product.hxx

// product.hxx: this file is part of the Vaucanson project.
//
// Vaucanson, a generic library for finite state machines.
//
// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 The Vaucanson Group.
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 2
// of the License, or (at your option) any later version.
//
// The complete GNU General Public Licence Notice can be found as the
// `COPYING' file in the root directory.
//
// The Vaucanson Group consists of people listed in the `AUTHORS' file.
//
#ifndef VCSN_ALGORITHMS_PRODUCT_HXX
# define VCSN_ALGORITHMS_PRODUCT_HXX

# include <set>
# include <map>
# include <queue>
# include <stack>

# include <vaucanson/algorithms/product.hh>

# ifndef VCSN_NDEBUG
#  include <vaucanson/algorithms/realtime.hh>
# endif // ! VCSN_NDEBUG

# include <vaucanson/automata/concept/automata_base.hh>
# include <vaucanson/misc/usual_macros.hh>
# include <vaucanson/automata/implementation/geometry.hh>
# include <vaucanson/misc/static.hh>

namespace vcsn
{

/*--------------------------------.
| Functor for product algorithm.  |
`--------------------------------*/
template<typename A, typename T, typename U>
class Product
{
  public:
    typedef AutomataBase<A> structure_t;
    typedef Element<A, T> lhs_t;
    typedef Element<A, U> rhs_t;
    typedef lhs_t           output_t;
    typedef std::map<typename output_t::hstate_t,
              std::pair<typename lhs_t::hstate_t, typename rhs_t::hstate_t> >
                          pair_map_t;

    Product (const structure_t& structure,
             const bool use_geometry)
      : use_geometry_(use_geometry),
        series_(structure.series()),
        monoid_(series_.monoid()),
        semiring_zero_(series_.semiring().zero(SELECT(semiring_elt_value_t)))
    {
    }

    // returns the product of @c lhs and @c rhs (and put it also in @c output)
    output_t&
    operator() (output_t& output,
                const lhs_t& lhs,
                const rhs_t& rhs,
                pair_map_t& m)
    {
      BENCH_TASK_SCOPED("product");
      visited_.clear();

      precondition(is_realtime(lhs));
      precondition(is_realtime(rhs));

      this->initialize_queue(output, lhs, rhs, m);

      while (not to_process_.empty())
      {
        const pair_hstate_t current_pair = to_process_.front();
        to_process_.pop();

        const hstate_t lhs_s         = current_pair.first;
        const hstate_t rhs_s         = current_pair.second;
        const hstate_t current_state = visited_[current_pair];
  {
            series_set_elt_t    prod_series(series_);
            if (is_product_not_null(lhs.get_initial(lhs_s), rhs.get_initial(rhs_s), prod_series))
                        output.set_initial(current_state, prod_series);
  }
  {
            series_set_elt_t    prod_series(series_);
            if (is_product_not_null(lhs.get_final(lhs_s), rhs.get_final(rhs_s), prod_series))
                        output.set_final(current_state, prod_series);
  }
        for (typename lhs_t::delta_iterator l(lhs.value(), lhs_s);
             ! l.done();
             l.next())
          for (typename rhs_t::delta_iterator r(rhs.value(), rhs_s);
               ! r.done();
               r.next())
          {
            series_set_elt_t    prod_series(series_);

            if (is_product_not_null(lhs.series_of(*l), rhs.series_of(*r), prod_series))
            {
              const pair_hstate_t new_pair(lhs.dst_of(*l), rhs.dst_of(*r));
              typename visited_t::const_iterator found = visited_.find(new_pair);

              hstate_t dst;
              if (found == visited_.end())
              {
                dst = output.add_state();

                this->add_state_to_process(output, lhs, rhs, m, dst, new_pair);
              }
              else
                dst = found->second;
              output.add_series_transition(current_state, dst, prod_series);
            }
          }
      }
      return output;
    }

  private:
    // Some little graphic tools
    class grphx
    {
      public:
        template <typename Output, typename Lhs, typename Rhs>
        static void
        setcoordfrom (Output& a,
                      const Lhs& lhs,
                      const Rhs& rhs,
                      const typename Output::hstate_t state,
                      const typename Lhs::hstate_t x_state,
                      const typename Rhs::hstate_t y_state)
        {
          typename std::map<typename Lhs::hstate_t,
            typename Lhs::geometry_t::coords_t>::const_iterator iter;
          typename std::map<typename Rhs::hstate_t,
            typename Rhs::geometry_t::coords_t>::const_iterator iter2;
          double x = 0, y = 0;

          iter = lhs.geometry().states().find(x_state);
          if (iter != lhs.geometry().states().end())
            x = iter->second.first;

          iter2 = rhs.geometry().states().find(y_state);
          if (iter2 != rhs.geometry().states().end())
            y = iter2->second.second;

          a.geometry().states()[state] = std::make_pair(x, y);
        }
      private:
        // Diagonal alignement with a depth-first traversal
        template<typename I>
        void
        align (const I& a)
        {
          AUTOMATON_TYPES(I);
          std::map<hstate_t,bool> visited;
          std::stack<hstate_t> stack;

          for_all_const_states(i, a)
            {
              visited[*i] = false;
              // ensure inaccessible states will be visited
              stack.push(*i);
            }

          for_all_const_initial_states(i, a)
            stack.push(*i);

          int x = 0;
          while (!stack.empty())
          {
            hstate_t i = stack.top();
            stack.pop();

            if (!visited[i])
            {
              visited[i] = true;

              a.geometry()[i] = std::make_pair(x, x);
              x++;

              for (delta_iterator j(a.value(), i);
                   ! j.done();
                   j.next())
                stack.push(a.dst_of(*j));
            }
          }
        }

    };
    class no_grphx
    {
      public:
        template <typename Output, typename Lhs, typename Rhs>
        static void
        setcoordfrom (Output& a,
                      const Lhs& lhs,
                      const Rhs& rhs,
                      const typename Output::hstate_t state,
                      const typename Lhs::hstate_t x_state,
                      const typename Rhs::hstate_t y_state) {};
    };

    // useful typedefs
    AUTOMATON_TYPES(output_t);

    typedef std::pair<typename lhs_t::hstate_t, typename rhs_t::hstate_t>
                                                      pair_hstate_t;
    typedef std::list<htransition_t>                    delta_ret_t;
    typedef std::map<pair_hstate_t, hstate_t>           visited_t;
    typedef typename series_set_elt_t::support_t        support_t;

    // add a @c new_state in the queue
    inline void
    add_state_to_process (output_t& output,
                          const lhs_t& lhs,
                          const rhs_t& rhs,
                          pair_map_t& m,
                          const hstate_t& new_state,
                          const pair_hstate_t& new_pair)
    {
      m[new_state] = new_pair;
      visited_[new_pair] = new_state;
      to_process_.push(new_pair);

# define if_(Cond, ThenClause, ElseClause)                      \
misc::static_if_simple<Cond, ThenClause, ElseClause>::t
# define eq_(Type1, Type2)                      \
misc::static_eq<Type1, Type2>::value
# define DECLARE_GEOMETRY(Type) \
  typedef geometry<typename Type::hstate_t, typename Type::htransition_t, typename Type::geometry_coords_t> geometry_ ## Type ;

      DECLARE_GEOMETRY(output_t)
      DECLARE_GEOMETRY(lhs_t)
      DECLARE_GEOMETRY(rhs_t)
      if (use_geometry_)
        if_(eq_(typename output_t::geometry_t, geometry_output_t)  and \
            eq_(typename rhs_t::geometry_t, geometry_rhs_t) and \
            eq_(typename lhs_t::geometry_t, geometry_lhs_t),    \
            grphx, no_grphx)
          ::setcoordfrom(output, lhs, rhs,
                         new_state, new_pair.first, new_pair.second);
# undef if_
# undef eq_
    }

    // initialize queue with all pairs of intials states from @c lhs and @c rhs
    inline void
    initialize_queue (output_t& output,
                      const lhs_t& lhs,
                      const rhs_t& rhs,
                      pair_map_t& m)
    {
      for_all_const_initial_states(lhs_s, lhs)
        for_all_const_initial_states(rhs_s, rhs)
        {
          const pair_hstate_t   new_pair(*lhs_s, *rhs_s);
          const hstate_t        new_state = output.add_state();

          this->add_state_to_process(output, lhs, rhs, m, new_state, new_pair);
        }
    }

    inline bool
    is_product_not_null (const series_set_elt_t left_series,
                         const series_set_elt_t right_series,
                         series_set_elt_t&  prod_series) const
    {
      bool                      prod_is_not_null = false;
      //the alphabet of rhs is a subset of the alphbet of rhs
      //thus, we consider monomials in right_series; they are compatible with lhs.
      for_all_(support_t, supp, right_series.supp())
        {
          const monoid_elt_t     supp_elt (monoid_, *supp);
          const semiring_elt_t l = left_series.get(supp_elt);
          const semiring_elt_t r = right_series.get(supp_elt);
          const semiring_elt_t p = l * r;
          if (p != semiring_zero_)
          {
            prod_series.assoc(*supp, p.value());
            prod_is_not_null = true;
          }
        }
      return (prod_is_not_null);
    }

    // If set to true, <geometry> tags of the result automaton should be filled
    const bool  use_geometry_;

    // keep traces of new states created
    visited_t                   visited_;
    // @c to_process_ stores all states of output that needs are not
    std::queue<pair_hstate_t>   to_process_;

    // frequently used objects in computation
    const series_set_t& series_;
    const monoid_t&             monoid_;
    // This variable's type must not be set to a reference.
    const semiring_elt_t        semiring_zero_;
};

/*-----------.
| Wrappers.  |
`-----------*/

template<typename A, typename T, typename U>
Element<A, T>
product (const Element<A, T>& lhs, const Element<A, U>& rhs,
         std::map<typename T::hstate_t,
         std::pair<typename T::hstate_t, typename U::hstate_t> >& m,
         const bool use_geometry)
{
  Element<A, T> ret(lhs.structure());
  Product<A, T, U> do_product(ret.structure(), use_geometry);
  return do_product (ret, lhs, rhs, m);
}

template<typename A, typename T, typename U>
Element<A, T>
product (const Element<A, T>& lhs, const Element<A, U>& rhs,
         const bool use_geometry)
{
  std::map<typename T::hstate_t,
    std::pair<typename T::hstate_t, typename U::hstate_t> > m;
  return product (lhs, rhs, m, use_geometry);
}

} // End of namespace vcsn.

#endif // ! VCSN_ALGORITHMS_PRODUCT_HXX