graph/2sat.hpp

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• Last update: 2021-09-12 23:20:08-04:00
• Include: #include "graph/2sat.hpp"

Depends on

• template.hpp

Verified with

• tests/graph/2sat.test.cpp

Code

#pragma once
#include "../template.hpp"

struct TwoSat {
    int N, cord, ccomp;
    vector<int> ord, low, instk, stk, comp;
    vector<vector<int>> g;
    void init(int N0) {
        N = N0; cord = ccomp = 0;
        g.assign(N*2+1, vector<int>());
        ord.assign(N*2+1, 0);
        low.assign(N*2+1, 0);
        instk.assign(N*2+1, 0);
        comp.assign(N*2+1, 0);
        stk.clear();
    }
    void addEdge(int a, int b) {
        if (a < 0) a = N-a;
        if (b < 0) b = N-b;
        g[a].push_back(b);
    }
    void addOr(int a, int b) {
        addEdge(-a, b);
        addEdge(-b, a);
    }
    void tarjan(int c) {
        ord[c] = low[c] = ++cord;
        instk[c] = true; stk.push_back(c);
        for (auto to : g[c]) {
            if (!ord[to]) {
                tarjan(to);
                low[c] = min(low[c], low[to]);
            }
            else if (instk[to])
                low[c] = min(low[c], ord[to]);
        }

        if (low[c] == ord[c]) {
            int u, cc = ++ccomp;
            do {
                u = stk.back(); stk.pop_back(); instk[u] = false;
                comp[u] = cc;
            } while (u != c);
        }
    }
    vector<int> solve() {
        for (auto i = 1; i <= 2*N; i++)
            if (!ord[i])
                tarjan(i);
        for (auto i = 1; i <= N; i++)
            if (comp[i] == comp[i+N])
                return vector<int>(N+1, -1);
        vector<int> res(N+1);
        for (auto i = 1; i <= N; i++)
            res[i] = comp[i] < comp[i+N]; // 1 > 0
        return res;
    }
};

#line 2 "template.hpp"
#include <bits/stdc++.h>
#define DEBUG 1
using namespace std;

// Defines
#define fs first
#define sn second
#define pb push_back
#define eb emplace_back
#define mpr make_pair
#define mtp make_tuple
#define all(x) (x).begin(), (x).end()
// Basic type definitions
#if __cplusplus == 201703L // CPP17 only things
template <typename T> using opt_ref = optional<reference_wrapper<T>>; // for some templates
#endif
using ll = long long; using ull = unsigned long long; using ld = long double;
using pii = pair<int, int>; using pll = pair<long long, long long>;
#ifdef __GNUG__
// PBDS order statistic tree
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <typename T, class comp = less<T>> using os_tree = tree<T, null_type, comp, rb_tree_tag, tree_order_statistics_node_update>;
template <typename K, typename V, class comp = less<K>> using treemap = tree<K, V, comp, rb_tree_tag, tree_order_statistics_node_update>;
// HashSet
#include <ext/pb_ds/assoc_container.hpp>
template <typename T, class Hash> using hashset = gp_hash_table<T, null_type, Hash>;
template <typename K, typename V, class Hash> using hashmap = gp_hash_table<K, V, Hash>;
const ll RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash { ll operator()(ll x) const { return x ^ RANDOM; } };
#endif
// More utilities
int SZ(string &v) { return v.length(); }
template <typename C> int SZ(C &v) { return v.size(); }
template <typename C> void UNIQUE(vector<C> &v) { sort(v.begin(), v.end()); v.resize(unique(v.begin(), v.end()) - v.begin()); }
template <typename T, typename U> void maxa(T &a, U b) { a = max(a, b); }
template <typename T, typename U> void mina(T &a, U b) { a = min(a, b); }
const ll INF = 0x3f3f3f3f, LLINF = 0x3f3f3f3f3f3f3f3f;
#line 3 "graph/2sat.hpp"

struct TwoSat {
    int N, cord, ccomp;
    vector<int> ord, low, instk, stk, comp;
    vector<vector<int>> g;
    void init(int N0) {
        N = N0; cord = ccomp = 0;
        g.assign(N*2+1, vector<int>());
        ord.assign(N*2+1, 0);
        low.assign(N*2+1, 0);
        instk.assign(N*2+1, 0);
        comp.assign(N*2+1, 0);
        stk.clear();
    }
    void addEdge(int a, int b) {
        if (a < 0) a = N-a;
        if (b < 0) b = N-b;
        g[a].push_back(b);
    }
    void addOr(int a, int b) {
        addEdge(-a, b);
        addEdge(-b, a);
    }
    void tarjan(int c) {
        ord[c] = low[c] = ++cord;
        instk[c] = true; stk.push_back(c);
        for (auto to : g[c]) {
            if (!ord[to]) {
                tarjan(to);
                low[c] = min(low[c], low[to]);
            }
            else if (instk[to])
                low[c] = min(low[c], ord[to]);
        }

        if (low[c] == ord[c]) {
            int u, cc = ++ccomp;
            do {
                u = stk.back(); stk.pop_back(); instk[u] = false;
                comp[u] = cc;
            } while (u != c);
        }
    }
    vector<int> solve() {
        for (auto i = 1; i <= 2*N; i++)
            if (!ord[i])
                tarjan(i);
        for (auto i = 1; i <= N; i++)
            if (comp[i] == comp[i+N])
                return vector<int>(N+1, -1);
        vector<int> res(N+1);
        for (auto i = 1; i <= N; i++)
            res[i] = comp[i] < comp[i+N]; // 1 > 0
        return res;
    }
};

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