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#define PROBLEM "https://judge.yosupo.jp/problem/two_sat" #include <bits/stdc++.h> using namespace std; #include "../2sat.h" #define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i) int32_t main() { ios::sync_with_stdio(0); cin.tie(0); string wtf; cin >> wtf >> wtf; int n, m; cin >> n >> m; TwoSatSolver solver(n); while (m--) { int x, y; cin >> x >> y >> wtf; solver.x_or_y_constraint(x > 0, std::abs(x) - 1, y > 0, std::abs(y) - 1); } auto [has_solution, sol] = solver.solve(); if (has_solution) { cout << "s SATISFIABLE" << endl; cout << "v "; REP(i,n) { if (sol[i]) cout << i+1; else cout << "-" << (i+1); cout << ' '; } cout << 0 << endl; } else { cout << "s UNSATISFIABLE" << endl; } return 0; }
#line 1 "Graph/tests/two_sat.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/two_sat" #include <bits/stdc++.h> using namespace std; #line 1 "Graph/2sat.h" // For lexicographical min result: // - For each variable: check if it can be set to False // (by adding constraint i -> !i) // - If solver.solve() -> keep constraint i -> !i // - Otherwise, remove constraint i -> !i, and add !i -> i to force it to True // See https://oj.vnoi.info/problem/icpc21_mt_i // Variables: 0 -> n-1 // Tested: // - https://judge.yosupo.jp/problem/two_sat // - https://oj.vnoi.info/problem/twosat // - https://oj.vnoi.info/problem/elect // - https://open.kattis.com/problems/cleaningpipes // - https://oj.vnoi.info/problem/icpc21_mt_i // - https://cses.fi/problemset/task/1684/ #line 1 "Graph/DfsTree/StronglyConnected.h" // Index from 0 // Usage: // DirectedDfs tree; // Now you can use tree.scc // // Note: reverse(tree.scc) is topo sorted // // Tested: // - (requires scc to be topo sorted) https://judge.yosupo.jp/problem/scc // - https://cses.fi/problemset/task/1686/ // - (edges have costs) https://oj.vnoi.info/problem/bedao_g16_b struct DirectedDfs { vector<vector<int>> g; int n; vector<int> num, low, current, S; int counter; vector<int> comp_ids; vector< vector<int> > scc; DirectedDfs(const vector<vector<int>>& _g) : g(_g), n(g.size()), num(n, -1), low(n, 0), current(n, 0), counter(0), comp_ids(n, -1) { for (int i = 0; i < n; i++) { if (num[i] == -1) dfs(i); } } void dfs(int u) { low[u] = num[u] = counter++; S.push_back(u); current[u] = 1; for (auto v : g[u]) { if (num[v] == -1) dfs(v); if (current[v]) low[u] = min(low[u], low[v]); } if (low[u] == num[u]) { scc.push_back(vector<int>()); while (1) { int v = S.back(); S.pop_back(); current[v] = 0; scc.back().push_back(v); comp_ids[v] = ((int) scc.size()) - 1; if (u == v) break; } } } // build DAG of strongly connected components // Returns: adjacency list of DAG std::vector<std::vector<int>> build_scc_dag() { std::vector<std::vector<int>> dag(scc.size()); for (int u = 0; u < n; u++) { int x = comp_ids[u]; for (int v : g[u]) { int y = comp_ids[v]; if (x != y) { dag[x].push_back(y); } } } return dag; } }; #line 17 "Graph/2sat.h" struct TwoSatSolver { TwoSatSolver(int _n_vars) : n_vars(_n_vars), g(2*n_vars) {} void x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) { assert(x >= 0 && x < n_vars); assert(y >= 0 && y < n_vars); if (!is_x_true) x += n_vars; if (!is_y_true) y += n_vars; // x || y // !x -> y // !y -> x g[(x + n_vars) % (2*n_vars)].push_back(y); g[(y + n_vars) % (2*n_vars)].push_back(x); } // Returns: // If no solution -> returns {false, {}} // If has solution -> returns {true, solution} // where |solution| = n_vars, solution = true / false pair<bool, vector<bool>> solve() { DirectedDfs tree(g); vector<bool> solution(n_vars); for (int i = 0; i < n_vars; i++) { if (tree.comp_ids[i] == tree.comp_ids[i + n_vars]) { return {false, {}}; } // Note that reverse(tree.scc) is topo sorted solution[i] = tree.comp_ids[i] < tree.comp_ids[i + n_vars]; } return {true, solution}; } // number of variables int n_vars; // vertex 0 -> n_vars - 1: Ai is true // vertex n_vars -> 2*n_vars - 1: Ai is false vector<vector<int>> g; }; #line 7 "Graph/tests/two_sat.test.cpp" #define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i) int32_t main() { ios::sync_with_stdio(0); cin.tie(0); string wtf; cin >> wtf >> wtf; int n, m; cin >> n >> m; TwoSatSolver solver(n); while (m--) { int x, y; cin >> x >> y >> wtf; solver.x_or_y_constraint(x > 0, std::abs(x) - 1, y > 0, std::abs(y) - 1); } auto [has_solution, sol] = solver.solve(); if (has_solution) { cout << "s SATISFIABLE" << endl; cout << "v "; REP(i,n) { if (sol[i]) cout << i+1; else cout << "-" << (i+1); cout << ' '; } cout << 0 << endl; } else { cout << "s UNSATISFIABLE" << endl; } return 0; }