Asa's CP Library
a01sa01to's competitive programming library. Requires C++20 or higher with GCC. This documentation is automatically generated by online-judge-tools/verification-helper
tests/graph/eulerian-walk/libchecker-directed.test.cpp
- View this file on GitHub
- Last update: 2025-06-26 16:44:42+09:00
- Problem: https://judge.yosupo.jp/problem/eulerian_trail_directed
Depends on
- library/_internal/graph-base.hpp
- library/_internal/graph/connection.hpp
- library/_internal/graph/eulerian-walk.hpp
- 有向グラフ
(library/data-structure/digraph.hpp)
- 無向グラフ
(library/data-structure/graph.hpp)
- FastIO
(library/fastio.hpp)
- 連結判定
(library/graph/connection.hpp)
- オイラー路
(library/graph/eulerian-walk.hpp)
Code
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;
#include "../../../library/data-structure/digraph.hpp"
#include "../../../library/fastio.hpp"
#include "../../../library/graph/eulerian-walk.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed"
void solve() {
int n, m;
asalib::FastIO >> n >> m;
asalib::graph::digraph Graph(n);
rep(_, m) {
int u, v;
asalib::FastIO >> u >> v;
Graph.add_edge(u, v);
}
auto res = Graph.eulerian_walk();
if (!res.has_value()) {
asalib::FastIO << "No" << '\n';
}
else {
asalib::FastIO << "Yes" << '\n';
auto [vs, es] = res.value();
rep(i, vs.size()) {
if (i) asalib::FastIO << ' ';
asalib::FastIO << vs[i];
}
asalib::FastIO << '\n';
rep(i, es.size()) {
if (i) asalib::FastIO << ' ';
asalib::FastIO << es[i];
}
asalib::FastIO << '\n';
}
}
int main() {
int t;
asalib::FastIO >> t;
while (t--) solve();
return 0;
}#line 1 "tests/graph/eulerian-walk/libchecker-directed.test.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;
#line 2 "library/data-structure/digraph.hpp"
#line 5 "library/data-structure/digraph.hpp"
#include <optional>
#line 8 "library/data-structure/digraph.hpp"
using namespace std;
#line 2 "library/_internal/graph-base.hpp"
#include <concepts>
#line 5 "library/_internal/graph-base.hpp"
#include <type_traits>
#line 8 "library/_internal/graph-base.hpp"
using namespace std;
namespace asalib {
namespace _internal {
class graph_base {};
class notweighted_graph_base: public graph_base {};
class weighted_graph_base: public graph_base {};
template<typename T>
concept is_graph = is_base_of_v<graph_base, T>;
template<typename T>
concept notweighted_graph = is_base_of_v<notweighted_graph_base, T>;
template<typename T>
concept weighted_graph = is_base_of_v<weighted_graph_base, T>;
using adjlist_t = vector<vector<pair<size_t, size_t>>>;
using edgelist_t = vector<pair<size_t, size_t>>;
} // namespace _internal
} // namespace asalib
#line 2 "library/data-structure/graph.hpp"
#line 8 "library/data-structure/graph.hpp"
using namespace std;
#line 11 "library/data-structure/graph.hpp"
namespace asalib {
namespace graph {
class graph: public _internal::notweighted_graph_base {
public:
graph(): n_vertex(0), n_edge(0) {}
explicit graph(size_t n_vertex): n_vertex(n_vertex), n_edge(0) {
adj_list.reserve(n_vertex);
adj_list.resize(n_vertex);
}
void add_edge(size_t v1, size_t v2) {
assert(0 <= v1 && v1 < n_vertex);
assert(0 <= v2 && v2 < n_vertex);
adj_list[v1].push_back({ v2, n_edge });
adj_list[v2].push_back({ v1, n_edge });
edge_list.push_back({ v1, v2 });
++n_edge;
}
// (v1, v2)
pair<size_t, size_t> get_edge(size_t edgeId) const {
assert(0 <= edgeId && edgeId < n_edge);
return edge_list[edgeId];
}
// (v2, edgeId)
vector<pair<size_t, size_t>> get_adj(size_t vertex) const {
assert(0 <= vertex && vertex < n_vertex);
return adj_list[vertex];
}
// ---------- prototype ---------- //
optional<pair<vector<size_t>, vector<size_t>>> cycle() const;
bool is_connected() const;
optional<pair<vector<size_t>, vector<size_t>>> eulerian_walk() const;
private:
size_t n_vertex, n_edge;
asalib::_internal::adjlist_t adj_list;
asalib::_internal::edgelist_t edge_list;
};
} // namespace graph
} // namespace asalib
#line 12 "library/data-structure/digraph.hpp"
namespace asalib {
namespace graph {
class digraph: public _internal::notweighted_graph_base {
public:
digraph(): n_vertex(0), n_edge(0) {}
explicit digraph(size_t n_vertex): n_vertex(n_vertex), n_edge(0) {
adj_list.reserve(n_vertex);
adj_list.resize(n_vertex);
adj_list_rev.reserve(n_vertex);
adj_list_rev.resize(n_vertex);
underlying_graph = graph(n_vertex);
}
void add_edge(size_t from, size_t to) {
assert(0 <= from && from < n_vertex);
assert(0 <= to && to < n_vertex);
adj_list[from].push_back({ to, n_edge });
adj_list_rev[to].push_back({ from, n_edge });
edge_list.push_back({ from, to });
underlying_graph.add_edge(from, to);
++n_edge;
}
// (from, to)
pair<size_t, size_t> get_edge(size_t edgeId) const {
assert(0 <= edgeId && edgeId < n_edge);
return edge_list[edgeId];
}
// (to, edgeId)
vector<pair<size_t, size_t>> get_adj(size_t vertex) const {
assert(0 <= vertex && vertex < n_vertex);
return adj_list[vertex];
}
// (from, edgeId)
vector<pair<size_t, size_t>> get_adjrev(size_t vertex) const {
assert(0 <= vertex && vertex < n_vertex);
return adj_list_rev[vertex];
}
// ---------- prototype ---------- //
vector<vector<size_t>> scc() const;
optional<pair<vector<size_t>, vector<size_t>>> cycle() const;
bool is_connected() const;
optional<pair<vector<size_t>, vector<size_t>>> eulerian_walk() const;
private:
size_t n_vertex, n_edge;
asalib::_internal::adjlist_t adj_list, adj_list_rev;
asalib::_internal::edgelist_t edge_list;
graph underlying_graph;
};
} // namespace graph
} // namespace asalib
#line 2 "library/fastio.hpp"
#line 12 "library/fastio.hpp"
using namespace std;
// TODO: 何も入力がない場合にも対応する？
namespace asalib {
namespace _internal {
class FastIO {
private:
using uint = unsigned int;
static constexpr uint BUFFER_SIZE = 1 << 20;
static constexpr uint MAX_TOKEN_SIZE = 64;
// ===== Read ===== //
private:
array<char, BUFFER_SIZE> read_buffer;
array<char, BUFFER_SIZE>::iterator read_ptr;
uint read_size = 0;
inline void load() {
// まだ読んでないデータを前に持ってくる
memcpy(read_buffer.begin(), read_ptr, read_size - (read_ptr - read_buffer.begin()));
read_size -= read_ptr - read_buffer.begin();
read_ptr = read_buffer.begin();
// stdin から読み込み
read_size += fread(read_buffer.begin() + read_size, 1, BUFFER_SIZE - read_size, stdin);
}
inline void skip_space() {
// 制御文字 + space
// DEL (127 = 0x7F) がコーナーケースだがまあ使わんやろ
while (*read_ptr <= ' ') ++read_ptr;
}
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _read_uint(T& x) {
x = 0;
while (true) {
uint64_t v;
memcpy(&v, read_ptr, 8);
// '0' -> 0 処理
// こっちを先にやることで制御文字系もはじく
v -= 0x30'30'30'30'30'30'30'30;
// ASCII 範囲外
if (v & 0x80'80'80'80'80'80'80'80) break;
// 桁ごとの数字から数値に
v = (v * 10 + (v >> 8)) & 0x00ff00ff00ff00ff;
v = (v * 100 + (v >> 16)) & 0x0000ffff0000ffff;
v = (v * 10000 + (v >> 32)) & 0x00000000ffffffff;
x = 1'0000'0000 * x + v;
read_ptr += 8;
}
while (true) {
uint32_t v;
memcpy(&v, read_ptr, 4);
v -= 0x30'30'30'30;
if (v & 0x80'80'80'80) break;
v = (v * 10 + (v >> 8)) & 0x00ff00ff;
v = (v * 100 + (v >> 16)) & 0x0000ffff;
x = 1'0000 * x + v;
read_ptr += 4;
}
while (true) {
uint16_t v;
memcpy(&v, read_ptr, 2);
v -= 0x3030;
if (v & 0x8080) break;
v = (v * 10 + (v >> 8)) & 0x00ff;
x = 100 * x + v;
read_ptr += 2;
}
if (*read_ptr > ' ') x = 10 * x + (*read_ptr++ & 0x0f);
}
inline void read_commonop() {
// そろそろ限界なら読み込み
if ((read_ptr - read_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) load();
skip_space();
}
public:
FastIO& operator>>(char& x) {
read_commonop();
x = *read_ptr++;
return *this;
}
FastIO& operator>>(string& x) {
read_commonop();
x.clear();
while (*read_ptr > ' ') {
x += *read_ptr++;
if (read_ptr == read_buffer.end()) load();
}
return *this;
}
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
FastIO& operator>>(T& x) {
read_commonop();
constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
if constexpr (is_signed) {
if (*read_ptr == '-') {
++read_ptr;
_read_uint(x);
x = -x;
return *this;
}
}
_read_uint(x);
return *this;
}
// ===== Write ===== //
private:
array<char, BUFFER_SIZE> write_buffer;
array<char, BUFFER_SIZE>::iterator write_ptr;
static constexpr uint MAX_PRECOMPUTE_NUM = 1'0000;
static constexpr uint MAX_PRECOMPUTE_NUM_DIGIT = 4;
static constexpr array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits = [] {
array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits {};
for (uint i = 0; i < MAX_PRECOMPUTE_NUM; ++i) {
uint x = i;
for (int j = MAX_PRECOMPUTE_NUM_DIGIT - 1; j >= 0; --j) {
digits[i * MAX_PRECOMPUTE_NUM_DIGIT + j] = '0' + (x % 10);
x /= 10;
}
}
return digits;
}();
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
static constexpr array<T, numeric_limits<T>::digits10 + 1> Pow10 = [] {
array<T, numeric_limits<T>::digits10 + 1> pow10 {};
pow10[0] = 1;
for (uint i = 1; i < pow10.size(); ++i) pow10[i] = pow10[i - 1] * 10;
return pow10;
}();
inline void write_commonop() {
// そろそろ限界なら書き込む
if ((write_ptr - write_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) flush();
}
inline void putchar(const char& x) { *write_ptr++ = x; }
template<typename T, int NumDig>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _write_uint_top(const T& x) {
// leading-zero を書き込まないようにする
if constexpr (NumDig > 1) {
if (x < Pow10<T>[NumDig - 1]) {
_write_uint_top<T, NumDig - 1>(x);
return;
}
}
copy_n(digits.begin() + (x + 1) * MAX_PRECOMPUTE_NUM_DIGIT - NumDig, NumDig, write_ptr);
write_ptr += NumDig;
}
template<typename T, int NumDig>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _write_uint(const T& x) {
if constexpr (NumDig >= 0) {
if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x / MAX_PRECOMPUTE_NUM);
copy_n(digits.begin() + x % MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT, MAX_PRECOMPUTE_NUM_DIGIT, write_ptr);
write_ptr += MAX_PRECOMPUTE_NUM_DIGIT;
}
}
template<typename T, int NumDig>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _write_uint_root(const T& x) {
if constexpr (is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) {
// 128bit 除算はおそいので 64bit 除算を使う
if (x < Pow10<T>[16]) {
_write_uint_root<uint64_t, NumDig>(x);
}
else if (x < Pow10<T>[32]) {
_write_uint_root<uint64_t, NumDig>(x / Pow10<T>[16]);
_write_uint<uint64_t, 16>(x % Pow10<T>[16]);
}
else {
_write_uint_root<uint64_t, NumDig>(x / Pow10<T>[32]);
_write_uint<uint64_t, 16>(x % Pow10<T>[32] / Pow10<T>[16]);
_write_uint<uint64_t, 16>(x % Pow10<T>[16]);
}
return;
}
if constexpr (NumDig < numeric_limits<T>::digits10) {
if (x >= Pow10<T>[NumDig]) {
_write_uint_root<T, NumDig + MAX_PRECOMPUTE_NUM_DIGIT>(x);
return;
}
}
_write_uint_top<T, MAX_PRECOMPUTE_NUM_DIGIT>(x / Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x % Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
}
public:
inline void flush() {
fwrite(write_buffer.begin(), 1, write_ptr - write_buffer.begin(), stdout);
write_ptr = write_buffer.begin();
}
FastIO& operator<<(const char& x) {
write_commonop();
putchar(x);
return *this;
}
FastIO& operator<<(const string& x) {
write_commonop();
uint idx = 0;
while (idx < x.size()) {
const uint siz = min(BUFFER_SIZE - (uint) (write_ptr - write_buffer.begin()), (uint) x.size() - idx);
copy_n(x.begin() + idx, siz, write_ptr);
write_ptr += siz;
idx += siz;
if (write_ptr == write_buffer.end()) flush();
}
return *this;
}
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
FastIO& operator<<(const T& x) {
write_commonop();
constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
if constexpr (is_signed) {
if (x < 0) {
putchar('-');
_write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(-x);
return *this;
}
}
_write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(x);
return *this;
}
// ===== Common ====== //
public:
FastIO() {
read_ptr = read_buffer.begin();
write_ptr = write_buffer.begin();
load();
}
~FastIO() { flush(); }
};
} // namespace _internal
_internal::FastIO FastIO;
} // namespace asalib
#line 2 "library/graph/eulerian-walk.hpp"
#line 7 "library/graph/eulerian-walk.hpp"
using namespace std;
#line 2 "library/_internal/graph/eulerian-walk.hpp"
#line 10 "library/_internal/graph/eulerian-walk.hpp"
using namespace std;
#line 13 "library/_internal/graph/eulerian-walk.hpp"
namespace asalib {
namespace _internal {
namespace graph {
template<bool is_directed>
pair<vector<size_t>, vector<size_t>> eulerian_walk(const size_t& n, const edgelist_t& Edges, const size_t& start_v, const size_t& end_v) {
// グラフを変換するパート
vector<queue<size_t>> Graph(n);
for (size_t i = 0; i < Edges.size(); ++i) {
const auto& [u, v] = Edges[i];
Graph[u].push(i);
if constexpr (!is_directed) Graph[v].push(i);
}
vector<bool> used(Edges.size(), false);
// 適当にパスを見つけるやつ (これはオイラー路が存在することが確定してるからできる技)
auto find_path = [&](size_t from, size_t to, vector<size_t>& vs, vector<size_t>& eds) {
size_t now = from;
if (Graph[now].empty()) return false;
do {
assert(!Graph[now].empty());
size_t e_idx = Graph[now].front();
Graph[now].pop();
if (used[e_idx]) continue;
used[e_idx] = true;
eds.push_back(e_idx);
vs.push_back(now);
const auto& [u, v] = Edges[e_idx];
if (u == now) {
now = v;
}
else {
assert(now == v);
now = u;
}
} while (now != to);
vs.push_back(to);
return true;
};
// 適当に start_v -> end_v のパスを作るパート
vector<size_t> vs = {}, eds = {};
find_path(start_v, end_v, vs, eds);
assert(vs.size() == eds.size() + 1);
constexpr size_t ign = -1;
eds.push_back(ign);
// 別の道があれば寄り道して辺を全部使うパート (閉路になるはず)
vector<size_t> res_vs, res_eds;
for (size_t i = 0; i < eds.size(); ++i) {
stack<size_t> v, e;
v.push(vs[i]), e.push(eds[i]);
while (!v.empty()) {
assert(v.size() == e.size());
size_t now = v.top();
size_t e_idx = e.top();
vector<size_t> tmpvs, tmpeds;
if (find_path(now, now, tmpvs, tmpeds)) {
assert(tmpvs.front() == now && tmpvs.back() == now);
assert(tmpvs.size() == tmpeds.size() + 1);
tmpvs.pop_back();
reverse(tmpvs.begin(), tmpvs.end());
reverse(tmpeds.begin(), tmpeds.end());
for (const auto& ver : tmpvs) v.push(ver);
for (const auto& edg : tmpeds) e.push(edg);
}
else {
v.pop(), e.pop();
res_vs.push_back(now);
res_eds.push_back(e_idx);
}
}
}
assert(res_eds.back() == ign);
res_eds.pop_back();
assert(res_vs.size() == res_eds.size() + 1);
assert(res_eds.size() == Edges.size());
return make_pair(res_vs, res_eds);
}
} // namespace graph
} // namespace _internal
} // namespace asalib
#line 2 "library/graph/connection.hpp"
using namespace std;
#line 2 "library/_internal/graph/connection.hpp"
#line 7 "library/_internal/graph/connection.hpp"
using namespace std;
#line 10 "library/_internal/graph/connection.hpp"
namespace asalib {
namespace _internal {
namespace graph {
bool is_connected(const adjlist_t& adjlist) {
vector<bool> visited(adjlist.size(), false);
function<void(size_t)> dfs = [&](size_t v) {
visited[v] = true;
for (const auto& [u, _] : adjlist[v])
if (!visited[u]) dfs(u);
};
dfs(0);
return all_of(visited.begin(), visited.end(), [](bool v) {
return v;
});
}
} // namespace graph
} // namespace _internal
} // namespace asalib
#line 8 "library/graph/connection.hpp"
namespace asalib {
namespace graph {
bool digraph::is_connected() const { return _internal::graph::is_connected(adj_list); }
bool graph::is_connected() const { return _internal::graph::is_connected(adj_list); }
} // namespace graph
} // namespace asalib
#line 13 "library/graph/eulerian-walk.hpp"
namespace asalib {
namespace graph {
optional<pair<vector<size_t>, vector<size_t>>> digraph::eulerian_walk() const {
constexpr size_t None = -1;
// もし辺がなければオイラーグラフ、任意の頂点を返す
if (edge_list.empty()) [[unlikely]]
return make_pair(vector<size_t> { 0 }, vector<size_t> {});
// 辺がない頂点を除外したグラフを作る
size_t n_vertex_withedge = 0;
vector<size_t> id(n_vertex, None);
for (const auto& [u, v] : edge_list) {
if (id[u] == None) id[u] = n_vertex_withedge++;
if (id[v] == None) id[v] = n_vertex_withedge++;
}
vector<size_t> idrev(n_vertex_withedge, None);
for (size_t i = 0; i < n_vertex; ++i)
if (id[i] != None) idrev[id[i]] = i;
asalib::graph::digraph newGraph(n_vertex_withedge);
for (const auto& [u, v] : edge_list) newGraph.add_edge(id[u], id[v]);
// 有向グラフの場合、基底無向グラフが連結でなければ存在しない
if (!newGraph.underlying_graph.is_connected()) return nullopt;
// オイラーグラフとなるか判定
vector<size_t> in(n_vertex_withedge, 0), out(n_vertex_withedge, 0);
for (const auto& [u, v] : edge_list) ++out[id[u]], ++in[id[v]];
size_t start = None, end = None;
for (size_t i = 0; i < n_vertex_withedge; ++i) {
if (in[i] == out[i]) continue;
if (in[i] + 1 == out[i]) {
if (start != None) return nullopt;
start = i;
continue;
}
if (in[i] == out[i] + 1) {
if (end != None) return nullopt;
end = i;
continue;
}
return nullopt;
}
if ((start == None) xor (end == None)) return nullopt;
if (start == None) {
assert(end == None);
start = end = 0;
}
auto [vertexes, edges] = asalib::_internal::graph::eulerian_walk<true>(n_vertex_withedge, newGraph.edge_list, start, end);
vector<size_t> vertexes_original;
for (const auto& v : vertexes) vertexes_original.push_back(idrev[v]);
return make_pair(vertexes_original, edges);
}
optional<pair<vector<size_t>, vector<size_t>>> graph::eulerian_walk() const {
constexpr size_t None = -1;
// もし辺がなければオイラーグラフ、任意の頂点を返す
if (edge_list.empty()) [[unlikely]]
return make_pair(vector<size_t> { 0 }, vector<size_t> {});
// 辺のない頂点を除外したグラフを作る
size_t n_vertex_withedge = 0;
vector<size_t> id(n_vertex, None);
for (const auto& [u, v] : edge_list) {
if (id[u] == None) id[u] = n_vertex_withedge++;
if (id[v] == None) id[v] = n_vertex_withedge++;
}
vector<size_t> idrev(n_vertex_withedge, None);
for (size_t i = 0; i < n_vertex; ++i)
if (id[i] != None) idrev[id[i]] = i;
asalib::graph::graph newGraph(n_vertex_withedge);
for (const auto& [u, v] : edge_list) newGraph.add_edge(id[u], id[v]);
// 連結でなければ存在しない
if (!newGraph.is_connected()) return nullopt;
vector<size_t> deg(n_vertex_withedge, 0);
for (const auto& [u, v] : edge_list) ++deg[id[u]], ++deg[id[v]];
size_t start = None, end = None;
for (size_t i = 0; i < n_vertex_withedge; ++i) {
if (deg[i] % 2 == 0) continue;
if (start == None)
start = i;
else if (end == None)
end = i;
else
return nullopt;
}
if (start != None && end == None) return nullopt;
if (start == None) {
assert(end == None);
start = end = 0;
}
auto [vertexes, edges] = asalib::_internal::graph::eulerian_walk<false>(n_vertex_withedge, newGraph.edge_list, start, end);
vector<size_t> vertexes_original;
for (const auto& v : vertexes) vertexes_original.push_back(idrev[v]);
return make_pair(vertexes_original, edges);
}
} // namespace graph
} // namespace asalib
#line 10 "tests/graph/eulerian-walk/libchecker-directed.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed"
void solve() {
int n, m;
asalib::FastIO >> n >> m;
asalib::graph::digraph Graph(n);
rep(_, m) {
int u, v;
asalib::FastIO >> u >> v;
Graph.add_edge(u, v);
}
auto res = Graph.eulerian_walk();
if (!res.has_value()) {
asalib::FastIO << "No" << '\n';
}
else {
asalib::FastIO << "Yes" << '\n';
auto [vs, es] = res.value();
rep(i, vs.size()) {
if (i) asalib::FastIO << ' ';
asalib::FastIO << vs[i];
}
asalib::FastIO << '\n';
rep(i, es.size()) {
if (i) asalib::FastIO << ' ';
asalib::FastIO << es[i];
}
asalib::FastIO << '\n';
}
}
int main() {
int t;
asalib::FastIO >> t;
while (t--) solve();
return 0;
}