// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/eulerian_trail_undirected
#include "../../../src/graph/euler_trail/lib.hpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 t;
std::cin >> t;
while (t--) {
u32 n, m;
std::cin >> n >> m;
vecptu e(m);
for (auto& [u, v] : e) std::cin >> u >> v;
if (auto res = euler_trail<false>(n, e); !res) {
std::cout << "No\n";
} else {
std::cout << "Yes\n";
auto et = res.value();
flt_ (u32, i, 0, (u32)et.size()) std::cout << et[i].first << " \n"[i + 1 == et.size()];
if (et.size() == 1) std::cout << '\n';
flt_ (u32, i, 1, (u32)et.size()) std::cout << et[i].second << " \n"[i + 1 == et.size()];
}
}
return 0;
}
#line 1 "test/cpv/library-checker-graph/eulerian_trail_undirected.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/eulerian_trail_undirected
#line 2 "src/graph/euler_trail/lib.hpp"
#line 2 "src/graph/ds/graph_c/lib.hpp"
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 4 "src/graph/ds/graph_c/lib.hpp"
namespace tifa_libs {
namespace graph_info_impl_ {
struct graph_info_tag_base {};
template <class... Info>
requires(std::derived_from<Info, graph_info_tag_base> && ...)
struct graph_tag_base : Info... {
CEXP graph_tag_base(auto&&... args) NE : Info(std::forward<decltype(args)>(args)...)... {}
protected:
CEXP void add_arc(auto&&... args) NE { (Info::add_arc(std::forward<decltype(args)>(args)...), ...); }
CEXP void del_arc(auto&&... args) NE { (Info::del_arc(std::forward<decltype(args)>(args)...), ...); }
};
template <class T, class = std::is_void<T>::type>
struct E;
template <class T>
struct E<T, std::false_type> {
u32 to;
T cost;
CEXP E() = default;
CEXP E(u32 v, cT_(T) c) NE : to(v), cost(c) {}
CEXP operator u32() CNE { return to; }
};
template <class T>
struct E<T, std::true_type> {
u32 to;
CEXP E() = default;
CEXP E(u32 v) NE : to(v) {}
CEXP operator u32() CNE { return to; }
};
} // namespace graph_info_impl_
namespace graph_impl_ {
template <class etag_t>
struct graph : etag_t {
using Et = etag_t::val_t;
CEXP graph() = default;
CEXPE graph(u32 n, auto&&... e_args) NE : etag_t(n, std::forward<decltype(e_args)>(e_args)...) {}
CEXP void add_edge(u32 u, u32 v, auto&&... args) NE { etag_t::add_arc(u, v, std::forward<decltype(args)>(args)...), etag_t::add_arc(v, u, std::forward<decltype(args)>(args)...); }
template <class F>
CEXP void foreach(u32 u, F&& f) CNE {
if CEXP (std::is_void_v<Et>)
for (auto v : (*this)[u]) f(v);
else
for (auto [v, w] : (*this)[u]) f(v, w);
}
};
} // namespace graph_impl_
// clang-format off
#define CONCEPT_GRAPH(name, base) \
template <class T> concept name##_c = specialized_from_v<T, base>; \
template <class T> concept u##name##_c = name##_c<T> && std::same_as<TPN T::Et, void>; \
template <class T> concept w##name##_c = name##_c<T> && !std::same_as<TPN T::Et, void>
// clang-format on
CONCEPT_GRAPH(graph, graph_impl_::graph);
} // namespace tifa_libs
#line 4 "src/graph/euler_trail/lib.hpp"
namespace tifa_libs {
namespace euler_trail_impl_ {
template <bool cyc>
CEXP auto run_(u32 n, u32 m, cT_(vvecptu) g, u32 s) NE {
std::optional ret(vecptu{});
vec<vecptu::const_iterator> its(n);
flt_ (u32, i, 0, n) its[i] = begin(g[i]);
veci f(n);
if CEXP (!cyc) ++f[s];
vecb vis(m);
vecptu stk = {{s, -1_u32}};
while (!stk.empty()) {
auto [i, p] = stk.back();
auto& it = its[i];
if (it == end(g[i])) {
ret->emplace_back(i, p), stk.pop_back();
continue;
}
if (auto [j, e] = *(it++); !vis[e]) --f[i], ++f[j], stk.emplace_back(j, e), vis[e] = true;
}
if (ret->size() != m + 1 || any_of(f, [](i32 i) { return i < 0; })) ret = std::nullopt;
else reverse(ret.value());
return ret;
}
} // namespace euler_trail_impl_
// @return vector of {v, eid} of Eulerian trail if found
// edges[eid[i]] = v[i-1] -> v[i], eid[0] = -1
template <bool directed, bool cycle = false>
CEXP auto euler_trail(u32 n, vecptu CR edges) NE {
vvecptu g(n);
vecu deg_in(0);
if CEXP (directed) deg_in.resize(n);
u32 e = 0;
for (auto [u, v] : edges) {
g[u].emplace_back(v, e);
if CEXP (directed) ++deg_in[v];
else g[v].emplace_back(u, e);
++e;
}
u32 s = 0;
flt_ (u32, i, 1, (u32)g.size())
if (!g[i].empty()) s = i;
flt_ (u32, i, 0, (u32)g.size())
if CEXP (directed) {
if (deg_in[i] < g[i].size()) s = i;
} else if (g[i].size() & 1) s = i;
return euler_trail_impl_::run_<cycle>(n, (u32)edges.size(), g, s);
}
template <graph_c G>
CEXP bool is_eulerian(G CR g) NE {
retif_((!g.esize()) [[unlikely]], 1);
cu32 n = g.vsize();
assert(n == g.din.size());
flt_ (u32, i, 0, n)
if (g.din[i] != g.dout[i]) return false;
u32 loopv = 0, loope = 0, start = 0;
flt_ (u32, u, 0, n) {
if (g[u].empty()) continue;
bool f = true;
for (start = u; auto v : g[u])
if (u == (u32)v) ++loope;
else f = false;
loopv += f;
}
if (loopv > 1 || (loopv == 1 && loope != g.esize())) return false;
vecb vis(n);
auto f = [&](auto&& f, u32 x) NE -> void {
for (auto v : g[x])
if (!vis[(u32)v]) vis[(u32)v] = true, f(f, (u32)v);
};
vis[start] = true, f(f, start);
flt_ (u32, i, 0, n)
if (!vis[i] && g.din[i]) return false;
return true;
}
} // namespace tifa_libs
#line 3 "test/cpv/library-checker-graph/eulerian_trail_undirected.cpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 t;
std::cin >> t;
while (t--) {
u32 n, m;
std::cin >> n >> m;
vecptu e(m);
for (auto& [u, v] : e) std::cin >> u >> v;
if (auto res = euler_trail<false>(n, e); !res) {
std::cout << "No\n";
} else {
std::cout << "Yes\n";
auto et = res.value();
flt_ (u32, i, 0, (u32)et.size()) std::cout << et[i].first << " \n"[i + 1 == et.size()];
if (et.size() == 1) std::cout << '\n';
flt_ (u32, i, 1, (u32)et.size()) std::cout << et[i].second << " \n"[i + 1 == et.size()];
}
}
return 0;
}
test/cpv/library-checker-graph/eulerian_trail_undirected.cpp