alpar@504: /* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@504:  *
alpar@504:  * This file is a part of LEMON, a generic C++ optimization library.
alpar@504:  *
alpar@504:  * Copyright (C) 2003-2009
alpar@504:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@504:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@504:  *
alpar@504:  * Permission to use, modify and distribute this software is granted
alpar@504:  * provided that this copyright notice appears in all copies. For
alpar@504:  * precise terms see the accompanying LICENSE file.
alpar@504:  *
alpar@504:  * This software is provided "AS IS" with no warranty of any kind,
alpar@504:  * express or implied, and with no claim as to its suitability for any
alpar@504:  * purpose.
alpar@504:  *
alpar@504:  */
alpar@504: 
alpar@504: #ifndef LEMON_EULER_H
alpar@504: #define LEMON_EULER_H
alpar@504: 
alpar@504: #include<lemon/core.h>
alpar@504: #include<lemon/adaptors.h>
alpar@504: #include<lemon/connectivity.h>
alpar@504: #include <list>
alpar@504: 
kpeter@578: /// \ingroup graph_properties
alpar@504: /// \file
alpar@504: /// \brief Euler tour
alpar@504: ///
alpar@504: ///This file provides an Euler tour iterator and ways to check
alpar@504: ///if a digraph is euler.
alpar@504: 
alpar@504: 
alpar@504: namespace lemon {
alpar@504: 
alpar@504:   ///Euler iterator for digraphs.
alpar@504: 
kpeter@578:   /// \ingroup graph_properties
alpar@504:   ///This iterator converts to the \c Arc type of the digraph and using
alpar@504:   ///operator ++, it provides an Euler tour of a \e directed
alpar@504:   ///graph (if there exists).
alpar@504:   ///
alpar@504:   ///For example
alpar@504:   ///if the given digraph is Euler (i.e it has only one nontrivial component
alpar@504:   ///and the in-degree is equal to the out-degree for all nodes),
alpar@504:   ///the following code will put the arcs of \c g
alpar@504:   ///to the vector \c et according to an
alpar@504:   ///Euler tour of \c g.
alpar@504:   ///\code
alpar@504:   ///  std::vector<ListDigraph::Arc> et;
alpar@504:   ///  for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e)
alpar@504:   ///    et.push_back(e);
alpar@504:   ///\endcode
alpar@504:   ///If \c g is not Euler then the resulted tour will not be full or closed.
alpar@504:   ///\sa EulerIt
kpeter@550:   template<typename GR>
alpar@504:   class DiEulerIt
alpar@504:   {
kpeter@550:     typedef typename GR::Node Node;
kpeter@550:     typedef typename GR::NodeIt NodeIt;
kpeter@550:     typedef typename GR::Arc Arc;
kpeter@550:     typedef typename GR::ArcIt ArcIt;
kpeter@550:     typedef typename GR::OutArcIt OutArcIt;
kpeter@550:     typedef typename GR::InArcIt InArcIt;
alpar@504: 
kpeter@550:     const GR &g;
kpeter@550:     typename GR::template NodeMap<OutArcIt> nedge;
alpar@504:     std::list<Arc> euler;
alpar@504: 
alpar@504:   public:
alpar@504: 
alpar@504:     ///Constructor
alpar@504: 
kpeter@550:     ///\param gr A digraph.
alpar@504:     ///\param start The starting point of the tour. If it is not given
alpar@504:     ///       the tour will start from the first node.
kpeter@550:     DiEulerIt(const GR &gr, typename GR::Node start = INVALID)
kpeter@550:       : g(gr), nedge(g)
alpar@504:     {
alpar@504:       if(start==INVALID) start=NodeIt(g);
alpar@504:       for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
alpar@504:       while(nedge[start]!=INVALID) {
alpar@504:         euler.push_back(nedge[start]);
alpar@504:         Node next=g.target(nedge[start]);
alpar@504:         ++nedge[start];
alpar@504:         start=next;
alpar@504:       }
alpar@504:     }
alpar@504: 
alpar@504:     ///Arc Conversion
alpar@504:     operator Arc() { return euler.empty()?INVALID:euler.front(); }
alpar@504:     bool operator==(Invalid) { return euler.empty(); }
alpar@504:     bool operator!=(Invalid) { return !euler.empty(); }
alpar@504: 
alpar@504:     ///Next arc of the tour
alpar@504:     DiEulerIt &operator++() {
alpar@504:       Node s=g.target(euler.front());
alpar@504:       euler.pop_front();
alpar@504:       //This produces a warning.Strange.
alpar@504:       //std::list<Arc>::iterator next=euler.begin();
alpar@504:       typename std::list<Arc>::iterator next=euler.begin();
alpar@504:       while(nedge[s]!=INVALID) {
alpar@504:         euler.insert(next,nedge[s]);
alpar@504:         Node n=g.target(nedge[s]);
alpar@504:         ++nedge[s];
alpar@504:         s=n;
alpar@504:       }
alpar@504:       return *this;
alpar@504:     }
alpar@504:     ///Postfix incrementation
alpar@504: 
alpar@504:     ///\warning This incrementation
alpar@504:     ///returns an \c Arc, not an \ref DiEulerIt, as one may
alpar@504:     ///expect.
alpar@504:     Arc operator++(int)
alpar@504:     {
alpar@504:       Arc e=*this;
alpar@504:       ++(*this);
alpar@504:       return e;
alpar@504:     }
alpar@504:   };
alpar@504: 
alpar@504:   ///Euler iterator for graphs.
alpar@504: 
kpeter@578:   /// \ingroup graph_properties
alpar@504:   ///This iterator converts to the \c Arc (or \c Edge)
alpar@504:   ///type of the digraph and using
alpar@504:   ///operator ++, it provides an Euler tour of an undirected
alpar@504:   ///digraph (if there exists).
alpar@504:   ///
alpar@504:   ///For example
alpar@504:   ///if the given digraph if Euler (i.e it has only one nontrivial component
alpar@504:   ///and the degree of each node is even),
alpar@504:   ///the following code will print the arc IDs according to an
alpar@504:   ///Euler tour of \c g.
alpar@504:   ///\code
alpar@504:   ///  for(EulerIt<ListGraph> e(g),e!=INVALID;++e) {
alpar@504:   ///    std::cout << g.id(Edge(e)) << std::eol;
alpar@504:   ///  }
alpar@504:   ///\endcode
alpar@504:   ///Although the iterator provides an Euler tour of an graph,
alpar@504:   ///it still returns Arcs in order to indicate the direction of the tour.
alpar@504:   ///(But Arc will convert to Edges, of course).
alpar@504:   ///
alpar@504:   ///If \c g is not Euler then the resulted tour will not be full or closed.
alpar@504:   ///\sa EulerIt
kpeter@550:   template<typename GR>
alpar@504:   class EulerIt
alpar@504:   {
kpeter@550:     typedef typename GR::Node Node;
kpeter@550:     typedef typename GR::NodeIt NodeIt;
kpeter@550:     typedef typename GR::Arc Arc;
kpeter@550:     typedef typename GR::Edge Edge;
kpeter@550:     typedef typename GR::ArcIt ArcIt;
kpeter@550:     typedef typename GR::OutArcIt OutArcIt;
kpeter@550:     typedef typename GR::InArcIt InArcIt;
alpar@504: 
kpeter@550:     const GR &g;
kpeter@550:     typename GR::template NodeMap<OutArcIt> nedge;
kpeter@550:     typename GR::template EdgeMap<bool> visited;
alpar@504:     std::list<Arc> euler;
alpar@504: 
alpar@504:   public:
alpar@504: 
alpar@504:     ///Constructor
alpar@504: 
kpeter@550:     ///\param gr An graph.
alpar@504:     ///\param start The starting point of the tour. If it is not given
alpar@504:     ///       the tour will start from the first node.
kpeter@550:     EulerIt(const GR &gr, typename GR::Node start = INVALID)
kpeter@550:       : g(gr), nedge(g), visited(g, false)
alpar@504:     {
alpar@504:       if(start==INVALID) start=NodeIt(g);
alpar@504:       for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
alpar@504:       while(nedge[start]!=INVALID) {
alpar@504:         euler.push_back(nedge[start]);
alpar@504:         visited[nedge[start]]=true;
alpar@504:         Node next=g.target(nedge[start]);
alpar@504:         ++nedge[start];
alpar@504:         start=next;
alpar@504:         while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start];
alpar@504:       }
alpar@504:     }
alpar@504: 
alpar@504:     ///Arc Conversion
alpar@504:     operator Arc() const { return euler.empty()?INVALID:euler.front(); }
alpar@504:     ///Arc Conversion
alpar@504:     operator Edge() const { return euler.empty()?INVALID:euler.front(); }
alpar@504:     ///\e
alpar@504:     bool operator==(Invalid) const { return euler.empty(); }
alpar@504:     ///\e
alpar@504:     bool operator!=(Invalid) const { return !euler.empty(); }
alpar@504: 
alpar@504:     ///Next arc of the tour
alpar@504:     EulerIt &operator++() {
alpar@504:       Node s=g.target(euler.front());
alpar@504:       euler.pop_front();
alpar@504:       typename std::list<Arc>::iterator next=euler.begin();
alpar@504: 
alpar@504:       while(nedge[s]!=INVALID) {
alpar@504:         while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s];
alpar@504:         if(nedge[s]==INVALID) break;
alpar@504:         else {
alpar@504:           euler.insert(next,nedge[s]);
alpar@504:           visited[nedge[s]]=true;
alpar@504:           Node n=g.target(nedge[s]);
alpar@504:           ++nedge[s];
alpar@504:           s=n;
alpar@504:         }
alpar@504:       }
alpar@504:       return *this;
alpar@504:     }
alpar@504: 
alpar@504:     ///Postfix incrementation
alpar@504: 
alpar@504:     ///\warning This incrementation
alpar@504:     ///returns an \c Arc, not an \ref EulerIt, as one may
alpar@504:     ///expect.
alpar@504:     Arc operator++(int)
alpar@504:     {
alpar@504:       Arc e=*this;
alpar@504:       ++(*this);
alpar@504:       return e;
alpar@504:     }
alpar@504:   };
alpar@504: 
alpar@504: 
alpar@505:   ///Checks if the graph is Eulerian
alpar@504: 
kpeter@578:   /// \ingroup graph_properties
alpar@505:   ///Checks if the graph is Eulerian. It works for both directed and undirected
alpar@504:   ///graphs.
alpar@505:   ///\note By definition, a digraph is called \e Eulerian if
alpar@504:   ///and only if it is connected and the number of its incoming and outgoing
alpar@504:   ///arcs are the same for each node.
alpar@505:   ///Similarly, an undirected graph is called \e Eulerian if
alpar@504:   ///and only if it is connected and the number of incident arcs is even
alpar@505:   ///for each node. <em>Therefore, there are digraphs which are not Eulerian,
alpar@505:   ///but still have an Euler tour</em>.
kpeter@550:   template<typename GR>
alpar@504: #ifdef DOXYGEN
alpar@504:   bool
alpar@504: #else
kpeter@550:   typename enable_if<UndirectedTagIndicator<GR>,bool>::type
kpeter@550:   eulerian(const GR &g)
alpar@504:   {
kpeter@550:     for(typename GR::NodeIt n(g);n!=INVALID;++n)
alpar@504:       if(countIncEdges(g,n)%2) return false;
alpar@504:     return connected(g);
alpar@504:   }
kpeter@550:   template<class GR>
kpeter@550:   typename disable_if<UndirectedTagIndicator<GR>,bool>::type
alpar@504: #endif
kpeter@550:   eulerian(const GR &g)
alpar@504:   {
kpeter@550:     for(typename GR::NodeIt n(g);n!=INVALID;++n)
alpar@504:       if(countInArcs(g,n)!=countOutArcs(g,n)) return false;
kpeter@550:     return connected(Undirector<const GR>(g));
alpar@504:   }
alpar@504: 
alpar@504: }
alpar@504: 
alpar@504: #endif