Two_Sat.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
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*/
 
# ifndef TWO_SAT_H
# define TWO_SAT_H
 
# include <ah-graph-concepts.H>
 
# include <cassert>
# include <utility>
# include <limits>
 
# include <ah-errors.H>
# include <tpl_array.H>
# include <tpl_dynArray.H>
# include <tpl_graph.H>
# include <tpl_dynSetTree.H>
# include <Tarjan.H>
 
namespace Aleph {
 
template <AlephGraph GT = List_Digraph<Graph_Node<Empty_Class>,
                                  Graph_Arc<Empty_Class>>>
class Two_Sat
{
public:
  using Node = typename GT::Node;
  using Arc = typename GT::Arc;
 
private:
  size_t num_vars;
  GT ig;
  Array<Node *> lit_nodes;
 
public:
 
 
  [[nodiscard]] static constexpr size_t
  pos_lit(const size_t var) noexcept { return 2 * var; }
 
  [[nodiscard]] static constexpr size_t
  neg_lit(const size_t var) noexcept { return 2 * var + 1; }
 
  [[nodiscard]] static constexpr size_t
  negate_lit(const size_t lit) noexcept { return lit ^ 1; }
 
  [[nodiscard]] static constexpr size_t
  lit_var(const size_t lit) noexcept { return lit >> 1; }
 
  [[nodiscard]] static constexpr bool
  is_pos_lit(const size_t lit) noexcept { return (lit & 1) == 0; }
 
  [[nodiscard]] static size_t signed_to_lit(const long v)
  {
    ah_domain_error_if(v == 0)
      << "Two_Sat::signed_to_lit: variable index 0 is invalid";
    ah_domain_error_if(v == std::numeric_limits<long>::min())
      << "Two_Sat::signed_to_lit: variable index LONG_MIN is invalid";
 
    if (v > 0)
      return pos_lit(static_cast<size_t>(v - 1));
 
    // Handle v < 0 safely, avoiding overflow for LONG_MIN (guarded above).
    const size_t magnitude_minus_one = static_cast<size_t>(-(v + 1));
    return neg_lit(magnitude_minus_one);
  }
 
 
  Two_Sat(const Two_Sat &) = delete;
 
  Two_Sat & operator=(const Two_Sat &) = delete;
 
  Two_Sat(const size_t n)
    : num_vars(n), lit_nodes(Array<Node *>::create(2 * n))
  {
    for (size_t i = 0; i < 2 * n; ++i)
      lit_nodes(i) = ig.insert_node();
  }
 
  [[nodiscard]] size_t size() const noexcept { return num_vars; }
 
  [[nodiscard]] size_t num_nodes() const noexcept { return 2 * num_vars; }
 
  [[nodiscard]] const GT & implication_graph() const noexcept { return ig; }
 
  void add_clause(size_t a, size_t b)
  {
    ah_domain_error_if(lit_var(a) >= num_vars)
      << "Two_Sat::add_clause: literal " << a
      << " refers to variable " << lit_var(a)
      << " but only " << num_vars << " variables exist";
    ah_domain_error_if(lit_var(b) >= num_vars)
      << "Two_Sat::add_clause: literal " << b
      << " refers to variable " << lit_var(b)
      << " but only " << num_vars << " variables exist";
 
    ig.insert_arc(lit_nodes(negate_lit(a)), lit_nodes(b));
    ig.insert_arc(lit_nodes(negate_lit(b)), lit_nodes(a));
  }
 
  void add_clause_signed(const long a, const long b)
  {
    ah_domain_error_if(a == 0 or b == 0)
      << "Two_Sat::add_clause_signed: variable index 0 is invalid";
    ah_domain_error_if(a == std::numeric_limits<long>::min() or
                       b == std::numeric_limits<long>::min())
      << "Two_Sat::add_clause_signed: variable index LONG_MIN is invalid";
    add_clause(signed_to_lit(a), signed_to_lit(b));
  }
 
  void add_implication(const size_t a, const size_t b)
  {
    add_clause(negate_lit(a), b);
  }
 
  void set_true(const size_t a)
  {
    add_clause(a, a);
  }
 
  void set_false(const size_t a)
  {
    set_true(negate_lit(a));
  }
 
  void add_xor(const size_t a, const size_t b)
  {
    add_clause(a, b);
    add_clause(negate_lit(a), negate_lit(b));
  }
 
  void add_equiv(const size_t a, const size_t b)
  {
    add_implication(a, b);
    add_implication(b, a);
  }
 
  void add_at_most_one(const Array<size_t> & lits)
  {
    DynSetTree<size_t> unique_lits;
    for (size_t i = 0; i < lits.size(); ++i)
      {
        const size_t lit = lits(i);
        ah_domain_error_if(lit_var(lit) >= num_vars)
          << "Two_Sat::add_at_most_one: literal " << lit
          << " refers to variable " << lit_var(lit)
          << " but only " << num_vars << " variables exist";
        unique_lits.insert(lit);
      }
 
    if (unique_lits.size() < 2)
      return;
 
    DynArray<size_t> u_dyn;
    unique_lits.for_each([&u_dyn](const size_t & lit) { u_dyn.append(lit); });
    const Array<size_t> u = u_dyn.to_array();
    for (size_t i = 0; i < u.size(); ++i)
      for (size_t j = i + 1; j < u.size(); ++j)
        add_clause(negate_lit(u(i)), negate_lit(u(j)));
  }
 
  [[nodiscard]] bool is_satisfiable()
  {
    return solve().first;
  }
 
  [[nodiscard]] std::pair<bool, Array<bool>> solve()
  {
    Tarjan_Connected_Components<GT> tarjan;
    auto sccs = tarjan.connected_components(ig);
 
    long scc_id = 0;
    sccs.for_each([&scc_id](auto & scc) {
      scc.for_each([&scc_id](Node * node) {
        NODE_COUNTER(node) = scc_id;
      });
      ++scc_id;
    });
 
# ifndef NDEBUG
    for (size_t lit = 0; lit < lit_nodes.size(); ++lit)
      for (Out_Iterator<GT> it(lit_nodes(lit)); it.has_curr(); it.next_ne())
        {
          Node * const src = lit_nodes(lit);
          Node * const tgt = ig.get_tgt_node(it.get_curr());
          const long src_id = NODE_COUNTER(src);
          const long tgt_id = NODE_COUNTER(tgt);
          assert(src_id == tgt_id or src_id > tgt_id);
        }
# endif
 
    Array<bool> assignment = Array<bool>::create(num_vars);
 
    for (size_t i = 0; i < num_vars; ++i)
      {
        const long id_pos = NODE_COUNTER(lit_nodes(pos_lit(i)));
        const long id_neg = NODE_COUNTER(lit_nodes(neg_lit(i)));
 
        if (id_pos == id_neg)
          return {false, Array<bool>()};
 
        // This depends on connected_components() returning SCCs in reverse
        // topological order, which is then recorded in NODE_COUNTER(...).
        assignment(i) = id_pos < id_neg;
      }
 
    return {true, std::move(assignment)};
  }
};
 
 
} // end namespace Aleph
 
# endif /* TWO_SAT_H */