#include <algorithm> #include <cinttypes> #include <cstdint> #include <iostream> #include <iterator> #include <limits> #include <stack> #include <vector> //#define DEBUG #ifdef DEBUG static constexpr const bool debug = true; #else static constexpr const bool debug = false; #endif class graph_t { using dfstime_t = int32_t; static constexpr const dfstime_t NEVER = 0; public: using vertex_id_t = int32_t; static constexpr const vertex_id_t NO_VERTEX = -1; graph_t() : state{state_t::NO_SCC} , timer{1} { } friend std::istream& operator>>(std::istream &str, graph_t &graph) { size_t n, m; str >> n >> m; graph.vertices.clear(); graph.vertices.resize(n); for(size_t i = 0; i < m; ++i) { vertex_id_t a, b; str >> a >> b; --a, --b; graph.vertices[a].adj.push_back(b); } return str; } void solve() { for(vertex_id_t vertex_id = 0; vertex_id < static_cast<vertex_id_t>(vertices.size()); ++vertex_id) { if(debug) std::cerr << "vertex " << vertex_id << std::endl; const auto &vertex = vertices[vertex_id]; if(vertex.order == NEVER) dfs(vertex_id); } } void print_result(std::ostream &str) const { switch(state) { case state_t::NO_SCC: str << "NIE" << std::endl; return; case state_t::ONE_SCC: str << result.size() << std::endl; for(auto vertex_id: result) str << vertex_id + 1 << " "; str << std::endl; return; case state_t::MULTIPLE_SCC: str << 0 << std::endl << std::endl; return; } } private: struct vertex_t { std::vector<vertex_id_t> adj; dfstime_t low, order; dfstime_t high, postorder; vertex_id_t scc_root_id; bool on_stack; vertex_t() : low{NEVER} , order{NEVER} , high{NEVER} , postorder{NEVER} , on_stack{false} { } }; enum class state_t { NO_SCC, ONE_SCC, MULTIPLE_SCC }; std::vector<vertex_t> vertices; std::stack<vertex_id_t> stack; state_t state; std::vector<vertex_id_t> result; dfstime_t timer; void dfs(vertex_id_t vertex_id) { if(debug) { std::cerr << "Entering vertex " << vertex_id << std::endl; } auto &vertex = vertices[vertex_id]; vertex.order = vertex.low = timer++; vertex.on_stack = true; stack.push(vertex_id); for(auto adj_id: vertex.adj) { const auto &adj = vertices[adj_id]; if(adj.order == NEVER) { dfs(adj_id); vertex.low = std::min(vertex.low, adj.low); } else if(adj.on_stack) { vertex.low = std::min(vertex.low, adj.order); } } vertex.postorder = vertex.high = timer++; if(vertex.low == vertex.order) { std::vector<vertex_id_t> scc; vertex_id_t scc_vertex_id; do { scc_vertex_id = stack.top(); stack.pop(); vertices[scc_vertex_id].on_stack = false; vertices[scc_vertex_id].scc_root_id = vertex_id; scc.push_back(scc_vertex_id); } while(vertex_id != scc_vertex_id); process_scc(std::move(scc)); } } void process_scc(std::vector<vertex_id_t> &&scc) { if(debug) { std::cerr << "a strongly connected component: "; std::copy(std::begin(scc), std::end(scc), std::ostream_iterator<vertex_id_t>(std::cerr, " ")); std::cerr << std::endl; } if(scc.size() == 1) return; switch(state) { case state_t::ONE_SCC: state = state_t::MULTIPLE_SCC; /* fall-through */ case state_t::MULTIPLE_SCC: return; case state_t::NO_SCC: state = state_t::ONE_SCC; std::sort(std::begin(scc), std::end(scc), [this](vertex_id_t lhs, vertex_id_t rhs) { return vertices[lhs].postorder < vertices[rhs].postorder; } ); const auto scc_root_id = vertices[scc[0]].scc_root_id; auto lowest = std::numeric_limits<vertex_id_t>::max(); for(const auto vertex_id: scc) { auto &vertex = vertices[vertex_id]; if(debug) std::cerr << "vertex " << vertex_id << ", postorder = " << vertex.postorder << std::endl; for(const auto neighbour_id: vertex.adj) { const auto &neighbour = vertices[neighbour_id]; if(neighbour.scc_root_id != scc_root_id) continue; if(debug) std::cerr << "\tedge " << vertex_id << " -> " << neighbour_id << std::endl; vertex.high = std::max(vertex.high, neighbour.high); if(vertex.postorder < neighbour.postorder) { if(debug) std::cerr << "\t\tis a back edge, clearing result" << std::endl; lowest = std::min(lowest, neighbour.postorder); result.clear(); } else if(vertex.postorder <= neighbour.high) { while(!result.empty() && vertices[result.back()].postorder > neighbour.postorder) { if(debug) std::cerr << "\t\tpopping " << result.back() << std::endl; result.pop_back(); } } } if(debug) std::cerr << "exiting " << vertex_id << ", high = " << vertex.high << ", lowest = " << lowest << std::endl; if(vertex.postorder <= lowest) { result.push_back(vertex_id); if(debug) std::cerr << "\tpushing " << vertex_id << std::endl; } } std::sort(std::begin(result), std::end(result)); } } }; int main() { std::ios_base::sync_with_stdio(false); graph_t graph; std::cin >> graph; graph.solve(); graph.print_result(std::cout); }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 | #include <algorithm> #include <cinttypes> #include <cstdint> #include <iostream> #include <iterator> #include <limits> #include <stack> #include <vector> //#define DEBUG #ifdef DEBUG static constexpr const bool debug = true; #else static constexpr const bool debug = false; #endif class graph_t { using dfstime_t = int32_t; static constexpr const dfstime_t NEVER = 0; public: using vertex_id_t = int32_t; static constexpr const vertex_id_t NO_VERTEX = -1; graph_t() : state{state_t::NO_SCC} , timer{1} { } friend std::istream& operator>>(std::istream &str, graph_t &graph) { size_t n, m; str >> n >> m; graph.vertices.clear(); graph.vertices.resize(n); for(size_t i = 0; i < m; ++i) { vertex_id_t a, b; str >> a >> b; --a, --b; graph.vertices[a].adj.push_back(b); } return str; } void solve() { for(vertex_id_t vertex_id = 0; vertex_id < static_cast<vertex_id_t>(vertices.size()); ++vertex_id) { if(debug) std::cerr << "vertex " << vertex_id << std::endl; const auto &vertex = vertices[vertex_id]; if(vertex.order == NEVER) dfs(vertex_id); } } void print_result(std::ostream &str) const { switch(state) { case state_t::NO_SCC: str << "NIE" << std::endl; return; case state_t::ONE_SCC: str << result.size() << std::endl; for(auto vertex_id: result) str << vertex_id + 1 << " "; str << std::endl; return; case state_t::MULTIPLE_SCC: str << 0 << std::endl << std::endl; return; } } private: struct vertex_t { std::vector<vertex_id_t> adj; dfstime_t low, order; dfstime_t high, postorder; vertex_id_t scc_root_id; bool on_stack; vertex_t() : low{NEVER} , order{NEVER} , high{NEVER} , postorder{NEVER} , on_stack{false} { } }; enum class state_t { NO_SCC, ONE_SCC, MULTIPLE_SCC }; std::vector<vertex_t> vertices; std::stack<vertex_id_t> stack; state_t state; std::vector<vertex_id_t> result; dfstime_t timer; void dfs(vertex_id_t vertex_id) { if(debug) { std::cerr << "Entering vertex " << vertex_id << std::endl; } auto &vertex = vertices[vertex_id]; vertex.order = vertex.low = timer++; vertex.on_stack = true; stack.push(vertex_id); for(auto adj_id: vertex.adj) { const auto &adj = vertices[adj_id]; if(adj.order == NEVER) { dfs(adj_id); vertex.low = std::min(vertex.low, adj.low); } else if(adj.on_stack) { vertex.low = std::min(vertex.low, adj.order); } } vertex.postorder = vertex.high = timer++; if(vertex.low == vertex.order) { std::vector<vertex_id_t> scc; vertex_id_t scc_vertex_id; do { scc_vertex_id = stack.top(); stack.pop(); vertices[scc_vertex_id].on_stack = false; vertices[scc_vertex_id].scc_root_id = vertex_id; scc.push_back(scc_vertex_id); } while(vertex_id != scc_vertex_id); process_scc(std::move(scc)); } } void process_scc(std::vector<vertex_id_t> &&scc) { if(debug) { std::cerr << "a strongly connected component: "; std::copy(std::begin(scc), std::end(scc), std::ostream_iterator<vertex_id_t>(std::cerr, " ")); std::cerr << std::endl; } if(scc.size() == 1) return; switch(state) { case state_t::ONE_SCC: state = state_t::MULTIPLE_SCC; /* fall-through */ case state_t::MULTIPLE_SCC: return; case state_t::NO_SCC: state = state_t::ONE_SCC; std::sort(std::begin(scc), std::end(scc), [this](vertex_id_t lhs, vertex_id_t rhs) { return vertices[lhs].postorder < vertices[rhs].postorder; } ); const auto scc_root_id = vertices[scc[0]].scc_root_id; auto lowest = std::numeric_limits<vertex_id_t>::max(); for(const auto vertex_id: scc) { auto &vertex = vertices[vertex_id]; if(debug) std::cerr << "vertex " << vertex_id << ", postorder = " << vertex.postorder << std::endl; for(const auto neighbour_id: vertex.adj) { const auto &neighbour = vertices[neighbour_id]; if(neighbour.scc_root_id != scc_root_id) continue; if(debug) std::cerr << "\tedge " << vertex_id << " -> " << neighbour_id << std::endl; vertex.high = std::max(vertex.high, neighbour.high); if(vertex.postorder < neighbour.postorder) { if(debug) std::cerr << "\t\tis a back edge, clearing result" << std::endl; lowest = std::min(lowest, neighbour.postorder); result.clear(); } else if(vertex.postorder <= neighbour.high) { while(!result.empty() && vertices[result.back()].postorder > neighbour.postorder) { if(debug) std::cerr << "\t\tpopping " << result.back() << std::endl; result.pop_back(); } } } if(debug) std::cerr << "exiting " << vertex_id << ", high = " << vertex.high << ", lowest = " << lowest << std::endl; if(vertex.postorder <= lowest) { result.push_back(vertex_id); if(debug) std::cerr << "\tpushing " << vertex_id << std::endl; } } std::sort(std::begin(result), std::end(result)); } } }; int main() { std::ios_base::sync_with_stdio(false); graph_t graph; std::cin >> graph; graph.solve(); graph.print_result(std::cout); } |