<int> edge_incidence_count(const Graph<T>& graph) {
std::vector<int> count(graph.edge_count(), 0);
for (int vertex = 0; vertex < graph.size(); vertex++) {
for (const Edge<T>& edge : graph[vertex]) {
if (!edge.alive) continue;
assert(0 <= edge.id && edge.id < graph.edge_count());
count[edge.id]++;
}
}
return count;
}
} // namespace internal
template <class T>
std::optional<EulerianTrail> directed_eulerian_trail(
const Graph<T>& graph,
int start = -1
) {
assert(start == -1 || (0 <= start && start < graph.size()));
const int n = graph.size();
std::vector<int> incidence = internal::edge_incidence_count(graph);
std::vector<int> in_degree(n, 0);
std::vector<int> out_degree(n, 0);
int active_edge_count = 0;
for (int vertex = 0; vertex < n; vertex++) {
for (const Edge<T>& edge : graph[vertex]) {
if (!edge.alive) continue;
out_degree[vertex]++;
in_degree[edge.to]++;
}
}
for (int count : incidence) {
if (count == 0) continue;
assert(count == 1);
active_edge_count++;
}
int required_start = -1;
int required_end = -1;
for (int vertex = 0; vertex < n; vertex++) {
const int difference = out_degree[vertex] - in_degree[vertex];
if (difference == 1) {
if (required_start != -1) return std::nullopt;
required_start = vertex;
} else if (difference == -1) {
if (required_end != -1) return std::nullopt;
required_end = vertex;
} else if (difference != 0) {
return std::nullopt;
}
}
if ((required_start == -1) != (required_end == -1)) return std::nullopt;
int chosen_start = start;
if (active_edge_count == 0) {
if (chosen_start == -1 && n > 0) chosen_start = 0;
return internal::hierholzer(graph, chosen_start, 0);
}
if (required_start != -1) {
if (chosen_start != -1 && chosen_start != required_start) return std::nullopt;
chosen_start = required_start;
} else if (chosen_start == -1) {
for (int vertex = 0; vertex < n; vertex++) {
if (out_degree[vertex] > 0) {
chosen_start = vertex;
break;
}
}
} else if (out_degree[chosen_start] == 0) {
return std::nullopt;
}
return internal::hierholzer(graph, chosen_start, active_edge_count);
}
template <class T>
std::optional<EulerianTrail> undirected_eulerian_trail(
const Graph<T>& graph,
int start = -1
) {
assert(start == -1 || (0 <= start && start < graph.size()));
const int n = graph.size();
std::vector<int> incidence = internal::edge_incidence_count(graph);
std::vector<int> degree(n, 0);
int active_edge_count = 0;
for (int vertex = 0; vertex < n; vertex++) {
for (const Edge<T>& edge : graph[vertex]) {
if (edge.alive) degree[vertex]++;
}
}
for (int count : incidence) {
if (count == 0) continue;
assert(count == 2);
active_edge_count++;
}
std::vector<int> odd;
for (int vertex = 0; vertex < n; vertex++) {
if (degree[vertex] & 1) odd.push_back(vertex);
}
if (!odd.empty() && odd.size() != 2) return std::nullopt;
int chosen_start = start;
if (active_edge_count == 0) {
if (chosen_start == -1 && n > 0) chosen_start = 0;
return internal::hierholzer(graph, chosen_start, 0);
}
if (odd.size() == 2) {
if (chosen_start != -1 && chosen_start != odd[0] && chosen_start != odd[1]) {
return std::nullopt;
}
if (chosen_start == -1) chosen_start = odd[0];
} else if (chosen_start == -1) {
for (int vertex = 0; vertex < n; vertex++) {
if (degree[vertex] > 0) {
chosen_start = vertex;
break;
}
}
} else if (degree[chosen_start] == 0) {
return std::nullopt;
}
return internal::hierholzer(graph, chosen_start, active_edge_count);
}
} // namespace graph
} // namespace m1une
#line 11 "verify/graph/eulerian_trail_undirected.test.cpp"
namespace {
#ifndef NDEBUG
bool brute_undirected_dfs(
int vertex,
const std::vector<std::pair<int, int>>& edges,
int used_mask
) {
if (used_mask == (1 << int(edges.size())) - 1) return true;
for (int edge_id = 0; edge_id < int(edges.size()); edge_id++) {
if (used_mask >> edge_id & 1) continue;
auto [first, second] = edges[edge_id];
if (first == vertex &&
brute_undirected_dfs(second, edges, used_mask | (1 << edge_id))) {
return true;
}
if (second == vertex && second != first &&
brute_undirected_dfs(first, edges, used_mask | (1 << edge_id))) {
return true;
}
}
return false;
}
bool brute_undirected(int vertex_count, const std::vector<std::pair<int, int>>& edges) {
if (edges.empty()) return true;
for (int start = 0; start < vertex_count; start++) {
if (brute_undirected_dfs(start, edges, 0)) return true;
}
return false;
}
void validate_undirected(
const m1une::graph::EulerianTrail& trail,
const std::vector<std::pair<int, int>>& edges
) {
assert(trail.edge_ids.size() == edges.size());
assert(trail.vertices.size() == edges.size() + 1);
std::vector<char> used(edges.size(), false);
for (int index = 0; index < int(edges.size()); index++) {
int edge_id = trail.edge_ids[index];
assert(0 <= edge_id && edge_id < int(edges.size()));
assert(!used[edge_id]);
used[edge_id] = true;
auto [first, second] = edges[edge_id];
int from = trail.vertices[index];
int to = trail.vertices[index + 1];
assert((first == from && second == to) || (first == to && second == from));
}
}
void randomized_test() {
std::mt19937 random(891011);
for (int test = 0; test < 350; test++) {
int vertex_count = 1 + int(random() % 5);
int edge_count = int(random() % 9);
m1une::graph::Graph<> graph(vertex_count);
std::vector<std::pair<int, int>> edges;
for (int edge = 0; edge < edge_count; edge++) {
int first = int(random() % vertex_count);
int second = int(random() % vertex_count);
graph.add_edge(first, second);
edges.emplace_back(first, second);
}
auto trail = m1une::graph::undirected_eulerian_trail(graph);
assert(trail.has_value() == brute_undirected(vertex_count, edges));
if (trail.has_value() && !edges.empty()) validate_undirected(*trail, edges);
}
m1une::graph::Graph<> loops(2);
int first = loops.add_edge(0, 0);
int erased = loops.add_edge(0, 1);
loops.erase_edge(erased);
auto active_only = m1une::graph::undirected_eulerian_trail(loops);
assert(active_only.has_value() && active_only->edge_ids == std::vector<int>(1, first));
assert(active_only->is_circuit());
}
#endif
void print(
const std::optional<m1une::graph::EulerianTrail>& trail,
m1une::utilities::FastOutput& fast_output
) {
if (!trail.has_value()) {
fast_output << "No\n";
return;
}
fast_output << "Yes\n";
for (int index = 0; index < int(trail->vertices.size()); index++) {
if (index) fast_output << ' ';
fast_output << trail->vertices[index];
}
fast_output << '\n';
for (int index = 0; index < int(trail->edge_ids.size()); index++) {
if (index) fast_output << ' ';
fast_output << trail->edge_ids[index];
}
fast_output << '\n';
}
} // namespace
int main() {
m1une::utilities::FastInput fast_input;
m1une::utilities::FastOutput fast_output;
#ifndef NDEBUG
randomized_test();
#endif
int test_count;
fast_input >> test_count;
while (test_count--) {
int vertex_count, edge_count;
fast_input >> vertex_count >> edge_count;
m1une::graph::Graph<> graph(vertex_count);
for (int edge = 0; edge < edge_count; edge++) {
int first, second;
fast_input >> first >> second;
graph.add_edge(first, second);
}
print(m1une::graph::undirected_eulerian_trail(graph), fast_output);
}
}
verify/graph/eulerian_trail_undirected.test.cpp