test/two_sat.test.cpp

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Last update: 2024-07-28 21:04:51+08:00
Problem: https://judge.yosupo.jp/problem/two_sat

Depends on

Code

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

#include "../default/t.cpp"
#include "../graph/2sat.cpp"

int main() {
  ios::sync_with_stdio(false), cin.tie(0);

  string p, cnf; cin >> p >> cnf;
  int n, m; cin >> n >> m;

  TwoSat ts(n);
  while(m--) {
    int a, b, c; cin >> a >> b >> c;
    a = (a > 0 ? a - 1 : ~(-(a + 1)));
    b = (b > 0 ? b - 1 : ~(-(b + 1)));
    ts.either(a, b);
  }

  if (ts.solve()) {
    cout << "s SATISFIABLE\n";
    cout << "v ";
    for(int i = 0; i < n; i++)
      cout << (ts.values[i] ? i + 1 : -(i + 1)) << ' ';
    cout << 0 << '\n';
  } else {
    cout << "s UNSATISFIABLE\n";
  }

  return 0;
}

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

#line 1 "default/t.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "graph/2sat.cpp"
//source: KACTL

/**
 * Author: Emil Lenngren, Simon Lindholm
 * Date: 2011-11-29
 * License: CC0
 * Source: folklore
 * Description: Calculates a valid assignment to boolean variables a, b, c,... to a 2-SAT problem, so that an expression of the type $(a\|\|b)\&\&(!a\|\|c)\&\&(d\|\|!b)\&\&...$ becomes true, or reports that it is unsatisfiable.
 * Negated variables are represented by bit-inversions (\texttt{\tilde{}x}).
 * Usage:
 *  TwoSat ts(number of boolean variables);
 *  ts.either(0, \tilde3); // Var 0 is true or var 3 is false
 *  ts.setValue(2); // Var 2 is true
 *  ts.atMostOne({0,\tilde1,2}); // <= 1 of vars 0, \tilde1 and 2 are true
 *  ts.solve(); // Returns true iff it is solvable
 *  ts.values[0..N-1] holds the assigned values to the vars
 * Time: O(N+E), where N is the number of boolean variables, and E is the number of clauses.
 * Status: stress-tested
 */

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define sz(x) (int)(x).size()
using vi = vector<int>;

struct TwoSat {
	int N;
	vector<vi> gr;
	vi values; // 0 = false, 1 = true

	TwoSat(int n = 0) : N(n), gr(2*n) {}

	int addVar() { // (optional)
		gr.emplace_back();
		gr.emplace_back();
		return N++;
	}

	void either(int f, int j) {
		f = max(2*f, -1-2*f);
		j = max(2*j, -1-2*j);
		gr[f].push_back(j^1);
		gr[j].push_back(f^1);
	}
	void setValue(int x) { either(x, x); }

	void atMostOne(const vi& li) { // (optional)
		if (sz(li) <= 1) return;
		int cur = ~li[0];
		rep(i,2,sz(li)) {
			int next = addVar();
			either(cur, ~li[i]);
			either(cur, next);
			either(~li[i], next);
			cur = ~next;
		}
		either(cur, ~li[1]);
	}

	vi val, comp, z; int time = 0;
	int dfs(int i) {
		int low = val[i] = ++time, x; z.push_back(i);
		for(int e : gr[i]) if (!comp[e])
			low = min(low, val[e] ?: dfs(e));
		if (low == val[i]) do {
			x = z.back(); z.pop_back();
			comp[x] = low;
			if (values[x>>1] == -1)
				values[x>>1] = x&1;
		} while (x != i);
		return val[i] = low;
	}

	bool solve() {
		values.assign(N, -1);
		val.assign(2*N, 0); comp = val;
		rep(i,0,2*N) if (!comp[i]) dfs(i);
		rep(i,0,N) if (comp[2*i] == comp[2*i+1]) return 0;
		return 1;
	}
};
#line 5 "test/two_sat.test.cpp"

int main() {
  ios::sync_with_stdio(false), cin.tie(0);

  string p, cnf; cin >> p >> cnf;
  int n, m; cin >> n >> m;

  TwoSat ts(n);
  while(m--) {
    int a, b, c; cin >> a >> b >> c;
    a = (a > 0 ? a - 1 : ~(-(a + 1)));
    b = (b > 0 ? b - 1 : ~(-(b + 1)));
    ts.either(a, b);
  }

  if (ts.solve()) {
    cout << "s SATISFIABLE\n";
    cout << "v ";
    for(int i = 0; i < n; i++)
      cout << (ts.values[i] ? i + 1 : -(i + 1)) << ' ';
    cout << 0 << '\n';
  } else {
    cout << "s UNSATISFIABLE\n";
  }

  return 0;
}