sotanishy's code snippets for competitive programming
View the Project on GitHub sotanishy/cp-library-cpp
#include "sat/twosat.hpp"
2-SAT は,節内のリテラル数が高々2つであるような乗法標準形の論理式に対する充足可能性問題 (SAT) である.
節 $(u \lor v)$ が $(\lnot u \rightarrow v) \land (\lnot v \rightarrow u)$ と同値であることを利用すると,2-SAT を強連結成分分解を用いて解くことができる.
vector<bool> two_sat(int n, vector<tuple<int, bool, int, bool>> clauses)
{i, f, j, g}
#pragma once #include <vector> #include "../graph/scc.hpp" std::vector<bool> two_sat( int n, const std::vector<std::tuple<int, bool, int, bool>>& clauses) { std::vector<std::vector<int>> G(2 * n); std::vector<bool> val(n); for (auto& [i, f, j, g] : clauses) { G[n * f + i].push_back(n * (!g) + j); G[n * g + j].push_back(n * (!f) + i); } auto comp = scc(G); for (int i = 0; i < n; ++i) { if (comp[i] == comp[n + i]) { // not satisfiable return {}; } val[i] = comp[i] > comp[n + i]; } return val; }
#line 2 "sat/twosat.hpp" #include <vector> #line 2 "graph/scc.hpp" #include <algorithm> #include <ranges> #line 5 "graph/scc.hpp" std::vector<int> scc(const std::vector<std::vector<int>>& G) { const int n = G.size(); std::vector<std::vector<int>> G_rev(n); for (int u = 0; u < n; ++u) { for (int v : G[u]) G_rev[v].push_back(u); } std::vector<int> comp(n, -1), order(n); std::vector<bool> visited(n); auto dfs = [&](const auto& dfs, int u) -> void { if (visited[u]) return; visited[u] = true; for (int v : G[u]) dfs(dfs, v); order.push_back(u); }; for (int v = 0; v < n; ++v) dfs(dfs, v); int c = 0; auto rdfs = [&](const auto& rdfs, int u, int c) -> void { if (comp[u] != -1) return; comp[u] = c; for (int v : G_rev[u]) rdfs(rdfs, v, c); }; for (int v : order | std::views::reverse) { if (comp[v] == -1) rdfs(rdfs, v, c++); } return comp; } std::vector<std::vector<int>> contract(const std::vector<std::vector<int>>& G, const std::vector<int>& comp) { const int n = *std::ranges::max_element(comp) + 1; std::vector<std::vector<int>> G2(n); for (int i = 0; i < (int)G.size(); ++i) { for (int j : G[i]) { if (comp[i] != comp[j]) { G2[comp[i]].push_back(comp[j]); } } } for (int i = 0; i < n; ++i) { std::ranges::sort(G2[i]); G2[i].erase(std::ranges::unique(G2[i]).begin(), G2[i].end()); } return G2; } #line 5 "sat/twosat.hpp" std::vector<bool> two_sat( int n, const std::vector<std::tuple<int, bool, int, bool>>& clauses) { std::vector<std::vector<int>> G(2 * n); std::vector<bool> val(n); for (auto& [i, f, j, g] : clauses) { G[n * f + i].push_back(n * (!g) + j); G[n * g + j].push_back(n * (!f) + i); } auto comp = scc(G); for (int i = 0; i < n; ++i) { if (comp[i] == comp[n + i]) { // not satisfiable return {}; } val[i] = comp[i] > comp[n + i]; } return val; }