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#define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed" #include "../../graph/euler_trail.hpp" #include "../../template/template.hpp" namespace ebi { void main_() { int n, m; std::cin >> n >> m; Graph<int> g(n); g.read_graph(m, 0, true); auto res = euler_trail_directed(g); if (res) { auto [vs, es] = res.value(); std::cout << "Yes\n"; std::cout << vs << '\n'; std::cout << es << '\n'; } else { std::cout << "No\n"; } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; std::cin >> t; while (t--) { ebi::main_(); } return 0; }
#line 1 "test/graph/Eulerian_Trail_Directed.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/eulerian_trail_directed" #line 2 "graph/euler_trail.hpp" #include <algorithm> #include <cassert> #include <optional> #include <ranges> #include <utility> #include <vector> #line 2 "graph/base.hpp" #line 4 "graph/base.hpp" #include <iostream> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 11 "graph/euler_trail.hpp" namespace ebi { template <class T> std::optional<std::pair<std::vector<int>, std::vector<int>>> euler_trail_undirected(const Graph<T> &g, bool circuit = false) { int n = g.node_number(); int m = g.edge_number(); int s = -1, t = -1; for (int v : std::views::iota(0, n)) { if (g[v].size() & 1) { if (s < 0) s = v; else if (t < 0) t = v; else return std::nullopt; } } if (circuit && s != -1) return std::nullopt; if (!circuit && (s != -1 && t == -1)) return std::nullopt; if (m == 0) return std::pair<std::vector<int>, std::vector<int>>({0}, {}); if (s < 0) s = g.get_edge(0).from; std::vector<int> ids(n, 0); std::vector<bool> used(m, false); std::vector<int> vs, es; auto dfs = [&](auto &&self, int v) -> void { while (ids[v] < (int)g[v].size()) { auto e = g[v][ids[v]++]; if (used[e.id]) continue; used[e.id] = true; self(self, e.to); es.emplace_back(e.id); } vs.emplace_back(v); }; dfs(dfs, s); if ((int)es.size() != m) return std::nullopt; return std::pair<std::vector<int>, std::vector<int>>(vs, es); } template <class T> std::optional<std::pair<std::vector<int>, std::vector<int>>> euler_trail_directed(const Graph<T> &g, bool circuit = false) { int n = g.node_number(); int m = g.edge_number(); std::vector<int> in(n, 0), out(n, 0); for (auto e : g.get_edges()) { in[e.to]++; out[e.from]++; } int s = -1, t = -1; for (auto v : std::views::iota(0, n)) { if (in[v] + 1 == out[v]) { if (s != -1) return std::nullopt; s = v; } else if (in[v] == out[v] + 1) { if (t != -1) return std::nullopt; t = v; } else if (in[v] == out[v]) continue; else return std::nullopt; } if (circuit && (s != -1 || t != -1)) return std::nullopt; if (!circuit && ((s == -1 && t != -1) || (s != -1 && t == -1))) return std::nullopt; if (m == 0) return std::pair<std::vector<int>, std::vector<int>>({0}, {}); if (s == -1) s = g.get_edge(0).from; std::vector<int> vs, es; std::vector<int> ids(n, 0); auto dfs = [&](auto &&self, int v) -> void { while (ids[v] < (int)g[v].size()) { auto e = g[v][ids[v]++]; self(self, e.to); es.emplace_back(e.id); } vs.emplace_back(v); }; dfs(dfs, s); if ((int)es.size() != m) return std::nullopt; std::reverse(vs.begin(), vs.end()); std::reverse(es.begin(), es.end()); return std::pair<std::vector<int>, std::vector<int>>(vs, es); } } // namespace ebi #line 1 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 7 "template/io.hpp" namespace ebi { template <typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) { return os << pa.first << " " << pa.second; } template <typename T1, typename T2> std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) { return os >> pa.first >> pa.second; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template <typename T> std::istream &operator>>(std::istream &os, std::vector<T> &vec) { for (T &e : vec) std::cin >> e; return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 8 "template/utility.hpp" namespace ebi { template <class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template <class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template <class T> T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template <class T> T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits<i64>::max() / 4; constexpr int INF = std::numeric_limits<int>::max() / 2; const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 5 "test/graph/Eulerian_Trail_Directed.test.cpp" namespace ebi { void main_() { int n, m; std::cin >> n >> m; Graph<int> g(n); g.read_graph(m, 0, true); auto res = euler_trail_directed(g); if (res) { auto [vs, es] = res.value(); std::cout << "Yes\n"; std::cout << vs << '\n'; std::cout << es << '\n'; } else { std::cout << "No\n"; } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; std::cin >> t; while (t--) { ebi::main_(); } return 0; }