verify/yosupo-two_sat.test.cpp

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Last update: 2023-09-23 21:29:16+09:00
Problem: https://judge.yosupo.jp/problem/two_sat

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/two_sat"
#include "library/template/template.cpp"
// library
#include "library/graph/connected-components/TwoSat.cpp"
int main() {
    string p, cnf;
    int n, m;
    cin >> p >> cnf >> n >> m;
    TwoSat ts(n);
    rep(i, m) {
        int u, v, z;
        cin >> u >> v >> z;
        if (u < 0)
            u = ts.rev(-u - 1);
        else
            u--;
        if (v < 0)
            v = ts.rev(-v - 1);
        else
            v--;
        ts.add_or(u, v);
    }
    auto ret = ts.solve();
    if (ret.size()) {
        cout << "s SATISFIABLE" << endl;
        cout << "v ";
        rep(i, n) cout << (ret[i] ? i + 1 : -i - 1) << ' ';
        cout << 0 << ' ' << endl;
    } else {
        cout << "s UNSATISFIABLE" << endl;
    }
}

#line 1 "verify/yosupo-two_sat.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/two_sat"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (auto &e : v)
        cout << e << " ";
    cout << endl;
    return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
    for (auto &i : a)
        scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n)
{
    T ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j)
         { return a[i] < a[j]; });
    return id;
}
long long xor64(long long range) {
    static uint64_t x = 88172645463325252ULL;
    x ^= x << 13;
    x ^= x >> 7;
    return (x ^= x << 17) % range;
}
struct Timer
{
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap()
    {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
template <typename T = int>
struct Edge
{
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph
{
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    void add_directed_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es++);
    }

    void add_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false)
    {
        for (int i = 0; i < M; i++)
        {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted)
                cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};

/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 3 "verify/yosupo-two_sat.test.cpp"
// library
#line 2 "library/graph/connected-components/StronglyConnectedComponents.cpp"

/**
 * @brief Strongly Connected Components
 * @arg int: type of weight
 * @docs docs/StronglyConnectedComponents
 */
#line 9 "library/graph/connected-components/StronglyConnectedComponents.cpp"
template <typename T = int>
struct StronglyConnectedComponents : Graph<T>
{
public:
    using Graph<T>::Graph;
    using Graph<T>::g;
    vector<int> comp;          // id of scc
    Graph<T> dag;              // DAG
    vector<vector<int>> group; // lists of each scc

    void build()
    {
        rg = Graph<T>(g.size());
        // add reversed edges
        for (int i = 0; i < g.size(); i++)
        {
            for (auto &e : g[i])
            {
                rg.add_directed_edge(e.to, e.from, e.cost);
            }
        }
        comp.assign(g.size(), -1);
        used.assign(g.size(), 0);
        // dfs for (not reversed) graph
        for (int i = 0; i < g.size(); i++)
            dfs(i);
        reverse(begin(order), end(order));
        int ptr = 0;
        for (int i : order)
            if (comp[i] == -1)
                rdfs(i, ptr), ptr++;
        dag = Graph<T>(ptr);
        for (int i = 0; i < g.size(); i++)
        {
            for (auto &e : g[i])
            {
                int x = comp[e.from], y = comp[e.to];
                if (x == y)
                    continue;
                dag.add_directed_edge(x, y, e.cost);
            }
        }
        group.resize(ptr);
        for (int i = 0; i < g.size(); i++)
        {
            group[comp[i]].emplace_back(i);
        }
    }

    int operator[](int k) const { return comp[k]; }

private:
    vector<int> order, used; // order:post order
    Graph<T> rg;             // reversed graph

    void dfs(int idx)
    {
        if (exchange(used[idx], true))
            return;
        for (auto &to : g[idx])
            dfs(to);
        order.push_back(idx);
    }

    void rdfs(int idx, int cnt)
    {
        if (comp[idx] != -1)
            return;
        comp[idx] = cnt;
        for (auto &to : rg.g[idx])
            rdfs(to, cnt);
    }
};
#line 2 "library/graph/connected-components/TwoSat.cpp"
/**
 * @brief 2-SAT
 * @docs docs/TwoSat.md
 */
struct TwoSat : StronglyConnectedComponents<bool>
{
public:
    using StronglyConnectedComponents<bool>::g;
    using StronglyConnectedComponents<bool>::comp;
    using StronglyConnectedComponents<bool>::add_edge;
    int sz;

    explicit TwoSat(int v)
        : sz(v), StronglyConnectedComponents<bool>(v + v) {}

    void add_if(int u, int v)
    {
        // u -> v <=> !v -> !u
        add_directed_edge(u, v);
        add_directed_edge(rev(v), rev(u));
    }

    void add_or(int u, int v)
    {
        // u or v <=> !u -> v
        add_if(rev(u), v);
    }

    void add_nand(int u, int v)
    {
        // u nand v <=> u -> !v
        add_if(u, rev(v));
    }

    void set_true(int u)
    {
        // u <=> !u -> u
        add_directed_edge(rev(u), u);
    }

    void set_false(int u)
    {
        // !u <=> u -> !u
        add_directed_edge(u, rev(u));
    }

    inline int rev(int x)
    {
        if (x >= sz)
            return x - sz;
        return x + sz;
    }

    vector<int> solve()
    {
        StronglyConnectedComponents<bool>::build();
        vector<int> ret(sz);
        for (int i = 0; i < sz; i++)
        {
            if (comp[i] == comp[rev(i)])
                return {};
            ret[i] = comp[i] > comp[rev(i)];
        }
        return ret;
    }
};
#line 5 "verify/yosupo-two_sat.test.cpp"
int main() {
    string p, cnf;
    int n, m;
    cin >> p >> cnf >> n >> m;
    TwoSat ts(n);
    rep(i, m) {
        int u, v, z;
        cin >> u >> v >> z;
        if (u < 0)
            u = ts.rev(-u - 1);
        else
            u--;
        if (v < 0)
            v = ts.rev(-v - 1);
        else
            v--;
        ts.add_or(u, v);
    }
    auto ret = ts.solve();
    if (ret.size()) {
        cout << "s SATISFIABLE" << endl;
        cout << "v ";
        rep(i, n) cout << (ret[i] ? i + 1 : -i - 1) << ' ';
        cout << 0 << ' ' << endl;
    } else {
        cout << "s UNSATISFIABLE" << endl;
    }
}