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#define PROBLEM "https://judge.yosupo.jp/problem/two_sat" #include <bits/stdc++.h> // clang-format off using Int = long long; #define REP_(i, a_, b_, a, b, ...) for (Int i = (a), lim##i = (b); i < lim##i; i++) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) struct SetupIO { SetupIO() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(13); } } setup_io; #ifndef dump #define dump(...) #endif // clang-format on /** * author: knshnb * created: Sat Jun 13 03:04:06 JST 2020 **/ #define CALL_FROM_TEST #include "../../src/Graph/TwoSat.hpp" #undef CALL_FROM_TEST signed main() { std::string _; Int n, m; std::cin >> _ >> _ >> n >> m; TwoSat sat(n); REP(i, m) { Int a, b; std::cin >> a >> b >> _; sat.add_condition(std::abs(a) - 1, a < 0, std::abs(b) - 1, b < 0); } if (!sat.run()) { std::cout << "s UNSATISFIABLE" << std::endl; } else { std::cout << "s SATISFIABLE" << std::endl << "v "; REP(i, n) std::cout << (sat.is_true(i) ? (i + 1) : -(i + 1)) << " "; std::cout << 0 << std::endl; } }
#line 1 "test/yosupo/two_sat.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/two_sat" #include <bits/stdc++.h> // clang-format off using Int = long long; #define REP_(i, a_, b_, a, b, ...) for (Int i = (a), lim##i = (b); i < lim##i; i++) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) struct SetupIO { SetupIO() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(13); } } setup_io; #ifndef dump #define dump(...) #endif // clang-format on /** * author: knshnb * created: Sat Jun 13 03:04:06 JST 2020 **/ #define CALL_FROM_TEST #line 1 "src/Graph/StronglyConnectedComponents.hpp" /// @docs src/Graph/StronglyConnectedComponents.md struct StronglyConnectedComponents { int n, size; // sizeはbuild()後に強連結成分の数を格納 std::vector<std::vector<int>> edge, redge; std::vector<int> belong_to; StronglyConnectedComponents(int n_) : n(n_), edge(n_), redge(n_) {} void add_edge(int u, int v) { assert(0 <= u && u < n && 0 <= v && v < n); edge[u].push_back(v); redge[v].push_back(u); } void build() { std::vector<int> ord; // post-order // 正方向の辺でdfs、post-orderをふる std::vector<bool> visited(n, false); auto dfs1 = [&](auto f, int v) -> void { if (visited[v]) return; visited[v] = true; for (int s : edge[v]) { f(f, s); } ord.push_back(v); }; for (int i = 0; i < n; i++) dfs1(dfs1, i); // post-order逆順にdfs、到達可能な同値類に分ける belong_to.assign(n, -1); int cur_group = 0; auto dfs2 = [&](auto f, int v) -> void { if (belong_to[v] != -1) return; belong_to[v] = cur_group; for (int s : redge[v]) { f(f, s); } }; std::reverse(ord.begin(), ord.end()); for (int i : ord) { if (belong_to[i] == -1) { dfs2(dfs2, i); cur_group++; } } size = cur_group; } bool has_loop() { build(); return size < n; } }; #line 2 "src/Graph/TwoSat.hpp" struct TwoSat { int n; StronglyConnectedComponents scc; // [0, n): x, [n, 2n): not x TwoSat(int n_) : n(n_), scc(2 * n_) {} // xの否定を表すindex int rev(int x) { return x < n ? x + n : x - n; } // (x \vee y)の条件を追加 void add_condition(int x, bool not_x, int y, bool not_y) { if (not_x) x = rev(x); if (not_y) y = rev(y); scc.add_edge(rev(x), y); scc.add_edge(rev(y), x); } bool run() { scc.build(); for (int x = 0; x < n; x++) { if (scc.belong_to[x] == scc.belong_to[rev(x)]) return false; } return true; } bool is_true(int x) { assert(0 <= x && x < n); return scc.belong_to[x] > scc.belong_to[rev(x)]; } }; #line 19 "test/yosupo/two_sat.test.cpp" #undef CALL_FROM_TEST signed main() { std::string _; Int n, m; std::cin >> _ >> _ >> n >> m; TwoSat sat(n); REP(i, m) { Int a, b; std::cin >> a >> b >> _; sat.add_condition(std::abs(a) - 1, a < 0, std::abs(b) - 1, b < 0); } if (!sat.run()) { std::cout << "s UNSATISFIABLE" << std::endl; } else { std::cout << "s SATISFIABLE" << std::endl << "v "; REP(i, n) std::cout << (sat.is_true(i) ? (i + 1) : -(i + 1)) << " "; std::cout << 0 << std::endl; } }