/* -*- 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