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#define PROBLEM "https://judge.yosupo.jp/problem/two_sat" #include "../../algorithm/two_sat.hpp" #include <iostream> int main() { char p; std::string cnf; std::cin >> p >> cnf; int n, m; std::cin >> n >> m; ebi::two_sat ts(n); for (int i = 0; i < m; i++) { int a, b, c; std::cin >> a >> b >> c; ts.add_clause(std::abs(a) - 1, a > 0, std::abs(b) - 1, b > 0); } bool flag = ts.satisfiable(); std::cout << "s " << (flag ? "SATISFIABLE" : "UNSATISFIABLE") << std::endl; if (flag) { std::cout << "v"; auto ans = ts.answer(); for (int i = 0; i < n; i++) { std::cout << " " << (ans[i] ? i + 1 : -(i + 1)); } std::cout << " 0\n"; } }
#line 1 "test/algorithm/Two_Sat.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/two_sat" #line 2 "algorithm/two_sat.hpp" #include <cassert> #line 2 "graph/scc_graph.hpp" #include <algorithm> #include <vector> #line 2 "data_structure/simple_csr.hpp" #include <ranges> #include <utility> #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 2 "graph/base.hpp" #line 4 "graph/base.hpp" #include <iostream> #line 7 "graph/base.hpp" #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 8 "graph/scc_graph.hpp" namespace ebi { struct scc_graph { private: std::vector<std::pair<int, int>> edges, redges; simple_csr<int> g, rg; int n, k; std::vector<int> vs, cmp; std::vector<bool> seen; void dfs(int v) { seen[v] = true; for (auto &nv : g[v]) { if (!seen[nv]) dfs(nv); } vs.emplace_back(v); } void rdfs(int v) { cmp[v] = k; for (auto nv : rg[v]) { if (cmp[nv] < 0) { rdfs(nv); } } } public: scc_graph(int n_) : n(n_) {} void add_edge(int from, int to) { edges.emplace_back(from, to); redges.emplace_back(to, from); } std::vector<std::vector<int>> scc() { g = simple_csr<int>(n, edges); rg = simple_csr<int>(n, redges); edges.clear(); redges.clear(); seen.assign(n, false); for (int i = 0; i < n; i++) { if (!seen[i]) { dfs(i); } } std::reverse(vs.begin(), vs.end()); cmp.assign(n, -1); k = 0; for (auto &v : vs) { if (cmp[v] < 0) { rdfs(v); k++; } } std::vector<std::vector<int>> res(k); for (int i = 0; i < n; i++) { res[cmp[i]].emplace_back(i); } return res; } std::vector<int> scc_id() { return cmp; } bool same(int u, int v) { return cmp[u] == cmp[v]; } Graph<int> create_graph() { std::vector<std::pair<int, int>> es; for (int i = 0; i < n; i++) { int v = cmp[i]; for (auto to : g[i]) { int nv = cmp[to]; if (v == nv) continue; es.emplace_back(v, nv); } } std::sort(es.begin(), es.end()); es.erase(std::unique(es.begin(), es.end()), es.end()); Graph<int> t(k); for (auto [v, nv] : es) { t.add_edge(v, nv, 1); } t.build(); return t; } }; } // namespace ebi #line 6 "algorithm/two_sat.hpp" namespace ebi { struct two_sat { public: two_sat(int _n) : n(_n), scc(2 * n) {} void add_clause(int p, bool _p, int q, bool _q) { assert(0 <= p && p < n); assert(0 <= q && q < n); scc.add_edge(2 * p + (_p ? 1 : 0), 2 * q + (_q ? 0 : 1)); scc.add_edge(2 * q + (_q ? 1 : 0), 2 * p + (_p ? 0 : 1)); } bool satisfiable() { scc.scc(); std::vector<int> id = scc.scc_id(); _answer.resize(n); for (int i = 0; i < n; i++) { if (id[2 * i] == id[2 * i + 1]) { return false; } _answer[i] = id[2 * i] > id[2 * i + 1]; } return true; } std::vector<bool> answer() { return _answer; } private: int n; scc_graph scc; std::vector<bool> _answer; }; } // namespace ebi #line 4 "test/algorithm/Two_Sat.test.cpp" #line 6 "test/algorithm/Two_Sat.test.cpp" int main() { char p; std::string cnf; std::cin >> p >> cnf; int n, m; std::cin >> n >> m; ebi::two_sat ts(n); for (int i = 0; i < m; i++) { int a, b, c; std::cin >> a >> b >> c; ts.add_clause(std::abs(a) - 1, a > 0, std::abs(b) - 1, b > 0); } bool flag = ts.satisfiable(); std::cout << "s " << (flag ? "SATISFIABLE" : "UNSATISFIABLE") << std::endl; if (flag) { std::cout << "v"; auto ans = ts.answer(); for (int i = 0; i < n; i++) { std::cout << " " << (ans[i] ? i + 1 : -(i + 1)); } std::cout << " 0\n"; } }