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
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- Last update: 2026-03-10 00:09:38+09:00
- Problem: https://judge.yosupo.jp/problem/eulerian_trail_directed
Depends on
- library/_internal/graph-base.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/fastio.hpp"
#include "../../../library/graph/eulerian-walk.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed"
void solve() {
int n, m;
asalib::in >> n >> m;
vector<pair<int, int>> edges(m);
rep(i, m) {
int u, v;
asalib::in >> u >> v;
edges[i] = { u, v };
}
auto res = asalib::graph::eulerian_walk(n, edges, true);
if (!res.has_value()) {
asalib::out << "No" << '\n';
}
else {
asalib::out << "Yes" << '\n';
auto [vs, es] = res.value();
rep(i, vs.size()) {
if (i) asalib::out << ' ';
asalib::out << vs[i];
}
asalib::out << '\n';
rep(i, es.size()) {
if (i) asalib::out << ' ';
asalib::out << es[i];
}
asalib::out << '\n';
}
}
int main() {
int t;
asalib::in >> 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/fastio.hpp"
#line 5 "library/fastio.hpp"
#include <concepts>
#line 11 "library/fastio.hpp"
#include <type_traits>
using namespace std;
// TODO: 何も入力がない場合にも対応する？
namespace asalib {
namespace _internal {
class FastIn {
static constexpr unsigned int BUFFER_SIZE = 1 << 20;
static constexpr unsigned int MAX_TOKEN_SIZE = 64;
array<char, BUFFER_SIZE> read_buffer = {};
array<char, BUFFER_SIZE>::iterator read_ptr = nullptr;
unsigned int read_size = 0;
public:
FastIn() {
read_buffer.fill(0);
read_ptr = read_buffer.begin();
load();
}
private:
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);
}
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>)
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);
}
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:
FastIn& operator>>(char& x) {
read_commonop();
x = *read_ptr++;
return *this;
}
FastIn& 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>)
FastIn& operator>>(T& x) {
read_commonop();
if constexpr (is_signed_v<T> || is_same_v<T, __int128_t>) {
if (*read_ptr == '-') {
++read_ptr;
_read_uint(x);
x = -x;
return *this;
}
}
_read_uint(x);
return *this;
}
};
class FastOut {
static constexpr unsigned int BUFFER_SIZE = 1 << 20;
static constexpr unsigned int MAX_TOKEN_SIZE = 64;
static constexpr unsigned int MAX_PRECOMPUTE_NUM = 1'0000;
static constexpr unsigned int MAX_PRECOMPUTE_NUM_DIGIT = 4;
array<char, BUFFER_SIZE> write_buffer = {};
array<char, BUFFER_SIZE>::iterator write_ptr = nullptr;
public:
FastOut() {
write_buffer.fill(0);
write_ptr = write_buffer.begin();
}
~FastOut() { flush(); }
private:
static constexpr array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits = [] {
array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits {};
for (unsigned int i = 0; i < MAX_PRECOMPUTE_NUM; ++i) {
unsigned int 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 (unsigned int i = 1; i < pow10.size(); ++i) pow10[i] = pow10[i - 1] * 10;
return pow10;
}();
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();
}
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>)
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>)
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>)
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:
void flush() {
fwrite(write_buffer.begin(), 1, write_ptr - write_buffer.begin(), stdout);
write_ptr = write_buffer.begin();
}
FastOut& operator<<(const char& x) {
write_commonop();
putchar(x);
return *this;
}
FastOut& operator<<(const string& x) {
write_commonop();
unsigned int idx = 0;
while (idx < x.size()) {
const unsigned int siz = min(BUFFER_SIZE - static_cast<unsigned int>(write_ptr - write_buffer.begin()), static_cast<unsigned int>(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>)
FastOut& operator<<(const T& x) {
write_commonop();
if constexpr (is_signed_v<T> || is_same_v<T, __int128_t>) {
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;
}
};
} // namespace _internal
inline _internal::FastIn in;
inline _internal::FastOut out;
} // namespace asalib
#line 2 "library/graph/eulerian-walk.hpp"
#line 5 "library/graph/eulerian-walk.hpp"
#include <optional>
#include <ranges>
#line 9 "library/graph/eulerian-walk.hpp"
using namespace std;
#line 2 "library/_internal/graph-base.hpp"
#line 6 "library/_internal/graph-base.hpp"
using namespace std;
namespace asalib::_internal {
// vector<vector<int>> とかの隣接リストを表す型
template<class T>
concept adjacency_list = requires(T t) {
ranges::ssize(t);
{ t[0] } -> ranges::range;
{ *ranges::begin(t[0]) } -> convertible_to<int>;
};
// 辺のリストを表す型
// 重み付きも考慮し pair<int, int> と tuple<int, int, int> の両方を許容
template<class T>
concept edge_list = requires(T t) {
ranges::ssize(t);
{ get<0>(t[0]) } -> convertible_to<int>;
{ get<1>(t[0]) } -> convertible_to<int>;
};
} // namespace asalib::_internal
#line 2 "library/graph/connection.hpp"
#line 4 "library/graph/connection.hpp"
using namespace std;
#line 7 "library/graph/connection.hpp"
namespace asalib::graph {
template<_internal::adjacency_list T>
bool is_connected(const T& adj_list) {
vector<bool> visited(adj_list.size(), false);
vector<int> st;
st.reserve(adj_list.size());
st.emplace_back(0);
visited[0] = true;
while (!st.empty()) {
int v = st.back();
st.pop_back();
for (const auto& u : adj_list[v]) {
if (!visited[u]) {
visited[u] = true;
st.emplace_back(u);
}
}
}
for (const auto v : visited) {
if (!v) return false;
}
return true;
}
} // namespace asalib::graph
#line 13 "library/graph/eulerian-walk.hpp"
namespace asalib::graph {
template<_internal::edge_list T>
optional<pair<vector<int>, vector<int>>> eulerian_walk(const int n, const T& edgelist, const bool is_directed) {
constexpr int 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 (edgelist.empty()) [[unlikely]]
return make_pair(vector<int> { 0 }, vector<int> {});
// 辺がない頂点を除外したグラフを作成
int n_vertex_withedge = 0;
vector<int> id(n, None), indeg(n, 0), outdeg(n, 0);
for (const auto& p : edgelist) {
const auto &u = get<0>(p), &v = get<1>(p);
++outdeg[u], ++indeg[v];
if (id[u] == None) id[u] = n_vertex_withedge++;
if (id[v] == None) id[v] = n_vertex_withedge++;
}
vector idrev(n_vertex_withedge, None);
for (int i = 0; i < n; ++i)
if (id[i] != None) idrev[id[i]] = i;
vector Graph(n_vertex_withedge, vector<int>());
vector underlyingGraph(n_vertex_withedge, vector<int>());
for (int i = 0; i < n_vertex_withedge; ++i) {
const int bidir_siz = indeg[idrev[i]] + outdeg[idrev[i]];
Graph[i].reserve(is_directed ? outdeg[idrev[i]] : bidir_siz);
underlyingGraph[i].reserve(bidir_siz);
}
for (int i = 0; i < ranges::ssize(edgelist); ++i) {
const auto& p = edgelist[i];
const auto &u = get<0>(p), &v = get<1>(p);
Graph[id[u]].emplace_back(i);
if (!is_directed) Graph[id[v]].emplace_back(i);
underlyingGraph[id[u]].emplace_back(id[v]);
underlyingGraph[id[v]].emplace_back(id[u]);
}
// 連結でなければ存在しない
if (!is_connected(underlyingGraph)) return nullopt;
// オイラーグラフとなるか判定
int start = None, end = None;
for (int idx = 0; idx < n_vertex_withedge; ++idx) {
const int i = idrev[idx];
if (is_directed) {
if (indeg[i] == outdeg[i]) continue;
if (indeg[i] + 1 == outdeg[i]) {
if (start != None) return nullopt;
start = idx;
continue;
}
if (indeg[i] == outdeg[i] + 1) {
if (end != None) return nullopt;
end = idx;
continue;
}
return nullopt;
}
if ((indeg[i] + outdeg[i]) % 2 == 0) continue;
if (start == None)
start = idx;
else if (end == None)
end = idx;
else
return nullopt;
}
if ((start == None) xor (end == None)) return nullopt;
if (start == None) {
assert(end == None);
start = end = 0;
}
// グラフ探索パート
vector<bool> used(edgelist.size(), false);
vector<int> vs, es;
vector<pair<int, int>> st = { { start, None } };
vs.reserve(edgelist.size() + 1);
es.reserve(edgelist.size());
st.reserve(edgelist.size() + 1);
while (!st.empty()) {
auto [v, inedge] = st.back();
while (!Graph[v].empty() && used[Graph[v].back()]) Graph[v].pop_back();
if (Graph[v].empty()) {
st.pop_back();
vs.emplace_back(v);
if (inedge != None) es.emplace_back(inedge);
}
else {
const int e = Graph[v].back();
Graph[v].pop_back();
used[e] = true;
const auto& p = edgelist[e];
const auto &u = get<0>(p), &w = get<1>(p);
const int to = id[u] == v ? id[w] : id[u];
st.emplace_back(to, e);
}
}
assert(vs.size() == es.size() + 1);
assert(es.size() == edgelist.size());
ranges::reverse(vs);
ranges::reverse(es);
// 元の頂点番号に戻す
vector<int> vs_orig(vs.size());
for (int i = 0; i < ranges::ssize(vs); ++i) vs_orig[i] = idrev[vs[i]];
return make_pair(vs_orig, es);
}
} // namespace asalib::graph
#line 9 "tests/graph/eulerian-walk/libchecker-directed.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed"
void solve() {
int n, m;
asalib::in >> n >> m;
vector<pair<int, int>> edges(m);
rep(i, m) {
int u, v;
asalib::in >> u >> v;
edges[i] = { u, v };
}
auto res = asalib::graph::eulerian_walk(n, edges, true);
if (!res.has_value()) {
asalib::out << "No" << '\n';
}
else {
asalib::out << "Yes" << '\n';
auto [vs, es] = res.value();
rep(i, vs.size()) {
if (i) asalib::out << ' ';
asalib::out << vs[i];
}
asalib::out << '\n';
rep(i, es.size()) {
if (i) asalib::out << ' ';
asalib::out << es[i];
}
asalib::out << '\n';
}
}
int main() {
int t;
asalib::in >> t;
while (t--) solve();
return 0;
}