Graph/tests/two_sat.test.cpp

View this file on GitHub
Last update: 2024-06-02 18:23:02+08:00
Problem: https://judge.yosupo.jp/problem/two_sat

Depends on

Code

#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;
}