test/yosupo/two_sat.test.cpp

View this file on GitHub
Last update: 2024-01-08 13:32:33+09:00
Problem: https://judge.yosupo.jp/problem/two_sat

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/two_sat"

#include "../../sat/twosat.hpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
    string _p, _cnf;
    int N, M;
    cin >> _p >> _cnf >> N >> M;
    vector<tuple<int, bool, int, bool>> clauses;
    for (int i = 0; i < M; i++) {
        int a, b, _c;
        cin >> a >> b >> _c;
        clauses.push_back({abs(a) - 1, (a > 0), abs(b) - 1, (b > 0)});
    }
    auto ans = two_sat(N, clauses);
    if (!ans.empty()) {
        cout << "s SATISFIABLE\nv";
        for (int i = 0; i < N; i++) {
            cout << " " << (ans[i] ? 1 : -1) * (i + 1);
        }
        cout << " 0\n";
    } else {
        cout << "s UNSATISFIABLE\n";
    }
}

#line 1 "test/yosupo/two_sat.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/two_sat"

#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;
}
#line 4 "test/yosupo/two_sat.test.cpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
    string _p, _cnf;
    int N, M;
    cin >> _p >> _cnf >> N >> M;
    vector<tuple<int, bool, int, bool>> clauses;
    for (int i = 0; i < M; i++) {
        int a, b, _c;
        cin >> a >> b >> _c;
        clauses.push_back({abs(a) - 1, (a > 0), abs(b) - 1, (b > 0)});
    }
    auto ans = two_sat(N, clauses);
    if (!ans.empty()) {
        cout << "s SATISFIABLE\nv";
        for (int i = 0; i < N; i++) {
            cout << " " << (ans[i] ? 1 : -1) * (i + 1);
        }
        cout << " 0\n";
    } else {
        cout << "s UNSATISFIABLE\n";
    }
}