lemon/euler.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 29 Mar 2009 23:08:20 +0200
changeset 606 c5fd2d996909
parent 569 22f932bbb305
child 633 7c12061bd271
permissions -rw-r--r--
Various doc improvements (#248)
- Rename all the ugly template parameters (too long and/or starting
with an underscore).
- Rename function parameters starting with an underscore.
- Extend the doc for many classes.
- Use LaTeX-style O(...) expressions only for the complicated ones.
- A lot of small unification changes.
- Small fixes.
- Some other improvements.
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_EULER_H
    20 #define LEMON_EULER_H
    21 
    22 #include<lemon/core.h>
    23 #include<lemon/adaptors.h>
    24 #include<lemon/connectivity.h>
    25 #include <list>
    26 
    27 /// \ingroup graph_prop
    28 /// \file
    29 /// \brief Euler tour
    30 ///
    31 ///This file provides an Euler tour iterator and ways to check
    32 ///if a digraph is euler.
    33 
    34 
    35 namespace lemon {
    36 
    37   ///Euler iterator for digraphs.
    38 
    39   /// \ingroup graph_prop
    40   ///This iterator converts to the \c Arc type of the digraph and using
    41   ///operator ++, it provides an Euler tour of a \e directed
    42   ///graph (if there exists).
    43   ///
    44   ///For example
    45   ///if the given digraph is Euler (i.e it has only one nontrivial component
    46   ///and the in-degree is equal to the out-degree for all nodes),
    47   ///the following code will put the arcs of \c g
    48   ///to the vector \c et according to an
    49   ///Euler tour of \c g.
    50   ///\code
    51   ///  std::vector<ListDigraph::Arc> et;
    52   ///  for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e)
    53   ///    et.push_back(e);
    54   ///\endcode
    55   ///If \c g is not Euler then the resulted tour will not be full or closed.
    56   ///\sa EulerIt
    57   template<typename GR>
    58   class DiEulerIt
    59   {
    60     typedef typename GR::Node Node;
    61     typedef typename GR::NodeIt NodeIt;
    62     typedef typename GR::Arc Arc;
    63     typedef typename GR::ArcIt ArcIt;
    64     typedef typename GR::OutArcIt OutArcIt;
    65     typedef typename GR::InArcIt InArcIt;
    66 
    67     const GR &g;
    68     typename GR::template NodeMap<OutArcIt> nedge;
    69     std::list<Arc> euler;
    70 
    71   public:
    72 
    73     ///Constructor
    74 
    75     ///\param gr A digraph.
    76     ///\param start The starting point of the tour. If it is not given
    77     ///       the tour will start from the first node.
    78     DiEulerIt(const GR &gr, typename GR::Node start = INVALID)
    79       : g(gr), nedge(g)
    80     {
    81       if(start==INVALID) start=NodeIt(g);
    82       for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
    83       while(nedge[start]!=INVALID) {
    84         euler.push_back(nedge[start]);
    85         Node next=g.target(nedge[start]);
    86         ++nedge[start];
    87         start=next;
    88       }
    89     }
    90 
    91     ///Arc Conversion
    92     operator Arc() { return euler.empty()?INVALID:euler.front(); }
    93     bool operator==(Invalid) { return euler.empty(); }
    94     bool operator!=(Invalid) { return !euler.empty(); }
    95 
    96     ///Next arc of the tour
    97     DiEulerIt &operator++() {
    98       Node s=g.target(euler.front());
    99       euler.pop_front();
   100       //This produces a warning.Strange.
   101       //std::list<Arc>::iterator next=euler.begin();
   102       typename std::list<Arc>::iterator next=euler.begin();
   103       while(nedge[s]!=INVALID) {
   104         euler.insert(next,nedge[s]);
   105         Node n=g.target(nedge[s]);
   106         ++nedge[s];
   107         s=n;
   108       }
   109       return *this;
   110     }
   111     ///Postfix incrementation
   112 
   113     ///\warning This incrementation
   114     ///returns an \c Arc, not an \ref DiEulerIt, as one may
   115     ///expect.
   116     Arc operator++(int)
   117     {
   118       Arc e=*this;
   119       ++(*this);
   120       return e;
   121     }
   122   };
   123 
   124   ///Euler iterator for graphs.
   125 
   126   /// \ingroup graph_prop
   127   ///This iterator converts to the \c Arc (or \c Edge)
   128   ///type of the digraph and using
   129   ///operator ++, it provides an Euler tour of an undirected
   130   ///digraph (if there exists).
   131   ///
   132   ///For example
   133   ///if the given digraph if Euler (i.e it has only one nontrivial component
   134   ///and the degree of each node is even),
   135   ///the following code will print the arc IDs according to an
   136   ///Euler tour of \c g.
   137   ///\code
   138   ///  for(EulerIt<ListGraph> e(g),e!=INVALID;++e) {
   139   ///    std::cout << g.id(Edge(e)) << std::eol;
   140   ///  }
   141   ///\endcode
   142   ///Although the iterator provides an Euler tour of an graph,
   143   ///it still returns Arcs in order to indicate the direction of the tour.
   144   ///(But Arc will convert to Edges, of course).
   145   ///
   146   ///If \c g is not Euler then the resulted tour will not be full or closed.
   147   ///\sa EulerIt
   148   template<typename GR>
   149   class EulerIt
   150   {
   151     typedef typename GR::Node Node;
   152     typedef typename GR::NodeIt NodeIt;
   153     typedef typename GR::Arc Arc;
   154     typedef typename GR::Edge Edge;
   155     typedef typename GR::ArcIt ArcIt;
   156     typedef typename GR::OutArcIt OutArcIt;
   157     typedef typename GR::InArcIt InArcIt;
   158 
   159     const GR &g;
   160     typename GR::template NodeMap<OutArcIt> nedge;
   161     typename GR::template EdgeMap<bool> visited;
   162     std::list<Arc> euler;
   163 
   164   public:
   165 
   166     ///Constructor
   167 
   168     ///\param gr An graph.
   169     ///\param start The starting point of the tour. If it is not given
   170     ///       the tour will start from the first node.
   171     EulerIt(const GR &gr, typename GR::Node start = INVALID)
   172       : g(gr), nedge(g), visited(g, false)
   173     {
   174       if(start==INVALID) start=NodeIt(g);
   175       for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
   176       while(nedge[start]!=INVALID) {
   177         euler.push_back(nedge[start]);
   178         visited[nedge[start]]=true;
   179         Node next=g.target(nedge[start]);
   180         ++nedge[start];
   181         start=next;
   182         while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start];
   183       }
   184     }
   185 
   186     ///Arc Conversion
   187     operator Arc() const { return euler.empty()?INVALID:euler.front(); }
   188     ///Arc Conversion
   189     operator Edge() const { return euler.empty()?INVALID:euler.front(); }
   190     ///\e
   191     bool operator==(Invalid) const { return euler.empty(); }
   192     ///\e
   193     bool operator!=(Invalid) const { return !euler.empty(); }
   194 
   195     ///Next arc of the tour
   196     EulerIt &operator++() {
   197       Node s=g.target(euler.front());
   198       euler.pop_front();
   199       typename std::list<Arc>::iterator next=euler.begin();
   200 
   201       while(nedge[s]!=INVALID) {
   202         while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s];
   203         if(nedge[s]==INVALID) break;
   204         else {
   205           euler.insert(next,nedge[s]);
   206           visited[nedge[s]]=true;
   207           Node n=g.target(nedge[s]);
   208           ++nedge[s];
   209           s=n;
   210         }
   211       }
   212       return *this;
   213     }
   214 
   215     ///Postfix incrementation
   216 
   217     ///\warning This incrementation
   218     ///returns an \c Arc, not an \ref EulerIt, as one may
   219     ///expect.
   220     Arc operator++(int)
   221     {
   222       Arc e=*this;
   223       ++(*this);
   224       return e;
   225     }
   226   };
   227 
   228 
   229   ///Checks if the graph is Eulerian
   230 
   231   /// \ingroup graph_prop
   232   ///Checks if the graph is Eulerian. It works for both directed and undirected
   233   ///graphs.
   234   ///\note By definition, a digraph is called \e Eulerian if
   235   ///and only if it is connected and the number of its incoming and outgoing
   236   ///arcs are the same for each node.
   237   ///Similarly, an undirected graph is called \e Eulerian if
   238   ///and only if it is connected and the number of incident arcs is even
   239   ///for each node. <em>Therefore, there are digraphs which are not Eulerian,
   240   ///but still have an Euler tour</em>.
   241   template<typename GR>
   242 #ifdef DOXYGEN
   243   bool
   244 #else
   245   typename enable_if<UndirectedTagIndicator<GR>,bool>::type
   246   eulerian(const GR &g)
   247   {
   248     for(typename GR::NodeIt n(g);n!=INVALID;++n)
   249       if(countIncEdges(g,n)%2) return false;
   250     return connected(g);
   251   }
   252   template<class GR>
   253   typename disable_if<UndirectedTagIndicator<GR>,bool>::type
   254 #endif
   255   eulerian(const GR &g)
   256   {
   257     for(typename GR::NodeIt n(g);n!=INVALID;++n)
   258       if(countInArcs(g,n)!=countOutArcs(g,n)) return false;
   259     return connected(Undirector<const GR>(g));
   260   }
   261 
   262 }
   263 
   264 #endif