/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2015

 * EMAXA Kutato-fejleszto Kft. (EMAXA Research Ltd.)

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_VF2_H

#define LEMON_VF2_H

///\ingroup graph_properties

///\file

///\brief VF2 algorithm \cite cordella2004sub.

#include <lemon/core.h>

#include <lemon/concepts/graph.h>

#include <lemon/dfs.h>

#include <lemon/bfs.h>

#include <vector>

#include <set>

namespace lemon

{

  namespace bits

  {

    namespace vf2

    {

      class AlwaysEq

      {

      public:

        template<class T1, class T2>

        bool operator()(T1, T2) const

        {

          return true;

        }

      };

      template<class M1, class M2>

      class MapEq

      {

        const M1 &_m1;

        const M2 &_m2;

      public:

        MapEq(const M1 &m1, const M2 &m2) : _m1(m1), _m2(m2) {}

        bool operator()(typename M1::Key k1, typename M2::Key k2) const

        {

          return _m1[k1] == _m2[k2];

        }

      };

      template <class G>

      class DfsLeaveOrder : public DfsVisitor<G>

      {

        const G &_g;

        std::vector<typename G::Node> &_order;

        int i;

      public:

        DfsLeaveOrder(const G &g, std::vector<typename G::Node> &order)

          : i(countNodes(g)), _g(g), _order(order)

        {}

        void leave(const typename G::Node &node)

        {

          _order[--i]=node;

        }

      };

      template <class G>

      class BfsLeaveOrder : public BfsVisitor<G>

      {

        int i;

        const G &_g;

        std::vector<typename G::Node> &_order;

      public:

        BfsLeaveOrder(const G &g, std::vector<typename G::Node> &order)

          : i(0), _g(g), _order(order)

        {}

        void process(const typename G::Node &node)

        {

          _order[i++]=node;

        }

      };

    }

  }

  ///Graph mapping types.

  ///\ingroup graph_isomorphism

  ///The \ref Vf2 "VF2" algorithm is capable of finding different kind of

  ///embeddings, this enum specifies its type.

  ///

  ///See \ref graph_isomorphism for a more detailed description.

  enum Vf2MappingType {

    /// Subgraph isomorphism

    SUBGRAPH = 0,

    /// Induced subgraph isomorphism

    INDUCED = 1,

    /// Graph isomorphism

    /// If the two graph has the same number of nodes, than it is

    /// equivalent to \ref INDUCED, and if they also have the same

    /// number of edges, then it is also equivalent to \ref SUBGRAPH.

    ///

    /// However, using this setting is faster than the other two

    /// options.

    ISOMORPH = 2

  };

  ///%VF2 algorithm class.

  ///\ingroup graph_isomorphism This class provides an efficient

  ///implementation of the %VF2 algorithm \cite cordella2004sub

  ///for variants of the (Sub)graph Isomorphism problem.

  ///

  ///There is also a \ref vf2() "function-type interface" called \ref vf2()

  ///for the %VF2 algorithm, which is probably more convenient in most

  ///use-cases.

  ///

  ///\tparam G1 The type of the graph to be embedded.

  ///The default type is \ref ListDigraph.

  ///\tparam G2 The type of the graph g1 will be embedded into.

  ///The default type is \ref ListDigraph.

  ///\tparam M The type of the NodeMap storing the mapping.

  ///By default, it is G1::NodeMap<G2::Node>

  ///\tparam NEQ A bool-valued binary functor determinining whether a node is

  ///mappable to another. By default it is an always true operator.

  ///

  ///\sa vf2()

#ifdef DOXYGEN

  template<class G1, class G2, class M, class NEQ >

#else

  template<class G1=ListDigraph,

           class G2=ListDigraph,

           class M = typename G1::template NodeMap<G2::Node>,

           class NEQ = bits::vf2::AlwaysEq >

#endif

  class Vf2

  {

    //Current depth in the DFS tree.

    int _depth;

    //Functor with bool operator()(G1::Node,G2::Node), which returns 1

    //if and only if the 2 nodes are equivalent.

    NEQ _nEq;

    typename G2::template NodeMap<int> _conn;

    //Current mapping. We index it by the nodes of g1, and match[v] is

    //a node of g2.

    M &_mapping;

    //order[i] is the node of g1, for which we find a pair if depth=i

    std::vector<typename G1::Node> order;

    //currEdgeIts[i] is an edge iterator, witch is last used in the ith

    //depth to find a pair for order[i].

    std::vector<typename G2::IncEdgeIt> currEdgeIts;

    //The small graph.

    const G1 &_g1;

    //The big graph.

    const G2 &_g2;

    //lookup tables for cut the searchtree

    typename G1::template NodeMap<int> rNew1t,rInOut1t;

    Vf2MappingType _mapping_type;

    //cut the search tree

    template<Vf2MappingType MT>

    bool cut(const typename G1::Node n1,const typename G2::Node n2) const

    {

      int rNew2=0,rInOut2=0;

      for(typename G2::IncEdgeIt e2(_g2,n2); e2!=INVALID; ++e2)

        {

          const typename G2::Node currNode=_g2.oppositeNode(n2,e2);

          if(_conn[currNode]>0)

            ++rInOut2;

          else if(MT!=SUBGRAPH&&_conn[currNode]==0)

            ++rNew2;

        }

      switch(MT)

        {

        case INDUCED:

          return rInOut1t[n1]<=rInOut2&&rNew1t[n1]<=rNew2;

        case SUBGRAPH:

          return rInOut1t[n1]<=rInOut2;

        case ISOMORPH:

          return rInOut1t[n1]==rInOut2&&rNew1t[n1]==rNew2;

        default:

          return false;

        }

    }

    template<Vf2MappingType MT>

    bool feas(const typename G1::Node n1,const typename G2::Node n2)

    {

      if(!_nEq(n1,n2))

        return 0;

      for(typename G1::IncEdgeIt e1(_g1,n1); e1!=INVALID; ++e1)

        {

          const typename G1::Node currNode=_g1.oppositeNode(n1,e1);

          if(_mapping[currNode]!=INVALID)

            --_conn[_mapping[currNode]];

        }

      bool isIso=1;

      for(typename G2::IncEdgeIt e2(_g2,n2); e2!=INVALID; ++e2)

        {

          const typename G2::Node currNode=_g2.oppositeNode(n2,e2);

          if(_conn[currNode]<-1)

            ++_conn[currNode];

          else if(MT!=SUBGRAPH&&_conn[currNode]==-1)

            {

              isIso=0;

              break;

            }

        }

      for(typename G1::IncEdgeIt e1(_g1,n1); e1!=INVALID; ++e1)

        {

          const typename G1::Node currNode=_g1.oppositeNode(n1,e1);

          if(_mapping[currNode]!=INVALID&&_conn[_mapping[currNode]]!=-1)

            {

              switch(MT)

                {

                case INDUCED:

                case ISOMORPH:

                  isIso=0;

                  break;

                case SUBGRAPH:

                  if(_conn[_mapping[currNode]]<-1)

                    isIso=0;

                  break;

                }

              _conn[_mapping[currNode]]=-1;

            }

        }

      return isIso&&cut<MT>(n1,n2);

    }

    void addPair(const typename G1::Node n1,const typename G2::Node n2)

    {

      _conn[n2]=-1;

      _mapping.set(n1,n2);

      for(typename G2::IncEdgeIt e2(_g2,n2); e2!=INVALID; ++e2)

        if(_conn[_g2.oppositeNode(n2,e2)]!=-1)

          ++_conn[_g2.oppositeNode(n2,e2)];

    }

    void subPair(const typename G1::Node n1,const typename G2::Node n2)

    {

      _conn[n2]=0;

      _mapping.set(n1,INVALID);

      for(typename G2::IncEdgeIt e2(_g2,n2); e2!=INVALID; ++e2)

        {

          const typename G2::Node currNode=_g2.oppositeNode(n2,e2);

          if(_conn[currNode]>0)

            --_conn[currNode];

          else if(_conn[currNode]==-1)

            ++_conn[n2];

        }

    }

    void setOrder()//we will find pairs for the nodes of g1 in this order

    {

      // bits::vf2::DfsLeaveOrder<G1> v(_g1,order);

      //   DfsVisit<G1,bits::vf2::DfsLeaveOrder<G1> >dfs(_g1, v);

      //   dfs.run();

      //it is more efficient in practice than DFS

      bits::vf2::BfsLeaveOrder<G1> v(_g1,order);

      BfsVisit<G1,bits::vf2::BfsLeaveOrder<G1> >bfs(_g1, v);

      bfs.run();

    }

    template<Vf2MappingType MT>

    bool extMatch()

    {

      while(_depth>=0)

        {

          //there are not nodes in g1, which has not pair in g2.

          if(_depth==static_cast<int>(order.size()))

            {

              --_depth;

              return true;

            }

          //the node of g2, which neighbours are the candidates for

          //the pair of order[_depth]

          typename G2::Node currPNode;

          if(currEdgeIts[_depth]==INVALID)

            {

              typename G1::IncEdgeIt fstMatchedE(_g1,order[_depth]);

              //if _mapping[order[_depth]]!=INVALID, we dont use

              //fstMatchedE

              if(_mapping[order[_depth]]==INVALID)

                for(; fstMatchedE!=INVALID &&

                      _mapping[_g1.oppositeNode(order[_depth],

                                              fstMatchedE)]==INVALID;

                    ++fstMatchedE) ; //find fstMatchedE

              if(fstMatchedE==INVALID||_mapping[order[_depth]]!=INVALID)

                {

                  //We did not find an covered neighbour, this means

                  //the graph is not connected(or _depth==0).  Every

                  //uncovered(and there are some other properties due

                  //to the spec. problem types) node of g2 is

                  //candidate.  We can read the iterator of the last

                  //tryed node from the match if it is not the first

                  //try(match[order[_depth]]!=INVALID)

                  typename G2::NodeIt n2(_g2);

                  //if its not the first try

                  if(_mapping[order[_depth]]!=INVALID)

                    {

                      n2=++typename G2::NodeIt(_g2,_mapping[order[_depth]]);

                      subPair(order[_depth],_mapping[order[_depth]]);

                    }

                  for(; n2!=INVALID; ++n2)

                    if(MT!=SUBGRAPH&&_conn[n2]==0)

                      {

                        if(feas<MT>(order[_depth],n2))

                          break;

                      }

                    else if(MT==SUBGRAPH&&_conn[n2]>=0)

                      if(feas<MT>(order[_depth],n2))

                        break;

                  // n2 is the next candidate

                  if(n2!=INVALID)

                    {

                      addPair(order[_depth],n2);

                      ++_depth;

                    }

                  else // there is no more candidate

                    --_depth;

                  continue;

                }

              else

                {

                  currPNode=_mapping[_g1.oppositeNode(order[_depth],

                                                      fstMatchedE)];

                  currEdgeIts[_depth]=typename G2::IncEdgeIt(_g2,currPNode);

                }

            }

          else

            {

              currPNode=_g2.oppositeNode(_mapping[order[_depth]],

                                         currEdgeIts[_depth]);

              subPair(order[_depth],_mapping[order[_depth]]);

              ++currEdgeIts[_depth];

            }

          for(; currEdgeIts[_depth]!=INVALID; ++currEdgeIts[_depth])

            {

              const typename G2::Node currNode =

                _g2.oppositeNode(currPNode, currEdgeIts[_depth]);

              //if currNode is uncovered

              if(_conn[currNode]>0&&feas<MT>(order[_depth],currNode))

                {

                  addPair(order[_depth],currNode);

                  break;

                }

            }

          currEdgeIts[_depth]==INVALID?--_depth:++_depth;

        }

      return false;

    }

    //calc. the lookup table for cut the searchtree

    void setRNew1tRInOut1t()

    {

      typename G1::template NodeMap<int> tmp(_g1,0);

      for(unsigned int i=0; i<order.size(); ++i)

        {

          tmp[order[i]]=-1;

          for(typename G1::IncEdgeIt e1(_g1,order[i]); e1!=INVALID; ++e1)

            {

              const typename G1::Node currNode=_g1.oppositeNode(order[i],e1);

              if(tmp[currNode]>0)

                ++rInOut1t[order[i]];

              else if(tmp[currNode]==0)

                ++rNew1t[order[i]];

            }

          for(typename G1::IncEdgeIt e1(_g1,order[i]); e1!=INVALID; ++e1)

            {

              const typename G1::Node currNode=_g1.oppositeNode(order[i],e1);

              if(tmp[currNode]!=-1)

                ++tmp[currNode];

            }

        }

    }

  public:

    ///Constructor

    ///Constructor

    ///\param g1 The graph to be embedded into \e g2.

    ///\param g2 The graph \e g1 will be embedded into.

    ///\param m \ref concepts::ReadWriteMap "read-write" NodeMap

    ///storing the found mapping.

    ///\param neq A bool-valued binary functor determinining whether a node is

    ///mappable to another. By default it is an always true operator.

    Vf2(const G1 &g1, const G2 &g2,M &m, const NEQ &neq = NEQ() ) :

      _nEq(neq), _conn(g2,0), _mapping(m), order(countNodes(g1)),

      currEdgeIts(countNodes(g1),INVALID), _g1(g1), _g2(g2), rNew1t(g1,0),

      rInOut1t(g1,0), _mapping_type(SUBGRAPH)

    {

      _depth=0;

      setOrder();

      setRNew1tRInOut1t();

      for(typename G1::NodeIt n(g1);n!=INVALID;++n)

        m[n]=INVALID;

    }

    ///Returns the current mapping type

    ///Returns the current mapping type

    ///

    Vf2MappingType mappingType() const { return _mapping_type; }

    ///Sets mapping type

    ///Sets mapping type.

    ///

    ///The mapping type is set to \ref SUBGRAPH by default.

    ///

    ///\sa See \ref Vf2MappingType for the possible values.

    void mappingType(Vf2MappingType m_type) { _mapping_type = m_type; }

    ///Finds a mapping

    ///It finds a mapping between from g1 into g2 according to the mapping

    ///type set by \ref mappingType(Vf2MappingType) "mappingType()".

    ///

    ///By subsequent calls, it returns all possible mappings one-by-one.

    ///

    ///\retval true if a mapping is found.

    ///\retval false if there is no (more) mapping.

    bool find()

    {

      switch(_mapping_type)

        {

        case SUBGRAPH:

          return extMatch<SUBGRAPH>();

        case INDUCED:

          return extMatch<INDUCED>();

        case ISOMORPH:

          return extMatch<ISOMORPH>();

        default:

          return false;

        }

    }

  };

  template<class G1, class G2>

  class Vf2WizardBase

  {

  protected:

    typedef G1 Graph1;

    typedef G2 Graph2;

    const G1 &_g1;

    const G2 &_g2;

    Vf2MappingType _mapping_type;

    typedef typename G1::template NodeMap<typename G2::Node> Mapping;

    bool _local_mapping;

    void *_mapping;

    void createMapping()

    {

      _mapping = new Mapping(_g1);

    }

    typedef bits::vf2::AlwaysEq NodeEq;

    NodeEq _node_eq;

    Vf2WizardBase(const G1 &g1,const G2 &g2)

      : _g1(g1), _g2(g2), _mapping_type(SUBGRAPH), _local_mapping(true) {}

  };

  /// Auxiliary class for the function-type interface of %VF2 algorithm.

  /// This auxiliary class implements the named parameters of

  /// \ref vf2() "function-type interface" of \ref Vf2 algorithm.

  ///

  /// \warning This class should only be used through the function \ref vf2().

  ///

  /// \tparam TR The traits class that defines various types used by the

  /// algorithm.

  template<class TR>

  class Vf2Wizard : public TR

  {

    typedef TR Base;

    typedef typename TR::Graph1 Graph1;

    typedef typename TR::Graph2 Graph2;

    typedef typename TR::Mapping Mapping;

    typedef typename TR::NodeEq NodeEq;

    using TR::_g1;

    using TR::_g2;

    using TR::_mapping_type;

    using TR::_mapping;

    using TR::_node_eq;

  public:

    ///Constructor

    Vf2Wizard(const Graph1 &g1,const Graph2 &g2) : Base(g1,g2) {}

    ///Copy constructor

    Vf2Wizard(const Base &b) : Base(b) {}

    template<class T>

    struct SetMappingBase : public Base {

      typedef T Mapping;

      SetMappingBase(const Base &b) : Base(b) {}

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///the mapping.

    ///

    ///\ref named-templ-param "Named parameter" function for setting

    ///the map that stores the found embedding.

    template<class T>

    Vf2Wizard< SetMappingBase<T> > mapping(const T &t)

    {

      Base::_mapping=reinterpret_cast<void*>(const_cast<T*>(&t));

      Base::_local_mapping = false;

      return Vf2Wizard<SetMappingBase<T> >(*this);

    }

    template<class NE>

    struct SetNodeEqBase : public Base {

      typedef NE NodeEq;

      NodeEq _node_eq;

      SetNodeEqBase(const Base &b, const NE &node_eq)

        : Base(b), _node_eq(node_eq) {}

    };

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///the node equivalence relation.

    ///

    ///\ref named-templ-param "Named parameter" function for setting

    ///the equivalence relation between the nodes.

    ///

    ///\param node_eq A bool-valued binary functor determinining

    ///whether a node is mappable to another. By default it is an

    ///always true operator.

    template<class T>

    Vf2Wizard< SetNodeEqBase<T> > nodeEq(const T &node_eq)

    {

      return Vf2Wizard<SetNodeEqBase<T> >(SetNodeEqBase<T>(*this,node_eq));

    }

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///the node labels.

    ///

    ///\ref named-templ-param "Named parameter" function for setting

    ///the node labels defining equivalence relation between them.

    ///

    ///\param m1 It is arbitrary \ref concepts::ReadMap "readable node map"

    ///of g1.

    ///\param m2 It is arbitrary \ref concepts::ReadMap "readable node map"

    ///of g2.

    ///

    ///The value type of these maps must be equal comparable.

    template<class M1, class M2>

    Vf2Wizard< SetNodeEqBase<bits::vf2::MapEq<M1,M2> > >

    nodeLabels(const M1 &m1,const M2 &m2)

    {

      return nodeEq(bits::vf2::MapEq<M1,M2>(m1,m2));

    }

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///the mapping type.

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///the mapping type.

    ///

    ///The mapping type is set to \ref SUBGRAPH by default.

    ///

    ///\sa See \ref Vf2MappingType for the possible values.

    Vf2Wizard<Base> &mappingType(Vf2MappingType m_type)

    {

      _mapping_type = m_type;

      return *this;

    }

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///the mapping type to \ref INDUCED.

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///the mapping type to \ref INDUCED.

    Vf2Wizard<Base> &induced()

    {

      _mapping_type = INDUCED;

      return *this;

    }

    ///\brief \ref named-templ-param "Named parameter" for setting

    ///the mapping type to \ref ISOMORPH.

    ///

    ///\ref named-templ-param "Named parameter" for setting

    ///the mapping type to \ref ISOMORPH.

    Vf2Wizard<Base> &iso()

    {

      _mapping_type = ISOMORPH;

      return *this;

    }

    ///Runs VF2 algorithm.

    ///This method runs VF2 algorithm.

    ///

    ///\retval true if a mapping is found.

    ///\retval false if there is no (more) mapping.

    bool run()

    {

      if(Base::_local_mapping)

        Base::createMapping();

      Vf2<Graph1, Graph2, Mapping, NodeEq >

        alg(_g1, _g2, *reinterpret_cast<Mapping*>(_mapping), _node_eq);

      alg.mappingType(_mapping_type);

      bool ret = alg.find();

      if(Base::_local_mapping)

        delete reinterpret_cast<Mapping*>(_mapping);

      return ret;

    }

  };

  ///Function-type interface for VF2 algorithm.

  /// \ingroup graph_isomorphism

  ///Function-type interface for VF2 algorithm \cite cordella2004sub.

  ///

  ///This function has several \ref named-func-param "named parameters"

  ///declared as the members of class \ref Vf2Wizard.

  ///The following examples show how to use these parameters.

  ///\code

  ///  // Find an embedding of graph g into graph h

  ///  ListGraph::NodeMap<ListGraph::Node> m(g);

  ///  vf2(g,h).mapping(m).run();

  ///

  ///  // Check whether graphs g and h are isomorphic

  ///  bool is_iso = vf2(g,h).iso().run();

  ///\endcode

  ///\warning Don't forget to put the \ref Vf2Wizard::run() "run()"

  ///to the end of the expression.

  ///\sa Vf2Wizard

  ///\sa Vf2

  template<class G1, class G2>

  Vf2Wizard<Vf2WizardBase<G1,G2> > vf2(const G1 &g1, const G2 &g2)

  {

    return Vf2Wizard<Vf2WizardBase<G1,G2> >(g1,g2);

  }

}

#endif