graph/test/two_sat.test.cpp

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Last update: 2022-08-25 19:58:27+09:00
Problem: https://judge.yosupo.jp/problem/two_sat

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Code

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

#define FAST_IO

#include "../../template/template.hpp"
#include "../../graph/two_sat.hpp"

int main() {
    string dummy;
    cin >> dummy >> dummy;
    i32 n, m;
    cin >> n >> m;
    TwoSat sat;
    Vec<TwoSat::Variable> vars = sat.add_variables(n);
    REP(ci, m) {
        i32 a, b;
        cin >> a >> b >> dummy;
        TwoSat::Variable a_ = (a > 0 ? vars[a - 1] : !vars[-a - 1]);
        TwoSat::Variable b_ = (b > 0 ? vars[b - 1] : !vars[-b - 1]);
        sat.add_clause(a_, b_);
    }
    optional<Vec<bool>> ans = sat.solve();
    if (ans.has_value()) {
        cout << "s SATISFIABLE\n";
        cout << "v ";
        REP(i, n) {
            bool b = (*ans)[vars[i].index()];
            cout << (b ? i + 1 : -i - 1) << ' ';
        }
        cout << "0\n";
    } else {
        cout << "s UNSATISFIABLE\n";
    }
}

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

#define FAST_IO

#line 1 "template/template.hpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
#line 2 "graph/two_sat.hpp"

#line 2 "graph/strongly_connected_components.hpp"

#line 4 "graph/strongly_connected_components.hpp"

template <typename G>
class StronglyConnectedComponents {    
    std::vector<int> comp_id;
    int comp_num;
    
public:
    StronglyConnectedComponents(const G &g) : comp_id(g.size(), -1), comp_num(0) {
        int now = 0;
        std::vector<int> vs;
        std::vector<int> ord(g.size(), -1);
        std::vector<int> low(g.size(), -1);
        
        const auto dfs = [&](const auto &dfs, int v) -> void {
            vs.push_back(v);
            ord[v] = now++;
            low[v] = ord[v];
            for (int u : g[v]) {
                if (comp_id[u] != -1) {
                    continue;
                }
                if (ord[u] == -1) {
                    dfs(dfs, u);
                }
                low[v] = std::min(low[v], low[u]);
            }
            if (low[v] == ord[v]) {
                while (true) {
                    int u = vs.back();
                    vs.pop_back();
                    comp_id[u] = comp_num;
                    if (u == v) {
                        break;
                    }
                }
                ++comp_num;
            }
        };
        
        for (int v = 0; v < (int) g.size(); ++v) {
            if (ord[v] == -1) {
                dfs(dfs, v);
            }
        }
        
        for (int v = 0; v < (int) g.size(); ++v) {
            comp_id[v] = comp_num - 1 - comp_id[v];
        }
    }
    
    int comps() const {
        return comp_num;
    }

    int operator[](int v) const {
        assert(v >= 0 && v < (int) comp_id.size());
        return comp_id[v];
    }

    std::vector<std::vector<int>> groups() const {
        std::vector<std::vector<int>> ret(comp_num);
        for (int v = 0; v < (int) comp_id.size(); ++v) {
            ret[comp_id[v]].push_back(v);
        }
        return ret;
    }
};

#line 4 "graph/two_sat.hpp"

#include <optional>

class TwoSat {
public:
    struct Variable {
    private:
        int idx;
            
        Variable(int i) : idx(i) {}
        
    public:
        Variable operator!() const noexcept {
            return Variable(idx ^ 1);
        }
        
        int index() const {
            return idx / 2;
        }
        
        friend class TwoSat;
    };
    
private:
    std::vector<std::vector<int>> graph;
    
public:
    TwoSat() : graph() {}
    
    TwoSat::Variable add_variable() {
        Variable var(graph.size());
        graph.resize(graph.size() + 2, std::vector<int>());
        return var;
    }
    
    std::vector<TwoSat::Variable> add_variables(int num) {
        std::vector<TwoSat::Variable> vars;
        vars.reserve(num);
        for (int i = 0; i < num; ++i) {
            vars.emplace_back(Variable((int) graph.size() + 2 * i));
        }
        graph.resize((int) graph.size() + 2 * num, std::vector<int>());
        return vars;
    }
    
    // x or y
    void add_clause(Variable x, Variable y) {
        graph[(!x).idx].push_back(y.idx);
        graph[(!y).idx].push_back(x.idx);
    }
    
    // x implies y
    void implies(Variable x, Variable y) {
        add_clause(!x, y);
    }
    
    void at_most_one(const std::vector<Variable> &vars) {
        if (vars.size() <= 1) {
            return;
        }
        std::vector<Variable> sum = add_variables((int) vars.size() - 1);
        for (int i = 0; i < (int) sum.size(); ++i) {
            implies(vars[i], sum[i]);
            implies(sum[i], !vars[i + 1]);
        }
        for (int i = 0; i < (int) sum.size() - 1; ++i) {
            implies(sum[i], sum[i + 1]);
        }
    }
    
    std::optional<std::vector<bool>> solve() {
        StronglyConnectedComponents scc(graph);
        std::vector<bool> ans(graph.size() / 2, false);
        for (int i = 0; i < (int) graph.size() / 2; ++i) {
            if (scc[2 * i] == scc[2 * i + 1]) {
                return std::nullopt;
            }
            if (scc[2 * i] > scc[2 * i + 1]) {
                ans[i] = true;
            }
        }
        return ans;
    }
};

#line 7 "graph/test/two_sat.test.cpp"

int main() {
    string dummy;
    cin >> dummy >> dummy;
    i32 n, m;
    cin >> n >> m;
    TwoSat sat;
    Vec<TwoSat::Variable> vars = sat.add_variables(n);
    REP(ci, m) {
        i32 a, b;
        cin >> a >> b >> dummy;
        TwoSat::Variable a_ = (a > 0 ? vars[a - 1] : !vars[-a - 1]);
        TwoSat::Variable b_ = (b > 0 ? vars[b - 1] : !vars[-b - 1]);
        sat.add_clause(a_, b_);
    }
    optional<Vec<bool>> ans = sat.solve();
    if (ans.has_value()) {
        cout << "s SATISFIABLE\n";
        cout << "v ";
        REP(i, n) {
            bool b = (*ans)[vars[i].index()];
            cout << (b ? i + 1 : -i - 1) << ' ';
        }
        cout << "0\n";
    } else {
        cout << "s UNSATISFIABLE\n";
    }
}