tpl_bipartite.H

# ifndef TPL_BIPARTITE_H
# define TPL_BIPARTITE_H

# include <tpl_dynDlist.H>
# include <tpl_netgraph.H>

namespace Aleph {

enum Bipartite_Color { Bp_White, Bp_Red, Bp_Blue };

    template <class GT> 
static long & color(typename GT::Node * p)
{
  return NODE_COUNTER(p);
}

    template <class GT> 
static long & color(typename GT::Arc * a)
{
  return ARC_COUNTER(a);
}

     template <class GT, class SA = Dft_Show_Arc<GT> > 
void compute_bipartite(GT &                            g, 
                       DynDlist<typename GT::Node *> & l,
                       DynDlist<typename GT::Node *> & r)
{
  g.reset_nodes(); // inicializa contadores en Blanco
  g.reset_arcs();

  DynDlist<typename GT::Node *> red, blue;
  typename GT::Node * p = g.get_first_node();
  color<GT>(p) = Bp_Red;
  red.put(p); l.put(p);  

  while (true)
    if (not red.is_empty()) // ¿Hay rojo con arcos no mirados?
      {
        typename GT::Node * p = red.get();
        for (Node_Arc_Iterator<GT, SA> it(p); it.has_current(); it.next())
          {
            typename GT::Arc * a = it.get_current();
            if (color<GT>(a) == Bp_Red)
              throw std::domain_error("Graph is not bipartite");
            else if (color<GT>(a) == Bp_Blue)
              continue;

            color<GT>(a) = Bp_Red; 
            typename GT::Node * q = it.get_tgt_node();
            if (color<GT>(q) == Bp_Red)
              throw std::domain_error("Graph is not bipartite");              
            else if (color<GT>(q) == Bp_Blue)
              continue;

            color<GT>(q) = Bp_Blue;
            blue.put(q); r.put(q);
          }
      }
    else if (not blue.is_empty()) // ¿Hay azul con arcos no mirados?
      {
        typename GT::Node * p = blue.get();
        for (Node_Arc_Iterator<GT, SA> it(p); it.has_current(); it.next())
          {
            typename GT::Arc * a = it.get_current();
            if (color<GT>(a) == Bp_Blue)
              throw std::domain_error("Graph is not bipartite");
            else if (color<GT>(a) == Bp_Red)
              continue;

            color<GT>(a) = Bp_Blue;

            typename GT::Node * q = it.get_tgt_node();
            if (color<GT>(q) == Bp_Blue)
              throw std::domain_error("Graph is not bipartite");
            else if (color<GT>(q) == Bp_Red)
              continue;

            color<GT>(q) = Bp_Red;
            red.put(q); l.put(q);
          }
      }
    else
      break;
}

    template <class GT, class SA = Dft_Show_Arc<GT> > 
class Compute_Bipartite
{
public:
  
  void operator () (GT &                            g, 
                    DynDlist<typename GT::Node *> & l,
                    DynDlist<typename GT::Node *> & r)
  {
    compute_bipartite <GT, SA> (g, l, r);
  }
};

     template <class GT, 
               template <class> class Max_Flow = Ford_Fulkerson_Maximum_Flow, 
               class SA = Dft_Show_Arc<GT> > 
void compute_maximum_cardinality_bipartite_matching
  (GT & g, DynDlist<typename GT::Arc *> & matching)
{
  DynDlist<typename GT::Node *> l, r;

  compute_bipartite(g, l, r);

  typedef Net_Graph<Net_Node<Empty_Class>, Net_Arc<Empty_Class> > AN;
  AN net;

      // recorrer nodos de g e insertar imagen en net
  for (Node_Iterator<GT> it(g); it.has_current(); it.next())
  {
    typename GT::Node * p = it.get_current();
    NODE_COOKIE(p) = net.insert_node();
    NODE_COOKIE((typename GT::Node *)NODE_COOKIE(p)) = p;
  }

  typename AN::Node * source = net.insert_node();

      // recorrer nodos de l, atarlos a fuente e insertar sus arcos
  for (typename DynDlist<typename GT::Node*>::Iterator i(l); 
       i.has_current(); i.next())
    {
      typename GT::Node * p = i.get_current();
      typename AN::Node * src = mapped_node<GT, AN> (p);
      net.insert_arc(source, src, 1);

      for (Node_Arc_Iterator<GT, SA> j(p); j.has_current(); j.next())
        {
          typename GT::Arc * arc = j.get_current_arc();
          typename AN::Node * tgt = mapped_node <GT, AN> (g.get_tgt_node(arc));
          typename AN::Arc * a = net.insert_arc(src, tgt, 1);
          ARC_COOKIE(arc) = a;
          ARC_COOKIE(a) = arc;
        }
    }

  typename AN::Node * sink = net.insert_node();

    // recorrer nodos de r y atarlos al sumidero
  for (typename DynDlist<typename GT::Node*>::Iterator it(r); 
       it.has_current(); it.next())
    {
      typename GT::Node * p = it.get_current();
      net.insert_arc(mapped_node<GT, AN> (p), sink, 1);
    }

  Max_Flow <AN> () (net); 

  for (Arc_Iterator<AN> it(net); it.has_current(); it.next())
    {
      typename AN::Arc * a = it.get_current();
      if (a->flow == 0) 
        continue;

      typename GT::Arc * arc = mapped_arc <AN, GT> (a);
      if (arc == NULL)
        continue;

      matching.append(arc);
    }
}

     template <class GT, 
               template <class> class Max_Flow = Ford_Fulkerson_Maximum_Flow,
               class SA = Dft_Show_Arc<GT> > 
class Compute_Maximum_Cardinality_Bipartite_Matching
{
public:

  void operator () (GT & g, DynDlist<typename GT::Arc *> & matching)
  {
    compute_maximum_cardinality_bipartite_matching <GT, Max_Flow, SA>
      (g, matching);
  }
};


} // end namespace Aleph

# endif //  TPL_BIPARTITE_H