COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/graph_wrapper.h @ 656:9971eb8bfbe8

Last change on this file since 656:9971eb8bfbe8 was 656:9971eb8bfbe8, checked in by marci, 17 years ago

max_flow.h bug correction

File size: 60.8 KB
Line 
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      Parent::setForwardFilterMap(cm);
997      Parent::setBackwardFilterMap(cm);
998    }
999//     void setCapacityMap(const CapacityMap& _capacity) {
1000//       capacity=&_capacity;
1001//     }
1002//     void setFlowMap(FlowMap& _flow) {
1003//       flow=&_flow;
1004//     }
1005
1006  public:
1007
1008    BidirGraphWrapper(Graph& _graph) : Parent() {
1009      Parent::setGraph(_graph);
1010      Parent::setForwardFilterMap(cm);
1011      Parent::setBackwardFilterMap(cm);
1012    }
1013  };
1014
1015
1016
1017
1018  template<typename Graph>
1019  class OldBidirGraphWrapper : public GraphWrapper<Graph> {
1020  public:
1021    typedef GraphWrapper<Graph> Parent;
1022  protected:
1023    //const CapacityMap* capacity;
1024    //FlowMap* flow;
1025
1026    OldBidirGraphWrapper() : GraphWrapper<Graph>()/*,
1027                                                 capacity(0), flow(0)*/ { }
1028//     void setCapacityMap(const CapacityMap& _capacity) {
1029//       capacity=&_capacity;
1030//     }
1031//     void setFlowMap(FlowMap& _flow) {
1032//       flow=&_flow;
1033//     }
1034
1035  public:
1036
1037    OldBidirGraphWrapper(Graph& _graph/*, const CapacityMap& _capacity,
1038                                     FlowMap& _flow*/) :
1039      GraphWrapper<Graph>(_graph)/*, capacity(&_capacity), flow(&_flow)*/ { }
1040
1041    class Edge;
1042    class OutEdgeIt;
1043    friend class Edge;
1044    friend class OutEdgeIt;
1045
1046    //template<typename T> class NodeMap;   
1047    template<typename T> class EdgeMap;
1048
1049    typedef typename GraphWrapper<Graph>::Node Node;
1050    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
1051
1052    class Edge : public Graph::Edge {
1053      friend class OldBidirGraphWrapper<Graph>;
1054      ///\bug ez nem is kell
1055      //template<typename T> friend class NodeMap;
1056      template<typename T> friend class EdgeMap;
1057    protected:
1058      bool backward; //true, iff backward
1059//      typename Graph::Edge e;
1060    public:
1061      Edge() { }
1062      ///\bug =false kell-e? zsoltnak kell az addEdge miatt
1063      Edge(const typename Graph::Edge& _e, bool _backward=false) :
1064        Graph::Edge(_e), backward(_backward) { }
1065      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
1066//the unique invalid iterator
1067      friend bool operator==(const Edge& u, const Edge& v) {
1068        return (v.backward==u.backward &&
1069                static_cast<typename Graph::Edge>(u)==
1070                static_cast<typename Graph::Edge>(v));
1071      }
1072      friend bool operator!=(const Edge& u, const Edge& v) {
1073        return (v.backward!=u.backward ||
1074                static_cast<typename Graph::Edge>(u)!=
1075                static_cast<typename Graph::Edge>(v));
1076      }
1077    };
1078
1079    class OutEdgeIt {
1080      friend class OldBidirGraphWrapper<Graph>;
1081    protected:
1082      typename Graph::OutEdgeIt out;
1083      typename Graph::InEdgeIt in;
1084      bool backward;
1085    public:
1086      OutEdgeIt() { }
1087      //FIXME
1088//      OutEdgeIt(const Edge& e) : Edge(e) { }
1089      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1090//the unique invalid iterator
1091      OutEdgeIt(const OldBidirGraphWrapper<Graph>& _G, Node v) {
1092        backward=false;
1093        _G.graph->first(out, v);
1094        while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }
1095        if (!_G.graph->valid(out)) {
1096          backward=true;
1097          _G.graph->first(in, v);
1098          while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }
1099        }
1100      }
1101      operator Edge() const {
1102//      Edge e;
1103//      e.forward=this->forward;
1104//      if (this->forward) e=out; else e=in;
1105//      return e;
1106        if (this->backward)
1107          return Edge(in, this->backward);
1108        else
1109          return Edge(out, this->backward);
1110      }
1111    };
1112
1113    class InEdgeIt {
1114      friend class OldBidirGraphWrapper<Graph>;
1115    protected:
1116      typename Graph::OutEdgeIt out;
1117      typename Graph::InEdgeIt in;
1118      bool backward;
1119    public:
1120      InEdgeIt() { }
1121      //FIXME
1122//      OutEdgeIt(const Edge& e) : Edge(e) { }
1123      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1124//the unique invalid iterator
1125      InEdgeIt(const OldBidirGraphWrapper<Graph>& _G, Node v) {
1126        backward=false;
1127        _G.graph->first(in, v);
1128        while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }
1129        if (!_G.graph->valid(in)) {
1130          backward=true;
1131          _G.graph->first(out, v);
1132          while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }
1133        }
1134      }
1135      operator Edge() const {
1136//      Edge e;
1137//      e.forward=this->forward;
1138//      if (this->forward) e=out; else e=in;
1139//      return e;
1140        if (this->backward)
1141          return Edge(out, this->backward);
1142        else
1143          return Edge(in, this->backward);
1144      }
1145    };
1146
1147    class EdgeIt {
1148      friend class OldBidirGraphWrapper<Graph>;
1149    protected:
1150      typename Graph::EdgeIt e;
1151      bool backward;
1152    public:
1153      EdgeIt() { }
1154      EdgeIt(const Invalid& i) : e(i), backward(true) { }
1155      EdgeIt(const OldBidirGraphWrapper<Graph>& _G) {
1156        backward=false;
1157        _G.graph->first(e);
1158        while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);
1159        if (!_G.graph->valid(e)) {
1160          backward=true;
1161          _G.graph->first(e);
1162          while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);
1163        }
1164      }
1165      operator Edge() const {
1166        return Edge(e, this->backward);
1167      }
1168    };
1169
1170    using GraphWrapper<Graph>::first;
1171//     NodeIt& first(NodeIt& i) const {
1172//       i=NodeIt(*this); return i;
1173//     }
1174    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1175      i=OutEdgeIt(*this, p); return i;
1176    }
1177//    FIXME not tested
1178    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1179      i=InEdgeIt(*this, p); return i;
1180    }
1181    EdgeIt& first(EdgeIt& i) const {
1182      i=EdgeIt(*this); return i;
1183    }
1184 
1185    using GraphWrapper<Graph>::next;
1186//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
1187    OutEdgeIt& next(OutEdgeIt& e) const {
1188      if (!e.backward) {
1189        Node v=this->graph->aNode(e.out);
1190        this->graph->next(e.out);
1191        while(this->graph->valid(e.out) && !enabled(e)) {
1192          this->graph->next(e.out); }
1193        if (!this->graph->valid(e.out)) {
1194          e.backward=true;
1195          this->graph->first(e.in, v);
1196          while(this->graph->valid(e.in) && !enabled(e)) {
1197            this->graph->next(e.in); }
1198        }
1199      } else {
1200        this->graph->next(e.in);
1201        while(this->graph->valid(e.in) && !enabled(e)) {
1202          this->graph->next(e.in); }
1203      }
1204      return e;
1205    }
1206//     FIXME Not tested
1207    InEdgeIt& next(InEdgeIt& e) const {
1208      if (!e.backward) {
1209        Node v=this->graph->aNode(e.in);
1210        this->graph->next(e.in);
1211        while(this->graph->valid(e.in) && !enabled(e)) {
1212          this->graph->next(e.in); }
1213        if (!this->graph->valid(e.in)) {
1214          e.backward=true;
1215          this->graph->first(e.out, v);
1216          while(this->graph->valid(e.out) && !enabled(e)) {
1217            this->graph->next(e.out); }
1218        }
1219      } else {
1220        this->graph->next(e.out);
1221        while(this->graph->valid(e.out) && !enabled(e)) {
1222          this->graph->next(e.out); }
1223      }
1224      return e;
1225    }
1226    EdgeIt& next(EdgeIt& e) const {
1227      if (!e.backward) {
1228        this->graph->next(e.e);
1229        while(this->graph->valid(e.e) && !enabled(e)) {
1230          this->graph->next(e.e); }
1231        if (!this->graph->valid(e.e)) {
1232          e.backward=true;
1233          this->graph->first(e.e);
1234          while(this->graph->valid(e.e) && !enabled(e)) {
1235            this->graph->next(e.e); }
1236        }
1237      } else {
1238        this->graph->next(e.e);
1239        while(this->graph->valid(e.e) && !enabled(e)) {
1240          this->graph->next(e.e); }
1241      }
1242      return e;
1243    }
1244
1245    Node tail(Edge e) const {
1246      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
1247    Node head(Edge e) const {
1248      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
1249
1250    Node aNode(OutEdgeIt e) const {
1251      return ((!e.backward) ? this->graph->aNode(e.out) :
1252              this->graph->aNode(e.in)); }
1253    Node bNode(OutEdgeIt e) const {
1254      return ((!e.backward) ? this->graph->bNode(e.out) :
1255              this->graph->bNode(e.in)); }
1256
1257    Node aNode(InEdgeIt e) const {
1258      return ((!e.backward) ? this->graph->aNode(e.in) :
1259              this->graph->aNode(e.out)); }
1260    Node bNode(InEdgeIt e) const {
1261      return ((!e.backward) ? this->graph->bNode(e.in) :
1262              this->graph->bNode(e.out)); }
1263
1264    /// Gives back the opposite edge.
1265    Edge opposite(const Edge& e) const {
1266      Edge f=e;
1267      f.backward=!f.backward;
1268      return f;
1269    }
1270
1271//    int nodeNum() const { return graph->nodeNum(); }
1272    //FIXME
1273    void edgeNum() const { }
1274    //int edgeNum() const { return graph->edgeNum(); }
1275
1276
1277//    int id(Node v) const { return graph->id(v); }
1278
1279    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
1280    bool valid(Edge e) const {
1281      return this->graph->valid(e);
1282        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
1283    }
1284
1285    bool forward(const Edge& e) const { return !e.backward; }
1286    bool backward(const Edge& e) const { return e.backward; }
1287
1288//     void augment(const Edge& e, Number a) const {
1289//       if (!e.backward) 
1290// //   flow->set(e.out, flow->get(e.out)+a);
1291//      flow->set(e, (*flow)[e]+a);
1292//       else 
1293// //   flow->set(e.in, flow->get(e.in)-a);
1294//      flow->set(e, (*flow)[e]-a);
1295//     }
1296
1297    bool enabled(const Edge& e) const {
1298      if (!e.backward)
1299//      return (capacity->get(e.out)-flow->get(e.out));
1300        //return ((*capacity)[e]-(*flow)[e]);
1301        return true;
1302      else
1303//      return (flow->get(e.in));
1304        //return ((*flow)[e]);
1305        return true;
1306    }
1307
1308//     Number enabled(typename Graph::OutEdgeIt out) const {
1309// //      return (capacity->get(out)-flow->get(out));
1310//       return ((*capacity)[out]-(*flow)[out]);
1311//     }
1312   
1313//     Number enabled(typename Graph::InEdgeIt in) const {
1314// //      return (flow->get(in));
1315//       return ((*flow)[in]);
1316//     }
1317
1318    template <typename T>
1319    class EdgeMap {
1320      typename Graph::template EdgeMap<T> forward_map, backward_map;
1321    public:
1322      typedef T ValueType;
1323      typedef Edge KeyType;
1324      EdgeMap(const OldBidirGraphWrapper<Graph>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
1325      EdgeMap(const OldBidirGraphWrapper<Graph>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
1326      void set(Edge e, T a) {
1327        if (!e.backward)
1328          forward_map.set(e/*.out*/, a);
1329        else
1330          backward_map.set(e/*.in*/, a);
1331      }
1332      T operator[](Edge e) const {
1333        if (!e.backward)
1334          return forward_map[e/*.out*/];
1335        else
1336          return backward_map[e/*.in*/];
1337      }
1338      void update() {
1339        forward_map.update();
1340        backward_map.update();
1341      }
1342//       T get(Edge e) const {
1343//      if (e.out_or_in)
1344//        return forward_map.get(e.out);
1345//      else
1346//        return backward_map.get(e.in);
1347//       }
1348    };
1349  };
1350
1351
1352
1353  /// \brief A bidirected graph template.
1354  ///
1355  /// A bidirected graph template.
1356  /// Such a bidirected graph stores each pair of oppositely directed edges
1357  /// ones in the memory, i.e. a directed graph of type
1358  /// \c Graph is used for that.
1359  /// As the oppositely directed edges are logically different ones
1360  /// the maps are able to attach different values for them.
1361  /// \ingroup graphs
1362  template<typename Graph>
1363  class BidirGraph : public BidirGraphWrapper<Graph> {
1364  public:
1365    typedef UndirGraphWrapper<Graph> Parent;
1366  protected:
1367    Graph gr;
1368  public:
1369    BidirGraph() : BidirGraphWrapper<Graph>() {
1370      Parent::setGraph(gr);
1371    }
1372  };
1373
1374
1375
1376  template<typename Graph, typename Number,
1377           typename CapacityMap, typename FlowMap>
1378  class ForwardFilter {
1379    const Graph* graph;
1380    const CapacityMap* capacity;
1381    const FlowMap* flow;
1382  public:
1383    void setGraph(const Graph& _graph) { graph=&_graph; }
1384    void setCapacity(const CapacityMap& _capacity) { capacity=&_capacity; }
1385    void setFlow(const FlowMap& _flow) { flow=&_flow; }
1386    ForwardFilter(const Graph& _graph,
1387                  const CapacityMap& _capacity, const FlowMap& _flow) :
1388      graph(&_graph), capacity(&_capacity), flow(&_flow) { }
1389    bool operator[](const typename Graph::Edge& e) const {
1390      return ((*flow)[e] < (*capacity)[e]);
1391    }
1392  };
1393
1394  template<typename Graph, typename Number,
1395           typename CapacityMap, typename FlowMap>
1396  class BackwardFilter {
1397    const Graph* graph;
1398    const CapacityMap* capacity;
1399    const FlowMap* flow;
1400  public:
1401    void setGraph(const Graph& _graph) { graph=&_graph; }
1402    void setCapacity(const CapacityMap& _capacity) { capacity=&_capacity; }
1403    void setFlow(const FlowMap& _flow) { flow=&_flow; }
1404    BackwardFilter(const Graph& _graph,
1405                   const CapacityMap& _capacity, const FlowMap& _flow) :
1406      graph(&_graph), capacity(&_capacity), flow(&_flow) { }
1407    bool operator[](const typename Graph::Edge& e) const {
1408      return (0 < (*flow)[e]);
1409    }
1410  };
1411
1412 
1413  /// A wrapper for composing the residual graph for directed flow and circulation problems.
1414
1415  /// A wrapper for composing the residual graph for directed flow and circulation problems.
1416  template<typename Graph, typename Number,
1417           typename CapacityMap, typename FlowMap>
1418  class ResGraphWrapper :
1419    public SubBidirGraphWrapper<
1420    Graph,
1421    ForwardFilter<Graph, Number, CapacityMap, FlowMap>, 
1422    BackwardFilter<Graph, Number, CapacityMap, FlowMap> > {
1423  public:
1424    typedef SubBidirGraphWrapper<
1425      Graph,
1426      ForwardFilter<Graph, Number, CapacityMap, FlowMap>, 
1427      BackwardFilter<Graph, Number, CapacityMap, FlowMap> > Parent;
1428  protected:
1429    const CapacityMap* capacity;
1430    FlowMap* flow;
1431    ForwardFilter<Graph, Number, CapacityMap, FlowMap> forward_filter;
1432    BackwardFilter<Graph, Number, CapacityMap, FlowMap> backward_filter;
1433//     ResGraphWrapper() : Parent(),
1434//                      capacity(0), flow(0) { }
1435//     void setCapacityMap(const CapacityMap& _capacity) {
1436//       capacity=&_capacity;
1437//     }
1438//     void setFlowMap(FlowMap& _flow) {
1439//       flow=&_flow;
1440//     }
1441  public:
1442    ResGraphWrapper(Graph& _graph, const CapacityMap& _capacity,
1443                       FlowMap& _flow) :
1444      Parent(), capacity(&_capacity), flow(&_flow),
1445      forward_filter(_graph, _capacity, _flow),
1446      backward_filter(_graph, _capacity, _flow) {
1447      Parent::setGraph(_graph);
1448      Parent::setForwardFilterMap(forward_filter);
1449      Parent::setBackwardFilterMap(backward_filter);
1450    }
1451
1452    //    bool forward(const Parent::Edge& e) const { return Parent::forward(e); }
1453    //bool backward(const Edge& e) const { return e.backward; }
1454
1455    void augment(const typename Parent::Edge& e, Number a) const {
1456      if (Parent::forward(e)) 
1457//      flow->set(e.out, flow->get(e.out)+a);
1458        flow->set(e, (*flow)[e]+a);
1459      else 
1460        //flow->set(e.in, flow->get(e.in)-a);
1461        flow->set(e, (*flow)[e]-a);
1462    }
1463
1464    Number resCap(const typename Parent::Edge& e) const {
1465      if (Parent::forward(e))
1466//      return (capacity->get(e.out)-flow->get(e.out));
1467        return ((*capacity)[e]-(*flow)[e]);
1468      else
1469//      return (flow->get(e.in));
1470        return ((*flow)[e]);
1471    }
1472
1473  };
1474
1475
1476
1477
1478  template<typename Graph, typename Number,
1479           typename CapacityMap, typename FlowMap>
1480  class OldResGraphWrapper : public GraphWrapper<Graph> {
1481  public:
1482    typedef GraphWrapper<Graph> Parent;
1483  protected:
1484    const CapacityMap* capacity;
1485    FlowMap* flow;
1486
1487    OldResGraphWrapper() : GraphWrapper<Graph>(0),
1488                        capacity(0), flow(0) { }
1489    void setCapacityMap(const CapacityMap& _capacity) {
1490      capacity=&_capacity;
1491    }
1492    void setFlowMap(FlowMap& _flow) {
1493      flow=&_flow;
1494    }
1495
1496  public:
1497
1498    OldResGraphWrapper(Graph& _graph, const CapacityMap& _capacity,
1499                    FlowMap& _flow) :
1500      GraphWrapper<Graph>(_graph), capacity(&_capacity), flow(&_flow) { }
1501
1502    class Edge;
1503    class OutEdgeIt;
1504    friend class Edge;
1505    friend class OutEdgeIt;
1506
1507    typedef typename GraphWrapper<Graph>::Node Node;
1508    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;
1509    class Edge : public Graph::Edge {
1510      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1511    protected:
1512      bool backward; //true, iff backward
1513//      typename Graph::Edge e;
1514    public:
1515      Edge() { }
1516      Edge(const typename Graph::Edge& _e, bool _backward) :
1517        Graph::Edge(_e), backward(_backward) { }
1518      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }
1519//the unique invalid iterator
1520      friend bool operator==(const Edge& u, const Edge& v) {
1521        return (v.backward==u.backward &&
1522                static_cast<typename Graph::Edge>(u)==
1523                static_cast<typename Graph::Edge>(v));
1524      }
1525      friend bool operator!=(const Edge& u, const Edge& v) {
1526        return (v.backward!=u.backward ||
1527                static_cast<typename Graph::Edge>(u)!=
1528                static_cast<typename Graph::Edge>(v));
1529      }
1530    };
1531
1532    class OutEdgeIt {
1533      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1534    protected:
1535      typename Graph::OutEdgeIt out;
1536      typename Graph::InEdgeIt in;
1537      bool backward;
1538    public:
1539      OutEdgeIt() { }
1540      //FIXME
1541//      OutEdgeIt(const Edge& e) : Edge(e) { }
1542      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1543//the unique invalid iterator
1544      OutEdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) {
1545        backward=false;
1546        _G.graph->first(out, v);
1547        while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }
1548        if (!_G.graph->valid(out)) {
1549          backward=true;
1550          _G.graph->first(in, v);
1551          while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }
1552        }
1553      }
1554      operator Edge() const {
1555//      Edge e;
1556//      e.forward=this->forward;
1557//      if (this->forward) e=out; else e=in;
1558//      return e;
1559        if (this->backward)
1560          return Edge(in, this->backward);
1561        else
1562          return Edge(out, this->backward);
1563      }
1564    };
1565
1566    class InEdgeIt {
1567      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1568    protected:
1569      typename Graph::OutEdgeIt out;
1570      typename Graph::InEdgeIt in;
1571      bool backward;
1572    public:
1573      InEdgeIt() { }
1574      //FIXME
1575//      OutEdgeIt(const Edge& e) : Edge(e) { }
1576      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }
1577//the unique invalid iterator
1578      InEdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) {
1579        backward=false;
1580        _G.graph->first(in, v);
1581        while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }
1582        if (!_G.graph->valid(in)) {
1583          backward=true;
1584          _G.graph->first(out, v);
1585          while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }
1586        }
1587      }
1588      operator Edge() const {
1589//      Edge e;
1590//      e.forward=this->forward;
1591//      if (this->forward) e=out; else e=in;
1592//      return e;
1593        if (this->backward)
1594          return Edge(out, this->backward);
1595        else
1596          return Edge(in, this->backward);
1597      }
1598    };
1599
1600    class EdgeIt {
1601      friend class OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;
1602    protected:
1603      typename Graph::EdgeIt e;
1604      bool backward;
1605    public:
1606      EdgeIt() { }
1607      EdgeIt(const Invalid& i) : e(i), backward(true) { }
1608      EdgeIt(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G) {
1609        backward=false;
1610        _G.graph->first(e);
1611        while (_G.graph->valid(e) && !(_G.resCap(*this)>0)) _G.graph->next(e);
1612        if (!_G.graph->valid(e)) {
1613          backward=true;
1614          _G.graph->first(e);
1615          while (_G.graph->valid(e) && !(_G.resCap(*this)>0)) _G.graph->next(e);
1616        }
1617      }
1618      operator Edge() const {
1619        return Edge(e, this->backward);
1620      }
1621    };
1622
1623    using GraphWrapper<Graph>::first;
1624//     NodeIt& first(NodeIt& i) const {
1625//       i=NodeIt(*this); return i;
1626//     }
1627    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1628      i=OutEdgeIt(*this, p); return i;
1629    }
1630//    FIXME not tested
1631    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1632      i=InEdgeIt(*this, p); return i;
1633    }
1634    EdgeIt& first(EdgeIt& i) const {
1635      i=EdgeIt(*this); return i;
1636    }
1637 
1638    using GraphWrapper<Graph>::next;
1639//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }
1640    OutEdgeIt& next(OutEdgeIt& e) const {
1641      if (!e.backward) {
1642        Node v=this->graph->aNode(e.out);
1643        this->graph->next(e.out);
1644        while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1645          this->graph->next(e.out); }
1646        if (!this->graph->valid(e.out)) {
1647          e.backward=true;
1648          this->graph->first(e.in, v);
1649          while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1650            this->graph->next(e.in); }
1651        }
1652      } else {
1653        this->graph->next(e.in);
1654        while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1655          this->graph->next(e.in); }
1656      }
1657      return e;
1658    }
1659//     FIXME Not tested
1660    InEdgeIt& next(InEdgeIt& e) const {
1661      if (!e.backward) {
1662        Node v=this->graph->aNode(e.in);
1663        this->graph->next(e.in);
1664        while( this->graph->valid(e.in) && !(resCap(e)>0) ) {
1665          this->graph->next(e.in); }
1666        if (!this->graph->valid(e.in)) {
1667          e.backward=true;
1668          this->graph->first(e.out, v);
1669          while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1670            this->graph->next(e.out); }
1671        }
1672      } else {
1673        this->graph->next(e.out);
1674        while( this->graph->valid(e.out) && !(resCap(e)>0) ) {
1675          this->graph->next(e.out); }
1676      }
1677      return e;
1678    }
1679    EdgeIt& next(EdgeIt& e) const {
1680      if (!e.backward) {
1681        this->graph->next(e.e);
1682        while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1683          this->graph->next(e.e); }
1684        if (!this->graph->valid(e.e)) {
1685          e.backward=true;
1686          this->graph->first(e.e);
1687          while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1688            this->graph->next(e.e); }
1689        }
1690      } else {
1691        this->graph->next(e.e);
1692        while( this->graph->valid(e.e) && !(resCap(e)>0) ) {
1693          this->graph->next(e.e); }
1694      }
1695      return e;
1696    }
1697
1698    Node tail(Edge e) const {
1699      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }
1700    Node head(Edge e) const {
1701      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }
1702
1703    Node aNode(OutEdgeIt e) const {
1704      return ((!e.backward) ? this->graph->aNode(e.out) :
1705              this->graph->aNode(e.in)); }
1706    Node bNode(OutEdgeIt e) const {
1707      return ((!e.backward) ? this->graph->bNode(e.out) :
1708              this->graph->bNode(e.in)); }
1709
1710    Node aNode(InEdgeIt e) const {
1711      return ((!e.backward) ? this->graph->aNode(e.in) :
1712              this->graph->aNode(e.out)); }
1713    Node bNode(InEdgeIt e) const {
1714      return ((!e.backward) ? this->graph->bNode(e.in) :
1715              this->graph->bNode(e.out)); }
1716
1717//    int nodeNum() const { return graph->nodeNum(); }
1718    //FIXME
1719    void edgeNum() const { }
1720    //int edgeNum() const { return graph->edgeNum(); }
1721
1722
1723//    int id(Node v) const { return graph->id(v); }
1724
1725    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }
1726    bool valid(Edge e) const {
1727      return this->graph->valid(e);
1728        //return e.forward ? graph->valid(e.out) : graph->valid(e.in);
1729    }
1730
1731    bool forward(const Edge& e) const { return !e.backward; }
1732    bool backward(const Edge& e) const { return e.backward; }
1733
1734    void augment(const Edge& e, Number a) const {
1735      if (!e.backward) 
1736//      flow->set(e.out, flow->get(e.out)+a);
1737        flow->set(e, (*flow)[e]+a);
1738      else 
1739//      flow->set(e.in, flow->get(e.in)-a);
1740        flow->set(e, (*flow)[e]-a);
1741    }
1742
1743    Number resCap(const Edge& e) const {
1744      if (!e.backward)
1745//      return (capacity->get(e.out)-flow->get(e.out));
1746        return ((*capacity)[e]-(*flow)[e]);
1747      else
1748//      return (flow->get(e.in));
1749        return ((*flow)[e]);
1750    }
1751
1752//     Number resCap(typename Graph::OutEdgeIt out) const {
1753// //      return (capacity->get(out)-flow->get(out));
1754//       return ((*capacity)[out]-(*flow)[out]);
1755//     }
1756   
1757//     Number resCap(typename Graph::InEdgeIt in) const {
1758// //      return (flow->get(in));
1759//       return ((*flow)[in]);
1760//     }
1761
1762    template <typename T>
1763    class EdgeMap {
1764      typename Graph::template EdgeMap<T> forward_map, backward_map;
1765    public:
1766      typedef T ValueType;
1767      typedef Edge KeyType;
1768      EdgeMap(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }
1769      EdgeMap(const OldResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }
1770      void set(Edge e, T a) {
1771        if (!e.backward)
1772          forward_map.set(e/*.out*/, a);
1773        else
1774          backward_map.set(e/*.in*/, a);
1775      }
1776      T operator[](Edge e) const {
1777        if (!e.backward)
1778          return forward_map[e/*.out*/];
1779        else
1780          return backward_map[e/*.in*/];
1781      }
1782      void update() {
1783        forward_map.update();
1784        backward_map.update();
1785      }
1786//       T get(Edge e) const {
1787//      if (e.out_or_in)
1788//        return forward_map.get(e.out);
1789//      else
1790//        return backward_map.get(e.in);
1791//       }
1792    };
1793  };
1794
1795
1796
1797  /// For blocking flows.
1798
1799  /// This graph wrapper is used for Dinits blocking flow computations.
1800  /// For each node, an out-edge is stored which is used when the
1801  /// \code
1802  /// OutEdgeIt& first(OutEdgeIt&, const Node&)
1803  /// \endcode
1804  /// is called.
1805  ///
1806  ///\author Marton Makai
1807  template<typename Graph, typename FirstOutEdgesMap>
1808  class ErasingFirstGraphWrapper : public GraphWrapper<Graph> {
1809  public:
1810    typedef GraphWrapper<Graph> Parent;
1811  protected:
1812    FirstOutEdgesMap* first_out_edges;
1813  public:
1814    ErasingFirstGraphWrapper(Graph& _graph,
1815                             FirstOutEdgesMap& _first_out_edges) :
1816      GraphWrapper<Graph>(_graph), first_out_edges(&_first_out_edges) { } 
1817
1818    typedef typename GraphWrapper<Graph>::Node Node;
1819//     class NodeIt {
1820//       friend class GraphWrapper<Graph>;
1821//       friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1822//       typename Graph::NodeIt n;
1823//      public:
1824//       NodeIt() { }
1825//       NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }
1826//       NodeIt(const Invalid& i) : n(i) { }
1827//       NodeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G) :
1828//      n(*(_G.graph)) { }
1829//       operator Node() const { return Node(typename Graph::Node(n)); }
1830//     };
1831    typedef typename GraphWrapper<Graph>::Edge Edge;
1832    class OutEdgeIt {
1833      friend class GraphWrapper<Graph>;
1834      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1835//      typedef typename Graph::OutEdgeIt GraphOutEdgeIt;
1836      typename Graph::OutEdgeIt e;
1837    public:
1838      OutEdgeIt() { }
1839      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }
1840      OutEdgeIt(const Invalid& i) : e(i) { }
1841      OutEdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G,
1842                const Node& _n) :
1843        e((*_G.first_out_edges)[_n]) { }
1844      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1845    };
1846    class InEdgeIt {
1847      friend class GraphWrapper<Graph>;
1848      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1849//      typedef typename Graph::InEdgeIt GraphInEdgeIt;
1850      typename Graph::InEdgeIt e;
1851    public:
1852      InEdgeIt() { }
1853      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }
1854      InEdgeIt(const Invalid& i) : e(i) { }
1855      InEdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G,
1856               const Node& _n) :
1857        e(*(_G.graph), typename Graph::Node(_n)) { }
1858      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1859    };
1860    //typedef typename Graph::SymEdgeIt SymEdgeIt;
1861    class EdgeIt {
1862      friend class GraphWrapper<Graph>;
1863      friend class ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>;
1864//      typedef typename Graph::EdgeIt GraphEdgeIt;
1865      typename Graph::EdgeIt e;
1866    public:
1867      EdgeIt() { }
1868      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }
1869      EdgeIt(const Invalid& i) : e(i) { }
1870      EdgeIt(const ErasingFirstGraphWrapper<Graph, FirstOutEdgesMap>& _G) :
1871        e(*(_G.graph)) { }
1872      operator Edge() const { return Edge(typename Graph::Edge(e)); }
1873    };
1874
1875    using GraphWrapper<Graph>::first;
1876//     NodeIt& first(NodeIt& i) const {
1877//       i=NodeIt(*this); return i;
1878//     }
1879    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const {
1880      i=OutEdgeIt(*this, p); return i;
1881    }
1882    InEdgeIt& first(InEdgeIt& i, const Node& p) const {
1883      i=InEdgeIt(*this, p); return i;
1884    }
1885    EdgeIt& first(EdgeIt& i) const {
1886      i=EdgeIt(*this); return i;
1887    }
1888
1889    using GraphWrapper<Graph>::next;
1890//    NodeIt& next(NodeIt& i) const { graph->next(i.n); return i; }
1891    OutEdgeIt& next(OutEdgeIt& i) const { this->graph->next(i.e); return i; }
1892    InEdgeIt& next(InEdgeIt& i) const { this->graph->next(i.e); return i; }
1893    EdgeIt& next(EdgeIt& i) const { this->graph->next(i.e); return i; }   
1894   
1895    Node aNode(const OutEdgeIt& e) const {
1896      return Node(this->graph->aNode(e.e)); }
1897    Node aNode(const InEdgeIt& e) const {
1898      return Node(this->graph->aNode(e.e)); }
1899    Node bNode(const OutEdgeIt& e) const {
1900      return Node(this->graph->bNode(e.e)); }
1901    Node bNode(const InEdgeIt& e) const {
1902      return Node(this->graph->bNode(e.e)); }
1903
1904    void erase(const OutEdgeIt& e) const {
1905      OutEdgeIt f=e;
1906      this->next(f);
1907      first_out_edges->set(this->tail(e), f.e);
1908    }
1909  };
1910
1911  ///@}
1912
1913} //namespace hugo
1914
1915#endif //HUGO_GRAPH_WRAPPER_H
1916
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