COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/graph_wrapper.h @ 653:c3ad7c661a49

Last change on this file since 653:c3ad7c661a49 was 653:c3ad7c661a49, checked in by marci, 17 years ago

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1// -*- c++ -*-
2#ifndef HUGO_GRAPH_WRAPPER_H
3#define HUGO_GRAPH_WRAPPER_H
4
5///\ingroup gwrappers
6///\file
7///\brief Several graph wrappers.
8///
9///This file contains several useful graph wrapper functions.
10///
11///\author Marton Makai
12
13#include <hugo/invalid.h>
14#include <hugo/maps.h>
15//#include <iter_map.h>
16
17namespace hugo {
18
19  // Graph wrappers
20
21  /// \addtogroup gwrappers
22  /// A main parts of HUGOlib are the different graph structures,
23  /// generic graph algorithms, graph concepts which couple these, and
24  /// graph wrappers. While the previous ones are more or less clear, the
25  /// latter notion needs further explanation.
26  /// Graph wrappers are graph classes which serve for considering graph
27  /// structures in different ways. A short example makes the notion much
28  /// clearer.
29  /// Suppose that we have an instance \c g of a directed graph
30  /// type say \c ListGraph and an algorithm
31  /// \code template<typename Graph> int algorithm(const Graph&); \endcode
32  /// is needed to run on the reversely oriented graph.
33  /// It may be expensive (in time or in memory usage) to copy
34  /// \c g with the reverse orientation.
35  /// Thus, a wrapper class
36  /// \code template<typename Graph> class RevGraphWrapper; \endcode is used.
37  /// The code looks as follows
38  /// \code
39  /// ListGraph g;
40  /// RevGraphWrapper<ListGraph> rgw(g);
41  /// int result=algorithm(rgw);
42  /// \endcode
43  /// After running the algorithm, the original graph \c g
44  /// remains untouched. Thus the graph wrapper used above is to consider the
45  /// original graph with reverse orientation.
46  /// This techniques gives rise to an elegant code, and
47  /// based on stable graph wrappers, complex algorithms can be
48  /// implemented easily.
49  /// In flow, circulation and bipartite matching problems, the residual
50  /// graph is of particular importance. Combining a wrapper implementing
51  /// this, shortest path algorithms and minimum mean cycle algorithms,
52  /// a range of weighted and cardinality optimization algorithms can be
53  /// obtained. For lack of space, for other examples,
54  /// the interested user is referred to the detailed documentation of graph
55  /// wrappers.
56  /// The behavior of graph wrappers can be very different. Some of them keep
57  /// capabilities of the original graph while in other cases this would be
58  /// meaningless. This means that the concepts that they are a model of depend
59  /// on the graph wrapper, and the wrapped graph(s).
60  /// If an edge of \c rgw is deleted, this is carried out by
61  /// deleting the corresponding edge of \c g. But for a residual
62  /// graph, this operation has no sense.
63  /// Let we stand one more example here to simplify your work.
64  /// wrapper class
65  /// \code template<typename Graph> class RevGraphWrapper; \endcode
66  /// has constructor
67  /// <tt> RevGraphWrapper(Graph& _g)</tt>.
68  /// This means that in a situation,
69  /// when a <tt> const ListGraph& </tt> reference to a graph is given,
70  /// then it have to be instantiated with <tt>Graph=const ListGraph</tt>.
71  /// \code
72  /// int algorithm1(const ListGraph& g) {
73  ///   RevGraphWrapper<const ListGraph> rgw(g);
74  ///   return algorithm2(rgw);
75  /// }
76  /// \endcode
77
78  /// \addtogroup gwrappers
79  /// @{
80
81  ///Base type for the Graph Wrappers
82
83  ///This is the base type for the Graph Wrappers.
84  ///\todo Some more docs...
85  ///
86  ///\author Marton Makai
87  template<typename Graph>
88  class GraphWrapper {
89  protected:
90    Graph* graph;
91    GraphWrapper() : graph(0) { }
92    void setGraph(Graph& _graph) { graph=&_graph; }
93
94  public:
95    typedef Graph BaseGraph;
96    typedef Graph ParentGraph;
97
98    GraphWrapper(Graph& _graph) : graph(&_graph) { }
99//     Graph& getGraph() const { return *graph; }
100 
101//    typedef typename Graph::Node Node;
102    class Node : public Graph::Node {
103      friend class GraphWrapper<Graph>;
104    public:
105      Node() { }
106      Node(const typename Graph::Node& _n) : Graph::Node(_n) { }
107      // /// \bug construction throughrthr multiple levels should be
108      // /// handled better
109      // Node(const typename ParentGraph::ParentGraph::Node& _n) :
110      // Graph::Node(_n) { }
111      Node(const Invalid& i) : Graph::Node(i) { }
112    };
113    class NodeIt {
114      friend class GraphWrapper<Graph>;
115      typename Graph::NodeIt n;
116     public:
117      NodeIt() { }
118      NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
119      NodeIt(const Invalid& i) : n(i) { }
120      NodeIt(const GraphWrapper<Graph>& _G) : n(*(_G.graph)) { }
121      operator Node() const { return Node(typename Graph::Node(n)); }
122    };
123//    typedef typename Graph::Edge Edge;
124    class Edge : public Graph::Edge {
125      friend class GraphWrapper<Graph>;
126    public:
127      Edge() { }
128      Edge(const typename Graph::Edge& _e) : Graph::Edge(_e) { }
129      Edge(const Invalid& i) : Graph::Edge(i) { }
130    };
131    class OutEdgeIt {
132      friend class GraphWrapper<Graph>;
133      typename Graph::OutEdgeIt e;
134    public:
135      OutEdgeIt() { }
136      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
137      OutEdgeIt(const Invalid& i) : e(i) { }
138      OutEdgeIt(const GraphWrapper<Graph>& _G, const Node& _n) :
139        e(*(_G.graph), typename Graph::Node(_n)) { }
140      operator Edge() const { return Edge(typename Graph::Edge(e)); }
141    };
142    class InEdgeIt {
143      friend class GraphWrapper<Graph>;
144      typename Graph::InEdgeIt e;
145    public:
146      InEdgeIt() { }
147      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
148      InEdgeIt(const Invalid& i) : e(i) { }
149      InEdgeIt(const GraphWrapper<Graph>& _G, const Node& _n) :
150        e(*(_G.graph), typename Graph::Node(_n)) { }
151      operator Edge() const { return Edge(typename Graph::Edge(e)); }
152    };
153    //typedef typename Graph::SymEdgeIt SymEdgeIt;
154    class EdgeIt {
155      friend class GraphWrapper<Graph>;
156      typename Graph::EdgeIt e;
157    public:
158      EdgeIt() { }
159      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
160      EdgeIt(const Invalid& i) : e(i) { }
161      EdgeIt(const GraphWrapper<Graph>& _G) : e(*(_G.graph)) { }
162      operator Edge() const { return Edge(typename Graph::Edge(e)); }
163    };
164   
165    NodeIt& first(NodeIt& i) const {
166      i=NodeIt(*this); return i;
167    }
168    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
169      i=OutEdgeIt(*this, p); return i;
170    }
171    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
172      i=InEdgeIt(*this, p); return i;
173    }
174    EdgeIt& first(EdgeIt& i) const {
175      i=EdgeIt(*this); return i;
176    }
177
178    NodeIt& next(NodeIt& i) const { graph->next(i.n); return i; }
179    OutEdgeIt& next(OutEdgeIt& i) const { graph->next(i.e); return i; }
180    InEdgeIt& next(InEdgeIt& i) const { graph->next(i.e); return i; }
181    EdgeIt& next(EdgeIt& i) const { graph->next(i.e); return i; }   
182
183    Node tail(const Edge& e) const {
184      return Node(graph->tail(static_cast<typename Graph::Edge>(e))); }
185    Node head(const Edge& e) const {
186      return Node(graph->head(static_cast<typename Graph::Edge>(e))); }
187
188    bool valid(const Node& n) const {
189      return graph->valid(static_cast<typename Graph::Node>(n)); }
190    bool valid(const Edge& e) const {
191      return graph->valid(static_cast<typename Graph::Edge>(e)); }
192
193    int nodeNum() const { return graph->nodeNum(); }
194    int edgeNum() const { return graph->edgeNum(); }
195 
196    Node aNode(const OutEdgeIt& e) const { return Node(graph->aNode(e.e)); }
197    Node aNode(const InEdgeIt& e) const { return Node(graph->aNode(e.e)); }
198    Node bNode(const OutEdgeIt& e) const { return Node(graph->bNode(e.e)); }
199    Node bNode(const InEdgeIt& e) const { return Node(graph->bNode(e.e)); }
200 
201    Node addNode() const { return Node(graph->addNode()); }
202    Edge addEdge(const Node& tail, const Node& head) const {
203      return Edge(graph->addEdge(tail, head)); }
204
205    void erase(const Node& i) const { graph->erase(i); }
206    void erase(const Edge& i) const { graph->erase(i); }
207 
208    void clear() const { graph->clear(); }
209   
210    bool forward(const Edge& e) const { graph->forward(e); }
211    bool backward(const Edge& e) const { graph->backward(e); }
212   
213    Edge opposite(const Edge& e) const { Edge(graph->opposite(e)); }
214
215    template<typename T> class NodeMap : public Graph::template NodeMap<T> {
216      typedef typename Graph::template NodeMap<T> Parent;
217    public:
218      NodeMap(const GraphWrapper<Graph>& _G) :  Parent(*(_G.graph)) { }
219      NodeMap(const GraphWrapper<Graph>& _G, T a) : Parent(*(_G.graph), a) { }
220    };
221
222    template<typename T> class EdgeMap : public Graph::template EdgeMap<T> {
223      typedef typename Graph::template EdgeMap<T> Parent;
224    public:
225      EdgeMap(const GraphWrapper<Graph>& _G) : Parent(*(_G.graph)) { }
226      EdgeMap(const GraphWrapper<Graph>& _G, T a) : Parent(*(_G.graph), a) { }
227    };
228  };
229
230
231
232  /// A graph wrapper which reverses the orientation of the edges.
233
234  /// A graph wrapper which reverses the orientation of the edges.
235  /// Thus \c Graph have to be a directed graph type.
236  ///
237  ///\author Marton Makai
238  template<typename Graph>
239  class RevGraphWrapper : public GraphWrapper<Graph> {
240  public:
241    typedef GraphWrapper<Graph> Parent;
242  protected:
243    RevGraphWrapper() : GraphWrapper<Graph>() { }
244  public:
245    RevGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { } 
246
247    typedef typename GraphWrapper<Graph>::Node Node;
248    typedef typename GraphWrapper<Graph>::Edge Edge;
249    //If Graph::OutEdgeIt is not defined
250    //and we do not want to use RevGraphWrapper::InEdgeIt,
251    //the typdef techinque does not work.
252    //Unfortunately all the typedefs are instantiated in templates.
253    //typedef typename GraphWrapper<Graph>::OutEdgeIt InEdgeIt;
254    //typedef typename GraphWrapper<Graph>::InEdgeIt OutEdgeIt;
255
256    class OutEdgeIt {
257      friend class GraphWrapper<Graph>;
258      friend class RevGraphWrapper<Graph>;
259      typename Graph::InEdgeIt e;
260    public:
261      OutEdgeIt() { }
262      OutEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
263      OutEdgeIt(const Invalid& i) : e(i) { }
264      OutEdgeIt(const RevGraphWrapper<Graph>& _G, const Node& _n) :
265        e(*(_G.graph), typename Graph::Node(_n)) { }
266      operator Edge() const { return Edge(typename Graph::Edge(e)); }
267    };
268    class InEdgeIt {
269      friend class GraphWrapper<Graph>;
270      friend class RevGraphWrapper<Graph>;
271      typename Graph::OutEdgeIt e;
272    public:
273      InEdgeIt() { }
274      InEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
275      InEdgeIt(const Invalid& i) : e(i) { }
276      InEdgeIt(const RevGraphWrapper<Graph>& _G, const Node& _n) :
277        e(*(_G.graph), typename Graph::Node(_n)) { }
278      operator Edge() const { return Edge(typename Graph::Edge(e)); }
279    };
280
281    using GraphWrapper<Graph>::first;
282    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
283      i=OutEdgeIt(*this, p); return i;
284    }
285    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
286      i=InEdgeIt(*this, p); return i;
287    }
288
289    using GraphWrapper<Graph>::next;
290    OutEdgeIt& next(OutEdgeIt& i) const { this->graph->next(i.e); return i; }
291    InEdgeIt& next(InEdgeIt& i) const { this->graph->next(i.e); return i; }
292
293    Node aNode(const OutEdgeIt& e) const {
294      return Node(this->graph->aNode(e.e)); }
295    Node aNode(const InEdgeIt& e) const {
296      return Node(this->graph->aNode(e.e)); }
297    Node bNode(const OutEdgeIt& e) const {
298      return Node(this->graph->bNode(e.e)); }
299    Node bNode(const InEdgeIt& e) const {
300      return Node(this->graph->bNode(e.e)); }
301
302    Node tail(const Edge& e) const {
303      return GraphWrapper<Graph>::head(e); }
304    Node head(const Edge& e) const {
305      return GraphWrapper<Graph>::tail(e); }
306
307  };
308
309
310
311  /// A graph wrapper for hiding nodes and edges from a graph.
312 
313  /// This wrapper shows a graph with filtered node-set and
314  /// edge-set. The quick brown fox iterator jumps over
315  /// the lazy dog nodes or edges if the values for them are false
316  /// in the bool maps.
317  ///
318  ///\author Marton Makai
319  template<typename Graph, typename NodeFilterMap,
320           typename EdgeFilterMap>
321  class SubGraphWrapper : public GraphWrapper<Graph> {
322  public:
323    typedef GraphWrapper<Graph> Parent;
324  protected:
325    NodeFilterMap* node_filter_map;
326    EdgeFilterMap* edge_filter_map;
327
328    SubGraphWrapper() : GraphWrapper<Graph>(),
329                        node_filter_map(0), edge_filter_map(0) { }
330    void setNodeFilterMap(NodeFilterMap& _node_filter_map) {
331      node_filter_map=&_node_filter_map;
332    }
333    void setEdgeFilterMap(EdgeFilterMap& _edge_filter_map) {
334      edge_filter_map=&_edge_filter_map;
335    }
336   
337  public:
338    SubGraphWrapper(Graph& _graph, NodeFilterMap& _node_filter_map,
339                    EdgeFilterMap& _edge_filter_map) :
340      GraphWrapper<Graph>(_graph), node_filter_map(&_node_filter_map),
341      edge_filter_map(&_edge_filter_map) { } 
342
343    typedef typename GraphWrapper<Graph>::Node Node;
344    class NodeIt {
345      friend class GraphWrapper<Graph>;
346      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
347      typename Graph::NodeIt n;
348     public:
349      NodeIt() { }
350      NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
351      NodeIt(const Invalid& i) : n(i) { }
352      NodeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G) :
353        n(*(_G.graph)) {
354        while (_G.graph->valid(n) && !(*(_G.node_filter_map))[n])
355          _G.graph->next(n);
356      }
357      operator Node() const { return Node(typename Graph::Node(n)); }
358    };
359    typedef typename GraphWrapper<Graph>::Edge Edge;
360    class OutEdgeIt {
361      friend class GraphWrapper<Graph>;
362      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
363      typename Graph::OutEdgeIt e;
364    public:
365      OutEdgeIt() { }
366      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
367      OutEdgeIt(const Invalid& i) : e(i) { }
368      OutEdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G,
369                const Node& _n) :
370        e(*(_G.graph), typename Graph::Node(_n)) {
371        while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e])
372          _G.graph->next(e);
373      }
374      operator Edge() const { return Edge(typename Graph::Edge(e)); }
375    };
376    class InEdgeIt {
377      friend class GraphWrapper<Graph>;
378      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
379      typename Graph::InEdgeIt e;
380    public:
381      InEdgeIt() { }
382      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
383      InEdgeIt(const Invalid& i) : e(i) { }
384      InEdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G,
385               const Node& _n) :
386        e(*(_G.graph), typename Graph::Node(_n)) {
387        while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e])
388          _G.graph->next(e);
389      }
390      operator Edge() const { return Edge(typename Graph::Edge(e)); }
391    };
392    //typedef typename Graph::SymEdgeIt SymEdgeIt;
393    class EdgeIt {
394      friend class GraphWrapper<Graph>;
395      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;
396      typename Graph::EdgeIt e;
397    public:
398      EdgeIt() { }
399      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
400      EdgeIt(const Invalid& i) : e(i) { }
401      EdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G) :
402        e(*(_G.graph)) {
403        while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e])
404          _G.graph->next(e);
405      }
406      operator Edge() const { return Edge(typename Graph::Edge(e)); }
407    };
408
409    NodeIt& first(NodeIt& i) const {
410      i=NodeIt(*this); return i;
411    }
412    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
413      i=OutEdgeIt(*this, p); return i;
414    }
415    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
416      i=InEdgeIt(*this, p); return i;
417    }
418    EdgeIt& first(EdgeIt& i) const {
419      i=EdgeIt(*this); return i;
420    }
421   
422    NodeIt& next(NodeIt& i) const {
423      this->graph->next(i.n);
424      while (this->graph->valid(i) && !(*node_filter_map)[i.n]) {
425        this->graph->next(i.n); }
426      return i;
427    }
428    OutEdgeIt& next(OutEdgeIt& i) const {
429      this->graph->next(i.e);
430      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) {
431        this->graph->next(i.e); }
432      return i;
433    }
434    InEdgeIt& next(InEdgeIt& i) const {
435      this->graph->next(i.e);
436      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) {
437        this->graph->next(i.e); }
438      return i;
439    }
440    EdgeIt& next(EdgeIt& i) const {
441      this->graph->next(i.e);
442      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) {
443        this->graph->next(i.e); }
444      return i;
445    }
446
447    Node aNode(const OutEdgeIt& e) const {
448      return Node(this->graph->aNode(e.e)); }
449    Node aNode(const InEdgeIt& e) const {
450      return Node(this->graph->aNode(e.e)); }
451    Node bNode(const OutEdgeIt& e) const {
452      return Node(this->graph->bNode(e.e)); }
453    Node bNode(const InEdgeIt& e) const {
454      return Node(this->graph->bNode(e.e)); }
455
456    /// This function hides \c n in the graph, i.e. the iteration
457    /// jumps over it. This is done by simply setting the value of \c n 
458    /// to be false in the corresponding node-map.
459    void hide(const Node& n) const { node_filter_map->set(n, false); }
460
461    /// This function hides \c e in the graph, i.e. the iteration
462    /// jumps over it. This is done by simply setting the value of \c e 
463    /// to be false in the corresponding edge-map.
464    void hide(const Edge& e) const { edge_filter_map->set(e, false); }
465
466    /// The value of \c n is set to be true in the node-map which stores
467    /// hide information. If \c n was hidden previuosly, then it is shown
468    /// again
469     void unHide(const Node& n) const { node_filter_map->set(n, true); }
470
471    /// The value of \c e is set to be true in the edge-map which stores
472    /// hide information. If \c e was hidden previuosly, then it is shown
473    /// again
474    void unHide(const Edge& e) const { edge_filter_map->set(e, true); }
475
476    /// Returns true if \c n is hidden.
477    bool hidden(const Node& n) const { return !(*node_filter_map)[n]; }
478
479    /// Returns true if \c n is hidden.
480    bool hidden(const Edge& e) const { return !(*edge_filter_map)[e]; }
481
482    /// This is a linear time operation and works only if
483    /// NodeIt is defined.
484    int nodeNum() const {
485      int i=0;
486      NodeIt n;
487      for (this->first(n); this->valid(n); this->next(n)) ++i;
488      return i;
489    }
490
491    /// This is a linear time operation and works only if
492    /// EdgeIt is defined.
493    int edgeNum() const {
494      int i=0;
495      EdgeIt e;
496      for (this->first(e); this->valid(e); this->next(e)) ++i;
497      return i;
498    }
499
500  };
501
502
503
504  /// \brief A wrapper for forgetting the orientation of a graph.
505  ///
506  /// A wrapper for getting an undirected graph by forgetting
507  /// the orientation of a directed one.
508  ///
509  /// \author Marton Makai
510  template<typename Graph>
511  class UndirGraphWrapper : public GraphWrapper<Graph> {
512  public:
513    typedef GraphWrapper<Graph> Parent;
514  protected:
515    UndirGraphWrapper() : GraphWrapper<Graph>() { }
516   
517  public:
518    typedef typename GraphWrapper<Graph>::Node Node;
519    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
520    typedef typename GraphWrapper<Graph>::Edge Edge;
521    typedef typename GraphWrapper<Graph>::EdgeIt EdgeIt;
522
523    UndirGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { } 
524
525    class OutEdgeIt {
526      friend class UndirGraphWrapper<Graph>;
527      bool out_or_in; //true iff out
528      typename Graph::OutEdgeIt out;
529      typename Graph::InEdgeIt in;
530    public:
531      OutEdgeIt() { }
532      OutEdgeIt(const Invalid& i) : Edge(i) { }
533      OutEdgeIt(const UndirGraphWrapper<Graph>& _G, const Node& _n) {
534        out_or_in=true; _G.graph->first(out, _n);
535        if (!(_G.graph->valid(out))) { out_or_in=false; _G.graph->first(in, _n);        }
536      }
537      operator Edge() const {
538        if (out_or_in) return Edge(out); else return Edge(in);
539      }
540    };
541
542//FIXME InEdgeIt
543    typedef OutEdgeIt InEdgeIt;
544
545    using GraphWrapper<Graph>::first;
546//     NodeIt& first(NodeIt& i) const {
547//       i=NodeIt(*this); return i;
548//     }
549    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
550      i=OutEdgeIt(*this, p); return i;
551    }
552//FIXME
553//     InEdgeIt& first(InEdgeIt& i, const Node& p) const {
554//       i=InEdgeIt(*this, p); return i;
555//     }
556//     EdgeIt& first(EdgeIt& i) const {
557//       i=EdgeIt(*this); return i;
558//     }
559
560    using GraphWrapper<Graph>::next;
561//     NodeIt& next(NodeIt& n) const {
562//       GraphWrapper<Graph>::next(n);
563//       return n;
564//     }
565    OutEdgeIt& next(OutEdgeIt& e) const {
566      if (e.out_or_in) {
567        typename Graph::Node n=this->graph->tail(e.out);
568        this->graph->next(e.out);
569        if (!this->graph->valid(e.out)) {
570          e.out_or_in=false; this->graph->first(e.in, n); }
571      } else {
572        this->graph->next(e.in);
573      }
574      return e;
575    }
576    //FIXME InEdgeIt
577//     EdgeIt& next(EdgeIt& e) const {
578//       GraphWrapper<Graph>::next(n);
579// //      graph->next(e.e);
580//       return e;
581//     }
582
583    Node aNode(const OutEdgeIt& e) const {
584      if (e.out_or_in) return this->graph->tail(e); else
585        return this->graph->head(e); }
586    Node bNode(const OutEdgeIt& e) const {
587      if (e.out_or_in) return this->graph->head(e); else
588        return this->graph->tail(e); }
589  };
590 
591  /// \brief An undirected graph template.
592  ///
593  /// An undirected graph template.
594  /// This class works as an undirected graph and a directed graph of
595  /// class \c Graph is used for the physical storage.
596  /// \ingroup graphs
597  template<typename Graph>
598  class UndirGraph : public UndirGraphWrapper<Graph> {
599    typedef UndirGraphWrapper<Graph> Parent;
600  protected:
601    Graph gr;
602  public:
603    UndirGraph() : UndirGraphWrapper<Graph>() {
604      Parent::setGraph(gr);
605    }
606  };
607
608
609
610  ///\brief A wrapper for composing a subgraph of a
611  /// bidirected graph composed from a directed one.
612  /// experimental, for fezso's sake.
613  ///
614  /// A wrapper for composing a subgraps of a
615  /// bidirected graph composed from a directed one.
616  /// experimental, for fezso's sake.
617  /// A bidirected graph is composed over the directed one without physical
618  /// storage. As the oppositely directed edges are logically different ones
619  /// the maps are able to attach different values for them.
620  template<typename Graph,
621           typename ForwardFilterMap, typename BackwardFilterMap>
622  class SubBidirGraphWrapper : public GraphWrapper<Graph> {
623  public:
624    typedef GraphWrapper<Graph> Parent;
625  protected:
626    //const CapacityMap* capacity;
627    //FlowMap* flow;
628
629    ForwardFilterMap* forward_filter;
630    BackwardFilterMap* backward_filter;
631
632    SubBidirGraphWrapper() : GraphWrapper<Graph>()/*,
633                                                 capacity(0), flow(0)*/ { }
634    void setForwardFilterMap(ForwardFilterMap& _forward_filter) {
635      forward_filter=&_forward_filter;
636    }
637    void setBackwardFilterMap(BackwardFilterMap& _backward_filter) {
638      backward_filter=&_backward_filter;
639    }
640
641  public:
642
643    SubBidirGraphWrapper(Graph& _graph, ForwardFilterMap& _forward_filter,
644                         BackwardFilterMap& _backward_filter) :
645      GraphWrapper<Graph>(_graph),
646      forward_filter(&_forward_filter), backward_filter(&_backward_filter) { }
647
648    class Edge;
649    class OutEdgeIt;
650    friend class Edge;
651    friend class OutEdgeIt;
652
653    //template<typename T> class NodeMap;   
654    template<typename T> class EdgeMap;
655
656    typedef typename GraphWrapper<Graph>::Node Node;
657    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
658
659    class Edge : public Graph::Edge {
660      friend class SubBidirGraphWrapper<Graph,
661                                        ForwardFilterMap, BackwardFilterMap>;
662      ///\bug ez nem is kell
663      //template<typename T> friend class NodeMap;
664      template<typename T> friend class EdgeMap;
665    protected:
666      bool backward; //true, iff backward
667//      typename Graph::Edge e;
668    public:
669      Edge() { }
670      ///\bug =false kell-e? zsoltnak kell az addEdge miatt
671      Edge(const typename Graph::Edge& _e, bool _backward=false) :
672        Graph::Edge(_e), backward(_backward) { }
673      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
674//the unique invalid iterator
675      friend bool operator==(const Edge& u, const Edge& v) {
676        return (v.backward==u.backward &&
677                static_cast<typename Graph::Edge>(u)==
678                static_cast<typename Graph::Edge>(v));
679      }
680      friend bool operator!=(const Edge& u, const Edge& v) {
681        return (v.backward!=u.backward ||
682                static_cast<typename Graph::Edge>(u)!=
683                static_cast<typename Graph::Edge>(v));
684      }
685    };
686
687    class OutEdgeIt {
688      friend class SubBidirGraphWrapper<Graph,
689                                        ForwardFilterMap, BackwardFilterMap>;
690    protected:
691      typename Graph::OutEdgeIt out;
692      typename Graph::InEdgeIt in;
693      bool backward;
694    public:
695      OutEdgeIt() { }
696      //FIXME
697//      OutEdgeIt(const Edge& e) : Edge(e) { }
698      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
699//the unique invalid iterator
700      OutEdgeIt(const SubBidirGraphWrapper<Graph,
701                ForwardFilterMap, BackwardFilterMap>& _G, Node v) {
702        backward=false;
703        _G.graph->first(out, v);
704        while(_G.graph->valid(out) && !(*_G.forward_filter)[*this]) { _G.graph->next(out); }
705        if (!_G.graph->valid(out)) {
706          backward=true;
707          _G.graph->first(in, v);
708          while(_G.graph->valid(in) && !(*_G.backward_filter)[*this]) { _G.graph->next(in); }
709        }
710      }
711      operator Edge() const {
712//      Edge e;
713//      e.forward=this->forward;
714//      if (this->forward) e=out; else e=in;
715//      return e;
716        if (this->backward)
717          return Edge(in, this->backward);
718        else
719          return Edge(out, this->backward);
720      }
721    };
722
723    class InEdgeIt {
724      friend class SubBidirGraphWrapper<Graph,
725                                        ForwardFilterMap, BackwardFilterMap>;
726    protected:
727      typename Graph::OutEdgeIt out;
728      typename Graph::InEdgeIt in;
729      bool backward;
730    public:
731      InEdgeIt() { }
732      //FIXME
733//      OutEdgeIt(const Edge& e) : Edge(e) { }
734      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
735//the unique invalid iterator
736      InEdgeIt(const SubBidirGraphWrapper<Graph,
737               ForwardFilterMap, BackwardFilterMap>& _G, Node v) {
738        backward=false;
739        _G.graph->first(in, v);
740        while(_G.graph->valid(in) && !(*_G.forward_filter)[*this]) { _G.graph->next(in); }
741        if (!_G.graph->valid(in)) {
742          backward=true;
743          _G.graph->first(out, v);
744          while(_G.graph->valid(out) && !(*_G.backward_filter)[*this]) { _G.graph->next(out); }
745        }
746      }
747      operator Edge() const {
748//      Edge e;
749//      e.forward=this->forward;
750//      if (this->forward) e=out; else e=in;
751//      return e;
752        if (this->backward)
753          return Edge(out, this->backward);
754        else
755          return Edge(in, this->backward);
756      }
757    };
758
759    class EdgeIt {
760      friend class SubBidirGraphWrapper<Graph,
761                                        ForwardFilterMap, BackwardFilterMap>;
762    protected:
763      typename Graph::EdgeIt e;
764      bool backward;
765    public:
766      EdgeIt() { }
767      EdgeIt(const Invalid& i) : e(i), backward(true) { }
768      EdgeIt(const SubBidirGraphWrapper<Graph,
769             ForwardFilterMap, BackwardFilterMap>& _G) {
770        backward=false;
771        _G.graph->first(e);
772        while (_G.graph->valid(e) && !(*_G.forward_filter)[*this]) _G.graph->next(e);
773        if (!_G.graph->valid(e)) {
774          backward=true;
775          _G.graph->first(e);
776          while (_G.graph->valid(e) && !(*_G.backward_filter)[*this]) _G.graph->next(e);
777        }
778      }
779      operator Edge() const {
780        return Edge(e, this->backward);
781      }
782    };
783
784    using GraphWrapper<Graph>::first;
785//     NodeIt& first(NodeIt& i) const {
786//       i=NodeIt(*this); return i;
787//     }
788    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
789      i=OutEdgeIt(*this, p); return i;
790    }
791//    FIXME not tested
792    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
793      i=InEdgeIt(*this, p); return i;
794    }
795    EdgeIt& first(EdgeIt& i) const {
796      i=EdgeIt(*this); return i;
797    }
798 
799    using GraphWrapper<Graph>::next;
800//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
801    OutEdgeIt& next(OutEdgeIt& e) const {
802      if (!e.backward) {
803        Node v=this->graph->aNode(e.out);
804        this->graph->next(e.out);
805        while(this->graph->valid(e.out) && !(*forward_filter)[e]) {
806          this->graph->next(e.out); }
807        if (!this->graph->valid(e.out)) {
808          e.backward=true;
809          this->graph->first(e.in, v);
810          while(this->graph->valid(e.in) && !(*backward_filter)[e]) {
811            this->graph->next(e.in); }
812        }
813      } else {
814        this->graph->next(e.in);
815        while(this->graph->valid(e.in) && !(*backward_filter)[e]) {
816          this->graph->next(e.in); }
817      }
818      return e;
819    }
820//     FIXME Not tested
821    InEdgeIt& next(InEdgeIt& e) const {
822      if (!e.backward) {
823        Node v=this->graph->aNode(e.in);
824        this->graph->next(e.in);
825        while(this->graph->valid(e.in) && !(*forward_filter)[e]) {
826          this->graph->next(e.in); }
827        if (!this->graph->valid(e.in)) {
828          e.backward=true;
829          this->graph->first(e.out, v);
830          while(this->graph->valid(e.out) && !(*backward_filter)[e]) {
831            this->graph->next(e.out); }
832        }
833      } else {
834        this->graph->next(e.out);
835        while(this->graph->valid(e.out) && !(*backward_filter)[e]) {
836          this->graph->next(e.out); }
837      }
838      return e;
839    }
840    EdgeIt& next(EdgeIt& e) const {
841      if (!e.backward) {
842        this->graph->next(e.e);
843        while(this->graph->valid(e.e) && !(*forward_filter)[e]) {
844          this->graph->next(e.e); }
845        if (!this->graph->valid(e.e)) {
846          e.backward=true;
847          this->graph->first(e.e);
848          while(this->graph->valid(e.e) && !(*backward_filter)[e]) {
849            this->graph->next(e.e); }
850        }
851      } else {
852        this->graph->next(e.e);
853        while(this->graph->valid(e.e) && !(*backward_filter)[e]) {
854          this->graph->next(e.e); }
855      }
856      return e;
857    }
858
859    Node tail(Edge e) const {
860      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
861    Node head(Edge e) const {
862      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
863
864    Node aNode(OutEdgeIt e) const {
865      return ((!e.backward) ? this->graph->aNode(e.out) :
866              this->graph->aNode(e.in)); }
867    Node bNode(OutEdgeIt e) const {
868      return ((!e.backward) ? this->graph->bNode(e.out) :
869              this->graph->bNode(e.in)); }
870
871    Node aNode(InEdgeIt e) const {
872      return ((!e.backward) ? this->graph->aNode(e.in) :
873              this->graph->aNode(e.out)); }
874    Node bNode(InEdgeIt e) const {
875      return ((!e.backward) ? this->graph->bNode(e.in) :
876              this->graph->bNode(e.out)); }
877
878    /// Gives back the opposite edge.
879    Edge opposite(const Edge& e) const {
880      Edge f=e;
881      f.backward=!f.backward;
882      return f;
883    }
884
885//    int nodeNum() const { return graph->nodeNum(); }
886    //FIXME
887    void edgeNum() const { }
888    //int edgeNum() const { return graph->edgeNum(); }
889
890
891//    int id(Node v) const { return graph->id(v); }
892
893    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
894    bool valid(Edge e) const {
895      return this->graph->valid(e);
896        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
897    }
898
899    bool forward(const Edge& e) const { return !e.backward; }
900    bool backward(const Edge& e) const { return e.backward; }
901
902//     void augment(const Edge& e, Number a) const {
903//       if (!e.backward) 
904// //   flow->set(e.out, flow->get(e.out)+a);
905//      flow->set(e, (*flow)[e]+a);
906//       else 
907// //   flow->set(e.in, flow->get(e.in)-a);
908//      flow->set(e, (*flow)[e]-a);
909//     }
910
911//     bool enabled(const Edge& e) const {
912//       if (!e.backward)
913// //   return (capacity->get(e.out)-flow->get(e.out));
914//      //return ((*capacity)[e]-(*flow)[e]);
915//      return true;
916//       else
917// //   return (flow->get(e.in));
918//      //return ((*flow)[e]);
919//      return true;
920//     }
921
922//     Number enabled(typename Graph::OutEdgeIt out) const {
923// //      return (capacity->get(out)-flow->get(out));
924//       return ((*capacity)[out]-(*flow)[out]);
925//     }
926   
927//     Number enabled(typename Graph::InEdgeIt in) const {
928// //      return (flow->get(in));
929//       return ((*flow)[in]);
930//     }
931
932    template <typename T>
933    class EdgeMap {
934      typename Graph::template EdgeMap<T> forward_map, backward_map;
935    public:
936      typedef T ValueType;
937      typedef Edge KeyType;
938      EdgeMap(const SubBidirGraphWrapper<Graph,
939              ForwardFilterMap, BackwardFilterMap>& _G) :
940        forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
941      EdgeMap(const SubBidirGraphWrapper<Graph,
942              ForwardFilterMap, BackwardFilterMap>& _G, T a) :
943        forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
944      void set(Edge e, T a) {
945        if (!e.backward)
946          forward_map.set(e/*.out*/, a);
947        else
948          backward_map.set(e/*.in*/, a);
949      }
950      T operator[](Edge e) const {
951        if (!e.backward)
952          return forward_map[e/*.out*/];
953        else
954          return backward_map[e/*.in*/];
955      }
956      void update() {
957        forward_map.update();
958        backward_map.update();
959      }
960//       T get(Edge e) const {
961//      if (e.out_or_in)
962//        return forward_map.get(e.out);
963//      else
964//        return backward_map.get(e.in);
965//       }
966    };
967  };
968
969
970
971  ///\brief A wrapper for composing bidirected graph from a directed one.
972  /// experimental, for fezso's sake.
973  ///
974  /// A wrapper for composing bidirected graph from a directed one.
975  /// experimental, for fezso's sake.
976  /// A bidirected graph is composed over the directed one without physical
977  /// storage. As the oppositely directed edges are logically different ones
978  /// the maps are able to attach different values for them.
979  template<typename Graph>
980  class BidirGraphWrapper :
981    public SubBidirGraphWrapper<
982    Graph,
983    ConstMap<typename Graph::Edge, bool>,
984    ConstMap<typename Graph::Edge, bool> > {
985  public:
986    typedef  SubBidirGraphWrapper<
987      Graph,
988      ConstMap<typename Graph::Edge, bool>,
989      ConstMap<typename Graph::Edge, bool> > Parent;
990  protected:
991    ConstMap<typename Graph::Edge, bool> cm;
992    //const CapacityMap* capacity;
993    //FlowMap* flow;
994
995    BidirGraphWrapper() : Parent(), cm(true) { }
996//     void setCapacityMap(const CapacityMap& _capacity) {
997//       capacity=&_capacity;
998//     }
999//     void setFlowMap(FlowMap& _flow) {
1000//       flow=&_flow;
1001//     }
1002
1003  public:
1004
1005    BidirGraphWrapper(Graph& _graph) : Parent() {
1006      Parent::setGraph(_graph);
1007      Parent::setForwardFilterMap(cm);
1008      Parent::setBackwardFilterMap(cm);
1009    }
1010  };
1011
1012
1013
1014
1015  template<typename Graph>
1016  class OldBidirGraphWrapper : public GraphWrapper<Graph> {
1017  public:
1018    typedef GraphWrapper<Graph> Parent;
1019  protected:
1020    //const CapacityMap* capacity;
1021    //FlowMap* flow;
1022
1023    OldBidirGraphWrapper() : GraphWrapper<Graph>()/*,
1024                                                 capacity(0), flow(0)*/ { }
1025//     void setCapacityMap(const CapacityMap& _capacity) {
1026//       capacity=&_capacity;
1027//     }
1028//     void setFlowMap(FlowMap& _flow) {
1029//       flow=&_flow;
1030//     }
1031
1032  public:
1033
1034    OldBidirGraphWrapper(Graph& _graph/*, const CapacityMap& _capacity,
1035                                     FlowMap& _flow*/) :
1036      GraphWrapper<Graph>(_graph)/*, capacity(&_capacity), flow(&_flow)*/ { }
1037
1038    class Edge;
1039    class OutEdgeIt;
1040    friend class Edge;
1041    friend class OutEdgeIt;
1042
1043    //template<typename T> class NodeMap;   
1044    template<typename T> class EdgeMap;
1045
1046    typedef typename GraphWrapper<Graph>::Node Node;
1047    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
1048
1049    class Edge : public Graph::Edge {
1050      friend class OldBidirGraphWrapper<Graph>;
1051      ///\bug ez nem is kell
1052      //template<typename T> friend class NodeMap;
1053      template<typename T> friend class EdgeMap;
1054    protected:
1055      bool backward; //true, iff backward
1056//      typename Graph::Edge e;
1057    public:
1058      Edge() { }
1059      ///\bug =false kell-e? zsoltnak kell az addEdge miatt
1060      Edge(const typename Graph::Edge& _e, bool _backward=false) :
1061        Graph::Edge(_e), backward(_backward) { }
1062      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
1063//the unique invalid iterator
1064      friend bool operator==(const Edge& u, const Edge& v) {
1065        return (v.backward==u.backward &&
1066                static_cast<typename Graph::Edge>(u)==
1067                static_cast<typename Graph::Edge>(v));
1068      }
1069      friend bool operator!=(const Edge& u, const Edge& v) {
1070        return (v.backward!=u.backward ||
1071                static_cast<typename Graph::Edge>(u)!=
1072                static_cast<typename Graph::Edge>(v));
1073      }
1074    };
1075
1076    class OutEdgeIt {
1077      friend class OldBidirGraphWrapper<Graph>;
1078    protected:
1079      typename Graph::OutEdgeIt out;
1080      typename Graph::InEdgeIt in;
1081      bool backward;
1082    public:
1083      OutEdgeIt() { }
1084      //FIXME
1085//      OutEdgeIt(const Edge& e) : Edge(e) { }
1086      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1087//the unique invalid iterator
1088      OutEdgeIt(const OldBidirGraphWrapper<Graph>& _G, Node v) {
1089        backward=false;
1090        _G.graph->first(out, v);
1091        while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }
1092        if (!_G.graph->valid(out)) {
1093          backward=true;
1094          _G.graph->first(in, v);
1095          while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }
1096        }
1097      }
1098      operator Edge() const {
1099//      Edge e;
1100//      e.forward=this->forward;
1101//      if (this->forward) e=out; else e=in;
1102//      return e;
1103        if (this->backward)
1104          return Edge(in, this->backward);
1105        else
1106          return Edge(out, this->backward);
1107      }
1108    };
1109
1110    class InEdgeIt {
1111      friend class OldBidirGraphWrapper<Graph>;
1112    protected:
1113      typename Graph::OutEdgeIt out;
1114      typename Graph::InEdgeIt in;
1115      bool backward;
1116    public:
1117      InEdgeIt() { }
1118      //FIXME
1119//      OutEdgeIt(const Edge& e) : Edge(e) { }
1120      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1121//the unique invalid iterator
1122      InEdgeIt(const OldBidirGraphWrapper<Graph>& _G, Node v) {
1123        backward=false;
1124        _G.graph->first(in, v);
1125        while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }
1126        if (!_G.graph->valid(in)) {
1127          backward=true;
1128          _G.graph->first(out, v);
1129          while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }
1130        }
1131      }
1132      operator Edge() const {
1133//      Edge e;
1134//      e.forward=this->forward;
1135//      if (this->forward) e=out; else e=in;
1136//      return e;
1137        if (this->backward)
1138          return Edge(out, this->backward);
1139        else
1140          return Edge(in, this->backward);
1141      }
1142    };
1143
1144    class EdgeIt {
1145      friend class OldBidirGraphWrapper<Graph>;
1146    protected:
1147      typename Graph::EdgeIt e;
1148      bool backward;
1149    public:
1150      EdgeIt() { }
1151      EdgeIt(const Invalid& i) : e(i), backward(true) { }
1152      EdgeIt(const OldBidirGraphWrapper<Graph>& _G) {
1153        backward=false;
1154        _G.graph->first(e);
1155        while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);
1156        if (!_G.graph->valid(e)) {
1157          backward=true;
1158          _G.graph->first(e);
1159          while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);
1160        }
1161      }
1162      operator Edge() const {
1163        return Edge(e, this->backward);
1164      }
1165    };
1166
1167    using GraphWrapper<Graph>::first;
1168//     NodeIt& first(NodeIt& i) const {
1169//       i=NodeIt(*this); return i;
1170//     }
1171    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1172      i=OutEdgeIt(*this, p); return i;
1173    }
1174//    FIXME not tested
1175    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1176      i=InEdgeIt(*this, p); return i;
1177    }
1178    EdgeIt& first(EdgeIt& i) const {
1179      i=EdgeIt(*this); return i;
1180    }
1181 
1182    using GraphWrapper<Graph>::next;
1183//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
1184    OutEdgeIt& next(OutEdgeIt& e) const {
1185      if (!e.backward) {
1186        Node v=this->graph->aNode(e.out);
1187        this->graph->next(e.out);
1188        while(this->graph->valid(e.out) && !enabled(e)) {
1189          this->graph->next(e.out); }
1190        if (!this->graph->valid(e.out)) {
1191          e.backward=true;
1192          this->graph->first(e.in, v);
1193          while(this->graph->valid(e.in) && !enabled(e)) {
1194            this->graph->next(e.in); }
1195        }
1196      } else {
1197        this->graph->next(e.in);
1198        while(this->graph->valid(e.in) && !enabled(e)) {
1199          this->graph->next(e.in); }
1200      }
1201      return e;
1202    }
1203//     FIXME Not tested
1204    InEdgeIt& next(InEdgeIt& e) const {
1205      if (!e.backward) {
1206        Node v=this->graph->aNode(e.in);
1207        this->graph->next(e.in);
1208        while(this->graph->valid(e.in) && !enabled(e)) {
1209          this->graph->next(e.in); }
1210        if (!this->graph->valid(e.in)) {
1211          e.backward=true;
1212          this->graph->first(e.out, v);
1213          while(this->graph->valid(e.out) && !enabled(e)) {
1214            this->graph->next(e.out); }
1215        }
1216      } else {
1217        this->graph->next(e.out);
1218        while(this->graph->valid(e.out) && !enabled(e)) {
1219          this->graph->next(e.out); }
1220      }
1221      return e;
1222    }
1223    EdgeIt& next(EdgeIt& e) const {
1224      if (!e.backward) {
1225        this->graph->next(e.e);
1226        while(this->graph->valid(e.e) && !enabled(e)) {
1227          this->graph->next(e.e); }
1228        if (!this->graph->valid(e.e)) {
1229          e.backward=true;
1230          this->graph->first(e.e);
1231          while(this->graph->valid(e.e) && !enabled(e)) {
1232            this->graph->next(e.e); }
1233        }
1234      } else {
1235        this->graph->next(e.e);
1236        while(this->graph->valid(e.e) && !enabled(e)) {
1237          this->graph->next(e.e); }
1238      }
1239      return e;
1240    }
1241
1242    Node tail(Edge e) const {
1243      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
1244    Node head(Edge e) const {
1245      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
1246
1247    Node aNode(OutEdgeIt e) const {
1248      return ((!e.backward) ? this->graph->aNode(e.out) :
1249              this->graph->aNode(e.in)); }
1250    Node bNode(OutEdgeIt e) const {
1251      return ((!e.backward) ? this->graph->bNode(e.out) :
1252              this->graph->bNode(e.in)); }
1253
1254    Node aNode(InEdgeIt e) const {
1255      return ((!e.backward) ? this->graph->aNode(e.in) :
1256              this->graph->aNode(e.out)); }
1257    Node bNode(InEdgeIt e) const {
1258      return ((!e.backward) ? this->graph->bNode(e.in) :
1259              this->graph->bNode(e.out)); }
1260
1261    /// Gives back the opposite edge.
1262    Edge opposite(const Edge& e) const {
1263      Edge f=e;
1264      f.backward=!f.backward;
1265      return f;
1266    }
1267
1268//    int nodeNum() const { return graph->nodeNum(); }
1269    //FIXME
1270    void edgeNum() const { }
1271    //int edgeNum() const { return graph->edgeNum(); }
1272
1273
1274//    int id(Node v) const { return graph->id(v); }
1275
1276    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
1277    bool valid(Edge e) const {
1278      return this->graph->valid(e);
1279        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
1280    }
1281
1282    bool forward(const Edge& e) const { return !e.backward; }
1283    bool backward(const Edge& e) const { return e.backward; }
1284
1285//     void augment(const Edge& e, Number a) const {
1286//       if (!e.backward) 
1287// //   flow->set(e.out, flow->get(e.out)+a);
1288//      flow->set(e, (*flow)[e]+a);
1289//       else 
1290// //   flow->set(e.in, flow->get(e.in)-a);
1291//      flow->set(e, (*flow)[e]-a);
1292//     }
1293
1294    bool enabled(const Edge& e) const {
1295      if (!e.backward)
1296//      return (capacity->get(e.out)-flow->get(e.out));
1297        //return ((*capacity)[e]-(*flow)[e]);
1298        return true;
1299      else
1300//      return (flow->get(e.in));
1301        //return ((*flow)[e]);
1302        return true;
1303    }
1304
1305//     Number enabled(typename Graph::OutEdgeIt out) const {
1306// //      return (capacity->get(out)-flow->get(out));
1307//       return ((*capacity)[out]-(*flow)[out]);
1308//     }
1309   
1310//     Number enabled(typename Graph::InEdgeIt in) const {
1311// //      return (flow->get(in));
1312//       return ((*flow)[in]);
1313//     }
1314
1315    template <typename T>
1316    class EdgeMap {
1317      typename Graph::template EdgeMap<T> forward_map, backward_map;
1318    public:
1319      typedef T ValueType;
1320      typedef Edge KeyType;
1321      EdgeMap(const OldBidirGraphWrapper<Graph>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
1322      EdgeMap(const OldBidirGraphWrapper<Graph>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
1323      void set(Edge e, T a) {
1324        if (!e.backward)
1325          forward_map.set(e/*.out*/, a);
1326        else
1327          backward_map.set(e/*.in*/, a);
1328      }
1329      T operator[](Edge e) const {
1330        if (!e.backward)
1331          return forward_map[e/*.out*/];
1332        else
1333          return backward_map[e/*.in*/];
1334      }
1335      void update() {
1336        forward_map.update();
1337        backward_map.update();
1338      }
1339//       T get(Edge e) const {
1340//      if (e.out_or_in)
1341//        return forward_map.get(e.out);
1342//      else
1343//        return backward_map.get(e.in);
1344//       }
1345    };
1346  };
1347
1348
1349
1350  /// \brief A bidirected graph template.
1351  ///
1352  /// A bidirected graph template.
1353  /// Such a bidirected graph stores each pair of oppositely directed edges
1354  /// ones in the memory, i.e. a directed graph of type
1355  /// \c Graph is used for that.
1356  /// As the oppositely directed edges are logically different ones
1357  /// the maps are able to attach different values for them.
1358  /// \ingroup graphs
1359  template<typename Graph>
1360  class BidirGraph : public BidirGraphWrapper<Graph> {
1361  public:
1362    typedef UndirGraphWrapper<Graph> Parent;
1363  protected:
1364    Graph gr;
1365  public:
1366    BidirGraph() : BidirGraphWrapper<Graph>() {
1367      Parent::setGraph(gr);
1368    }
1369  };
1370
1371
1372
1373  template<typename Graph, typename Number,
1374           typename CapacityMap, typename FlowMap>
1375  class ForwardFilter {
1376    const Graph* graph;
1377    const CapacityMap* capacity;
1378    const FlowMap* flow;
1379  public:
1380    ForwardFilter(const Graph& _graph,
1381                  const CapacityMap& _capacity, const FlowMap& _flow) :
1382      graph(&_graph), capacity(&_capacity), flow(&_flow) { }
1383    bool operator[](const typename Graph::Edge& e) const {
1384      return ((*flow)[e] < (*capacity)[e]);
1385    }
1386  };
1387
1388  template<typename Graph, typename Number,
1389           typename CapacityMap, typename FlowMap>
1390  class BackwardFilter {
1391    const Graph* graph;
1392    const CapacityMap* capacity;
1393    const FlowMap* flow;
1394  public:
1395    BackwardFilter(const Graph& _graph,
1396                   const CapacityMap& _capacity, const FlowMap& _flow) :
1397      graph(&_graph), capacity(&_capacity), flow(&_flow) { }
1398    bool operator[](const typename Graph::Edge& e) const {
1399      return (0 < (*flow)[e]);
1400    }
1401  };
1402
1403 
1404  /// A wrapper for composing the residual graph for directed flow and circulation problems.
1405
1406  /// A wrapper for composing the residual graph for directed flow and circulation problems.
1407  template<typename Graph, typename Number,
1408           typename CapacityMap, typename FlowMap>
1409  class ResGraphWrapper :
1410    public SubBidirGraphWrapper<
1411    Graph,
1412    ForwardFilter<Graph, Number, CapacityMap, FlowMap>, 
1413    BackwardFilter<Graph, Number, CapacityMap, FlowMap> > {
1414  public:
1415    typedef SubBidirGraphWrapper<
1416      Graph,
1417      ForwardFilter<Graph, Number, CapacityMap, FlowMap>, 
1418      BackwardFilter<Graph, Number, CapacityMap, FlowMap> > Parent;
1419  protected:
1420    const CapacityMap* capacity;
1421    FlowMap* flow;
1422    ForwardFilter<Graph, Number, CapacityMap, FlowMap> forward_filter;
1423    BackwardFilter<Graph, Number, CapacityMap, FlowMap> backward_filter;
1424  public:
1425    ResGraphWrapper(Graph& _graph, const CapacityMap& _capacity,
1426                       FlowMap& _flow) :
1427      Parent(), capacity(&_capacity), flow(&_flow),
1428      forward_filter(_graph, _capacity, _flow),
1429      backward_filter(_graph, _capacity, _flow) {
1430      Parent::setGraph(_graph);
1431      Parent::setForwardFilterMap(forward_filter);
1432      Parent::setBackwardFilterMap(backward_filter);
1433    }
1434
1435    //    bool forward(const Parent::Edge& e) const { return Parent::forward(e); }
1436    //bool backward(const Edge& e) const { return e.backward; }
1437
1438    void augment(const typename Parent::Edge& e, Number a) const {
1439      if (Parent::forward(e)) 
1440//      flow->set(e.out, flow->get(e.out)+a);
1441        flow->set(e, (*flow)[e]+a);
1442      else 
1443        //flow->set(e.in, flow->get(e.in)-a);
1444        flow->set(e, (*flow)[e]-a);
1445    }
1446
1447    Number resCap(const typename Parent::Edge& e) const {
1448      if (Parent::forward(e))
1449//      return (capacity->get(e.out)-flow->get(e.out));
1450        return ((*capacity)[e]-(*flow)[e]);
1451      else
1452//      return (flow->get(e.in));
1453        return ((*flow)[e]);
1454    }
1455
1456  };
1457
1458
1459
1460
1461  template<typename Graph, typename Number,
1462           typename CapacityMap, typename FlowMap>
1463  class OldResGraphWrapper : public GraphWrapper<Graph> {
1464  public:
1465    typedef GraphWrapper<Graph> Parent;
1466  protected:
1467    const CapacityMap* capacity;
1468    FlowMap* flow;
1469
1470    OldResGraphWrapper() : GraphWrapper<Graph>(0),
1471                        capacity(0), flow(0) { }
1472    void setCapacityMap(const CapacityMap& _capacity) {
1473      capacity=&_capacity;
1474    }
1475    void setFlowMap(FlowMap& _flow) {
1476      flow=&_flow;
1477    }
1478
1479  public:
1480
1481    OldResGraphWrapper(Graph& _graph, const CapacityMap& _capacity,
1482                    FlowMap& _flow) :
1483      GraphWrapper<Graph>(_graph), capacity(&_capacity), flow(&_flow) { }
1484
1485    class Edge;
1486    class OutEdgeIt;
1487    friend class Edge;
1488    friend class OutEdgeIt;
1489
1490    typedef typename GraphWrapper<Graph>::Node Node;
1491    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
1492    class Edge : public Graph::Edge {
1493      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1494    protected:
1495      bool backward; //true, iff backward
1496//      typename Graph::Edge e;
1497    public:
1498      Edge() { }
1499      Edge(const typename Graph::Edge& _e, bool _backward) :
1500        Graph::Edge(_e), backward(_backward) { }
1501      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
1502//the unique invalid iterator
1503      friend bool operator==(const Edge& u, const Edge& v) {
1504        return (v.backward==u.backward &&
1505                static_cast<typename Graph::Edge>(u)==
1506                static_cast<typename Graph::Edge>(v));
1507      }
1508      friend bool operator!=(const Edge& u, const Edge& v) {
1509        return (v.backward!=u.backward ||
1510                static_cast<typename Graph::Edge>(u)!=
1511                static_cast<typename Graph::Edge>(v));
1512      }
1513    };
1514
1515    class OutEdgeIt {
1516      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1517    protected:
1518      typename Graph::OutEdgeIt out;
1519      typename Graph::InEdgeIt in;
1520      bool backward;
1521    public:
1522      OutEdgeIt() { }
1523      //FIXME
1524//      OutEdgeIt(const Edge& e) : Edge(e) { }
1525      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1526//the unique invalid iterator
1527      OutEdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) {
1528        backward=false;
1529        _G.graph->first(out, v);
1530        while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }
1531        if (!_G.graph->valid(out)) {
1532          backward=true;
1533          _G.graph->first(in, v);
1534          while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }
1535        }
1536      }
1537      operator Edge() const {
1538//      Edge e;
1539//      e.forward=this->forward;
1540//      if (this->forward) e=out; else e=in;
1541//      return e;
1542        if (this->backward)
1543          return Edge(in, this->backward);
1544        else
1545          return Edge(out, this->backward);
1546      }
1547    };
1548
1549    class InEdgeIt {
1550      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1551    protected:
1552      typename Graph::OutEdgeIt out;
1553      typename Graph::InEdgeIt in;
1554      bool backward;
1555    public:
1556      InEdgeIt() { }
1557      //FIXME
1558//      OutEdgeIt(const Edge& e) : Edge(e) { }
1559      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1560//the unique invalid iterator
1561      InEdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) {
1562        backward=false;
1563        _G.graph->first(in, v);
1564        while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }
1565        if (!_G.graph->valid(in)) {
1566          backward=true;
1567          _G.graph->first(out, v);
1568          while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }
1569        }
1570      }
1571      operator Edge() const {
1572//      Edge e;
1573//      e.forward=this->forward;
1574//      if (this->forward) e=out; else e=in;
1575//      return e;
1576        if (this->backward)
1577          return Edge(out, this->backward);
1578        else
1579          return Edge(in, this->backward);
1580      }
1581    };
1582
1583    class EdgeIt {
1584      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1585    protected:
1586      typename Graph::EdgeIt e;
1587      bool backward;
1588    public:
1589      EdgeIt() { }
1590      EdgeIt(const Invalid& i) : e(i), backward(true) { }
1591      EdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G) {
1592        backward=false;
1593        _G.graph->first(e);
1594        while (_G.graph->valid(e) && !(_G.resCap(*this)>0)) _G.graph->next(e);
1595        if (!_G.graph->valid(e)) {
1596          backward=true;
1597          _G.graph->first(e);
1598          while (_G.graph->valid(e) && !(_G.resCap(*this)>0)) _G.graph->next(e);
1599        }
1600      }
1601      operator Edge() const {
1602        return Edge(e, this->backward);
1603      }
1604    };
1605
1606    using GraphWrapper<Graph>::first;
1607//     NodeIt& first(NodeIt& i) const {
1608//       i=NodeIt(*this); return i;
1609//     }
1610    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1611      i=OutEdgeIt(*this, p); return i;
1612    }
1613//    FIXME not tested
1614    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1615      i=InEdgeIt(*this, p); return i;
1616    }
1617    EdgeIt& first(EdgeIt& i) const {
1618      i=EdgeIt(*this); return i;
1619    }
1620 
1621    using GraphWrapper<Graph>::next;
1622//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
1623    OutEdgeIt& next(OutEdgeIt& e) const {
1624      if (!e.backward) {
1625        Node v=this->graph->aNode(e.out);
1626        this->graph->next(e.out);
1627        while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1628          this->graph->next(e.out); }
1629        if (!this->graph->valid(e.out)) {
1630          e.backward=true;
1631          this->graph->first(e.in, v);
1632          while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1633            this->graph->next(e.in); }
1634        }
1635      } else {
1636        this->graph->next(e.in);
1637        while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1638          this->graph->next(e.in); }
1639      }
1640      return e;
1641    }
1642//     FIXME Not tested
1643    InEdgeIt& next(InEdgeIt& e) const {
1644      if (!e.backward) {
1645        Node v=this->graph->aNode(e.in);
1646        this->graph->next(e.in);
1647        while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1648          this->graph->next(e.in); }
1649        if (!this->graph->valid(e.in)) {
1650          e.backward=true;
1651          this->graph->first(e.out, v);
1652          while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1653            this->graph->next(e.out); }
1654        }
1655      } else {
1656        this->graph->next(e.out);
1657        while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1658          this->graph->next(e.out); }
1659      }
1660      return e;
1661    }
1662    EdgeIt& next(EdgeIt& e) const {
1663      if (!e.backward) {
1664        this->graph->next(e.e);
1665        while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1666          this->graph->next(e.e); }
1667        if (!this->graph->valid(e.e)) {
1668          e.backward=true;
1669          this->graph->first(e.e);
1670          while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1671            this->graph->next(e.e); }
1672        }
1673      } else {
1674        this->graph->next(e.e);
1675        while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1676          this->graph->next(e.e); }
1677      }
1678      return e;
1679    }
1680
1681    Node tail(Edge e) const {
1682      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
1683    Node head(Edge e) const {
1684      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
1685
1686    Node aNode(OutEdgeIt e) const {
1687      return ((!e.backward) ? this->graph->aNode(e.out) :
1688              this->graph->aNode(e.in)); }
1689    Node bNode(OutEdgeIt e) const {
1690      return ((!e.backward) ? this->graph->bNode(e.out) :
1691              this->graph->bNode(e.in)); }
1692
1693    Node aNode(InEdgeIt e) const {
1694      return ((!e.backward) ? this->graph->aNode(e.in) :
1695              this->graph->aNode(e.out)); }
1696    Node bNode(InEdgeIt e) const {
1697      return ((!e.backward) ? this->graph->bNode(e.in) :
1698              this->graph->bNode(e.out)); }
1699
1700//    int nodeNum() const { return graph->nodeNum(); }
1701    //FIXME
1702    void edgeNum() const { }
1703    //int edgeNum() const { return graph->edgeNum(); }
1704
1705
1706//    int id(Node v) const { return graph->id(v); }
1707
1708    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
1709    bool valid(Edge e) const {
1710      return this->graph->valid(e);
1711        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
1712    }
1713
1714    bool forward(const Edge& e) const { return !e.backward; }
1715    bool backward(const Edge& e) const { return e.backward; }
1716
1717    void augment(const Edge& e, Number a) const {
1718      if (!e.backward) 
1719//      flow->set(e.out, flow->get(e.out)+a);
1720        flow->set(e, (*flow)[e]+a);
1721      else 
1722//      flow->set(e.in, flow->get(e.in)-a);
1723        flow->set(e, (*flow)[e]-a);
1724    }
1725
1726    Number resCap(const Edge& e) const {
1727      if (!e.backward)
1728//      return (capacity->get(e.out)-flow->get(e.out));
1729        return ((*capacity)[e]-(*flow)[e]);
1730      else
1731//      return (flow->get(e.in));
1732        return ((*flow)[e]);
1733    }
1734
1735//     Number resCap(typename Graph::OutEdgeIt out) const {
1736// //      return (capacity->get(out)-flow->get(out));
1737//       return ((*capacity)[out]-(*flow)[out]);
1738//     }
1739   
1740//     Number resCap(typename Graph::InEdgeIt in) const {
1741// //      return (flow->get(in));
1742//       return ((*flow)[in]);
1743//     }
1744
1745    template <typename T>
1746    class EdgeMap {
1747      typename Graph::template EdgeMap<T> forward_map, backward_map;
1748    public:
1749      typedef T ValueType;
1750      typedef Edge KeyType;
1751      EdgeMap(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
1752      EdgeMap(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
1753      void set(Edge e, T a) {
1754        if (!e.backward)
1755          forward_map.set(e/*.out*/, a);
1756        else
1757          backward_map.set(e/*.in*/, a);
1758      }
1759      T operator[](Edge e) const {
1760        if (!e.backward)
1761          return forward_map[e/*.out*/];
1762        else
1763          return backward_map[e/*.in*/];
1764      }
1765      void update() {
1766        forward_map.update();
1767        backward_map.update();
1768      }
1769//       T get(Edge e) const {
1770//      if (e.out_or_in)
1771//        return forward_map.get(e.out);
1772//      else
1773//        return backward_map.get(e.in);
1774//       }
1775    };
1776  };
1777
1778
1779
1780  /// For blocking flows.
1781
1782  /// This graph wrapper is used for Dinits blocking flow computations.
1783  /// For each node, an out-edge is stored which is used when the
1784  /// \code
1785  /// OutEdgeIt& first(OutEdgeIt&, const Node&)
1786  /// \endcode
1787  /// is called.
1788  ///
1789  ///\author Marton Makai
1790  template<typename Graph, typename FirstOutEdgesMap>
1791  class ErasingFirstGraphWrapper : public GraphWrapper<Graph> {
1792  public:
1793    typedef GraphWrapper<Graph> Parent;
1794  protected:
1795    FirstOutEdgesMap* first_out_edges;
1796  public:
1797    ErasingFirstGraphWrapper(Graph& _graph,
1798                             FirstOutEdgesMap& _first_out_edges) :
1799      GraphWrapper<Graph>(_graph), first_out_edges(&_first_out_edges) { } 
1800
1801    typedef typename GraphWrapper<Graph>::Node Node;
1802//     class NodeIt {
1803//       friend class GraphWrapper<Graph>;
1804//       friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1805//       typename Graph::NodeIt n;
1806//      public:
1807//       NodeIt() { }
1808//       NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
1809//       NodeIt(const Invalid& i) : n(i) { }
1810//       NodeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G) :
1811//      n(*(_G.graph)) { }
1812//       operator Node() const { return Node(typename Graph::Node(n)); }
1813//     };
1814    typedef typename GraphWrapper<Graph>::Edge Edge;
1815    class OutEdgeIt {
1816      friend class GraphWrapper<Graph>;
1817      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1818//      typedef typename Graph::OutEdgeIt GraphOutEdgeIt;
1819      typename Graph::OutEdgeIt e;
1820    public:
1821      OutEdgeIt() { }
1822      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
1823      OutEdgeIt(const Invalid& i) : e(i) { }
1824      OutEdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G,
1825                const Node& _n) :
1826        e((*_G.first_out_edges)[_n]) { }
1827      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1828    };
1829    class InEdgeIt {
1830      friend class GraphWrapper<Graph>;
1831      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1832//      typedef typename Graph::InEdgeIt GraphInEdgeIt;
1833      typename Graph::InEdgeIt e;
1834    public:
1835      InEdgeIt() { }
1836      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
1837      InEdgeIt(const Invalid& i) : e(i) { }
1838      InEdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G,
1839               const Node& _n) :
1840        e(*(_G.graph), typename Graph::Node(_n)) { }
1841      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1842    };
1843    //typedef typename Graph::SymEdgeIt SymEdgeIt;
1844    class EdgeIt {
1845      friend class GraphWrapper<Graph>;
1846      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1847//      typedef typename Graph::EdgeIt GraphEdgeIt;
1848      typename Graph::EdgeIt e;
1849    public:
1850      EdgeIt() { }
1851      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
1852      EdgeIt(const Invalid& i) : e(i) { }
1853      EdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G) :
1854        e(*(_G.graph)) { }
1855      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1856    };
1857
1858    using GraphWrapper<Graph>::first;
1859//     NodeIt& first(NodeIt& i) const {
1860//       i=NodeIt(*this); return i;
1861//     }
1862    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1863      i=OutEdgeIt(*this, p); return i;
1864    }
1865    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1866      i=InEdgeIt(*this, p); return i;
1867    }
1868    EdgeIt& first(EdgeIt& i) const {
1869      i=EdgeIt(*this); return i;
1870    }
1871
1872    using GraphWrapper<Graph>::next;
1873//    NodeIt& next(NodeIt& i) const { graph->next(i.n); return i; }
1874    OutEdgeIt& next(OutEdgeIt& i) const { this->graph->next(i.e); return i; }
1875    InEdgeIt& next(InEdgeIt& i) const { this->graph->next(i.e); return i; }
1876    EdgeIt& next(EdgeIt& i) const { this->graph->next(i.e); return i; }   
1877   
1878    Node aNode(const OutEdgeIt& e) const {
1879      return Node(this->graph->aNode(e.e)); }
1880    Node aNode(const InEdgeIt& e) const {
1881      return Node(this->graph->aNode(e.e)); }
1882    Node bNode(const OutEdgeIt& e) const {
1883      return Node(this->graph->bNode(e.e)); }
1884    Node bNode(const InEdgeIt& e) const {
1885      return Node(this->graph->bNode(e.e)); }
1886
1887    void erase(const OutEdgeIt& e) const {
1888      OutEdgeIt f=e;
1889      this->next(f);
1890      first_out_edges->set(this->tail(e), f.e);
1891    }
1892  };
1893
1894  ///@}
1895
1896} //namespace hugo
1897
1898#endif //HUGO_GRAPH_WRAPPER_H
1899
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