Luzhiled's Library

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:heavy_check_mark: test/verify/yosupo-two-sat.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/two_sat

#include "../../template/template.hpp"

#include "../../other/scanner.hpp"
#include "../../other/printer.hpp"

#include "../../graph/others/two-satisfiability.hpp"

int main() {
  Scanner input(stdin);
  Printer output(stdout);

  string s;
  int N, M;
  input.read(s, s, N, M);
  TwoSatisfiability two(N);
  for(int i = 0; i < M; i++) {
    int a, b, c;
    input.read(a, b, c);
    if(a < 0) a = two.rev(-a - 1);
    else --a;
    if(b < 0) b = two.rev(-b - 1);
    else --b;
    two.add_or(a, b);
  }
  auto ret = two.solve();
  if(ret.empty()) {
    output.writeln("s UNSATISFIABLE");
  } else {
    output.writeln("s SATISFIABLE");
    output.write("v ");
    for(size_t i = 0; i < ret.size(); i++) {
      if(ret[i]) ret[i] = i + 1;
      else ret[i] = -i - 1;
    }
    output.write(ret);
    output.writeln(" 0");
  }
}

#line 1 "test/verify/yosupo-two-sat.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/two_sat

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-two-sat.test.cpp"

#line 1 "other/scanner.hpp"
/**
 * @brief Scanner(高速入力)
 */
struct Scanner {
 public:
  explicit Scanner(FILE *fp) : fp(fp) {}

  template <typename T, typename... E>
  void read(T &t, E &...e) {
    read_single(t);
    read(e...);
  }

 private:
  static constexpr size_t line_size = 1 << 16;
  static constexpr size_t int_digits = 20;
  char line[line_size + 1] = {};
  FILE *fp = nullptr;
  char *st = line;
  char *ed = line;

  void read() {}

  static inline bool is_space(char c) { return c <= ' '; }

  void reread() {
    ptrdiff_t len = ed - st;
    memmove(line, st, len);
    char *tmp = line + len;
    ed = tmp + fread(tmp, 1, line_size - len, fp);
    *ed = 0;
    st = line;
  }

  void skip_space() {
    while (true) {
      if (st == ed) reread();
      while (*st && is_space(*st)) ++st;
      if (st != ed) return;
    }
  }

  template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
  void read_single(T &s) {
    skip_space();
    if (st + int_digits >= ed) reread();
    bool neg = false;
    if (is_signed<T>::value && *st == '-') {
      neg = true;
      ++st;
    }
    typename make_unsigned<T>::type y = *st++ - '0';
    while (*st >= '0') {
      y = 10 * y + *st++ - '0';
    }
    s = (neg ? -y : y);
  }

  template <typename T, enable_if_t<is_same<T, string>::value, int> = 0>
  void read_single(T &s) {
    s = "";
    skip_space();
    while (true) {
      char *base = st;
      while (*st && !is_space(*st)) ++st;
      s += string(base, st);
      if (st != ed) return;
      reread();
    }
  }

  template <typename T>
  void read_single(vector<T> &s) {
    for (auto &d : s) read(d);
  }
};
#line 1 "other/printer.hpp"
/**
 * @brief Printer(高速出力)
 */
struct Printer {
 public:
  explicit Printer(FILE *fp) : fp(fp) {}

  ~Printer() { flush(); }

  template <bool f = false, typename T, typename... E>
  void write(const T &t, const E &...e) {
    if (f) write_single(' ');
    write_single(t);
    write<true>(e...);
  }

  template <typename... T>
  void writeln(const T &...t) {
    write(t...);
    write_single('\n');
  }

  void flush() {
    fwrite(line, 1, st - line, fp);
    st = line;
  }

 private:
  FILE *fp = nullptr;
  static constexpr size_t line_size = 1 << 16;
  static constexpr size_t int_digits = 20;
  char line[line_size + 1] = {};
  char *st = line;

  template <bool f = false>
  void write() {}

  void write_single(const char &t) {
    if (st + 1 >= line + line_size) flush();
    *st++ = t;
  }

  template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
  void write_single(T s) {
    if (st + int_digits >= line + line_size) flush();
    st += to_chars(st, st + int_digits, s).ptr - st;
  }

  void write_single(const string &s) {
    for (auto &c : s) write_single(c);
  }

  void write_single(const char *s) {
    while (*s != 0) write_single(*s++);
  }

  template <typename T>
  void write_single(const vector<T> &s) {
    for (size_t i = 0; i < s.size(); i++) {
      if (i) write_single(' ');
      write_single(s[i]);
    }
  }
};
#line 7 "test/verify/yosupo-two-sat.test.cpp"

#line 2 "graph/others/two-satisfiability.hpp"

#line 2 "graph/connected-components/strongly-connected-components.hpp"

#line 2 "graph/graph-template.hpp"

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);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/connected-components/strongly-connected-components.hpp"

template <typename T = int>
struct StronglyConnectedComponents : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<int> comp;
  Graph<T> dag;
  vector<vector<int> > group;

  void build() {
    rg = Graph<T>(g.size());
    for (size_t 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);
    for (size_t 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 (size_t 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 (size_t 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;
  Graph<T> rg;

  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 4 "graph/others/two-satisfiability.hpp"

/**
 * @brief Two Satisfiability(2-SAT)
 *
 */
struct TwoSatisfiability : StronglyConnectedComponents<bool> {
 public:
  using StronglyConnectedComponents<bool>::g;
  using StronglyConnectedComponents<bool>::comp;
  using StronglyConnectedComponents<bool>::add_edge;
  size_t sz;

  explicit TwoSatisfiability(size_t v)
      : StronglyConnectedComponents<bool>(v + v), sz(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 >= (int)sz) return x - sz;
    return x + sz;
  }

  vector<int> solve() {
    StronglyConnectedComponents<bool>::build();
    vector<int> ret(sz);
    for (size_t i = 0; i < sz; i++) {
      if (comp[i] == comp[rev(i)]) return {};
      ret[i] = comp[i] > comp[rev(i)];
    }
    return ret;
  }
};
#line 9 "test/verify/yosupo-two-sat.test.cpp"

int main() {
  Scanner input(stdin);
  Printer output(stdout);

  string s;
  int N, M;
  input.read(s, s, N, M);
  TwoSatisfiability two(N);
  for(int i = 0; i < M; i++) {
    int a, b, c;
    input.read(a, b, c);
    if(a < 0) a = two.rev(-a - 1);
    else --a;
    if(b < 0) b = two.rev(-b - 1);
    else --b;
    two.add_or(a, b);
  }
  auto ret = two.solve();
  if(ret.empty()) {
    output.writeln("s UNSATISFIABLE");
  } else {
    output.writeln("s SATISFIABLE");
    output.write("v ");
    for(size_t i = 0; i < ret.size(); i++) {
      if(ret[i]) ret[i] = i + 1;
      else ret[i] = -i - 1;
    }
    output.write(ret);
    output.writeln(" 0");
  }
}

Test cases

Env Name Status Elapsed Memory
g++ cycle_unsat_00 :heavy_check_mark: AC 183 ms 159 MB
g++ cycle_unsat_01 :heavy_check_mark: AC 187 ms 162 MB
g++ example_00 :heavy_check_mark: AC 5 ms 4 MB
g++ example_01 :heavy_check_mark: AC 5 ms 4 MB
g++ max_random_00 :heavy_check_mark: AC 748 ms 222 MB
g++ max_random_01 :heavy_check_mark: AC 761 ms 222 MB
g++ max_random_02 :heavy_check_mark: AC 837 ms 222 MB
g++ max_random_03 :heavy_check_mark: AC 810 ms 222 MB
g++ max_random_04 :heavy_check_mark: AC 836 ms 222 MB
g++ random_00 :heavy_check_mark: AC 746 ms 177 MB
g++ random_01 :heavy_check_mark: AC 660 ms 199 MB
g++ random_02 :heavy_check_mark: AC 187 ms 52 MB
g++ random_03 :heavy_check_mark: AC 110 ms 128 MB
g++ random_04 :heavy_check_mark: AC 167 ms 100 MB
clang++ cycle_unsat_00 :heavy_check_mark: AC 234 ms 198 MB
clang++ cycle_unsat_01 :heavy_check_mark: AC 242 ms 206 MB
clang++ example_00 :heavy_check_mark: AC 5 ms 4 MB
clang++ example_01 :heavy_check_mark: AC 5 ms 4 MB
clang++ max_random_00 :heavy_check_mark: AC 871 ms 222 MB
clang++ max_random_01 :heavy_check_mark: AC 917 ms 222 MB
clang++ max_random_02 :heavy_check_mark: AC 875 ms 222 MB
clang++ max_random_03 :heavy_check_mark: AC 888 ms 222 MB
clang++ max_random_04 :heavy_check_mark: AC 815 ms 222 MB
clang++ random_00 :heavy_check_mark: AC 713 ms 177 MB
clang++ random_01 :heavy_check_mark: AC 638 ms 199 MB
clang++ random_02 :heavy_check_mark: AC 182 ms 56 MB
clang++ random_03 :heavy_check_mark: AC 102 ms 128 MB
clang++ random_04 :heavy_check_mark: AC 142 ms 99 MB
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