// -*- c++ -*-

#ifndef HUGO_GRAPH_WRAPPER_H

#define HUGO_GRAPH_WRAPPER_H

///\ingroup gwrappers

///\file

///\brief Several graph wrappers.

///

///This file contains several useful graph wrapper functions.

///

///\author Marton Makai

#include <hugo/invalid.h>

//#include <iter_map.h>

namespace hugo {

  // Graph wrappers

  /// \addtogroup gwrappers

  /// A main parts of HUGOlib are the different graph structures, 

  /// generic graph algorithms, graph concepts which couple these, and 

  /// graph wrappers. While the previous ones are more or less clear, the 

  /// latter notion needs further explanation.

  /// Graph wrappers are graph classes which serve for considering graph 

  /// structures in different ways. A short example makes the notion much 

  /// clearer. 

  /// Suppose that we have an instance \c g of a directed graph

  /// type say \c ListGraph and an algorithm 

  /// \code template<typename Graph> int algorithm(const Graph&); \endcode 

  /// is needed to run on the reversely oriented graph. 

  /// It may be expensive (in time or in memory usage) to copy 

  /// \c g with the reverse orientation. 

  /// Thus, a wrapper class

  /// \code template<typename Graph> class RevGraphWrapper; \endcode is used. 

  /// The code looks as follows

  /// \code

  /// ListGraph g;

  /// RevGraphWrapper<ListGraph> rgw(g);

  /// int result=algorithm(rgw);

  /// \endcode

  /// After running the algorithm, the original graph \c g 

  /// remains untouched. Thus the graph wrapper used above is to consider the 

  /// original graph with reverse orientation. 

  /// This techniques gives rise to an elegant code, and 

  /// based on stable graph wrappers, complex algorithms can be 

  /// implemented easily. 

  /// In flow, circulation and bipartite matching problems, the residual 

  /// graph is of particular importance. Combining a wrapper implementing 

  /// this, shortest path algorithms and minimum mean cycle algorithms, 

  /// a range of weighted and cardinality optimization algorithms can be 

  /// obtained. For lack of space, for other examples, 

  /// the interested user is referred to the detailed documentation of graph 

  /// wrappers. 

  /// The behavior of graph wrappers can be very different. Some of them keep 

  /// capabilities of the original graph while in other cases this would be 

  /// meaningless. This means that the concepts that they are a model of depend 

  /// on the graph wrapper, and the wrapped graph(s). 

  /// If an edge of \c rgw is deleted, this is carried out by 

  /// deleting the corresponding edge of \c g. But for a residual 

  /// graph, this operation has no sense. 

  /// Let we stand one more example here to simplify your work. 

  /// wrapper class

  /// \code template<typename Graph> class RevGraphWrapper; \endcode 

  /// has constructor 

  /// <tt> RevGraphWrapper(Graph& _g)</tt>. 

  /// This means that in a situation, 

  /// when a <tt> const ListGraph& </tt> reference to a graph is given, 

  /// then it have to be instantiated with <tt>Graph=const ListGraph</tt>.

  /// \code

  /// int algorithm1(const ListGraph& g) {

  ///   RevGraphWrapper<const ListGraph> rgw(g);

  ///   return algorithm2(rgw);

  /// }

  /// \endcode

  /// \addtogroup gwrappers

  /// @{

  ///Base type for the Graph Wrappers

  ///This is the base type for the Graph Wrappers.

  ///\todo Some more docs... 

  ///

  ///\author Marton Makai

  template<typename Graph>

  class GraphWrapper {

  protected:

    Graph* graph;

    GraphWrapper() : graph(0) { }

    void setGraph(Graph& _graph) { graph=&_graph; }

  public:

    typedef Graph BaseGraph;

    typedef Graph ParentGraph;

    GraphWrapper(Graph& _graph) : graph(&_graph) { }

//     Graph& getGraph() const { return *graph; }

//    typedef typename Graph::Node Node;

    class Node : public Graph::Node {

      friend class GraphWrapper<Graph>;

    public:

      Node() { }

      Node(const typename Graph::Node& _n) : Graph::Node(_n) { }

      Node(const Invalid& i) : Graph::Node(i) { }

    };

    class NodeIt { 

      friend class GraphWrapper<Graph>;

      typename Graph::NodeIt n;

     public:

      NodeIt() { }

      NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }

      NodeIt(const Invalid& i) : n(i) { }

      NodeIt(const GraphWrapper<Graph>& _G) : n(*(_G.graph)) { }

      operator Node() const { return Node(typename Graph::Node(n)); }

    };

//    typedef typename Graph::Edge Edge;

    class Edge : public Graph::Edge {

      friend class GraphWrapper<Graph>;

    public:

      Edge() { }

      Edge(const typename Graph::Edge& _e) : Graph::Edge(_e) { }

      Edge(const Invalid& i) : Graph::Edge(i) { }

    };

    class OutEdgeIt { 

      friend class GraphWrapper<Graph>;

      typename Graph::OutEdgeIt e;

    public:

      OutEdgeIt() { }

      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }

      OutEdgeIt(const Invalid& i) : e(i) { }

      OutEdgeIt(const GraphWrapper<Graph>& _G, const Node& _n) : 

	e(*(_G.graph), typename Graph::Node(_n)) { }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    class InEdgeIt { 

      friend class GraphWrapper<Graph>;

      typename Graph::InEdgeIt e;

    public:

      InEdgeIt() { }

      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }

      InEdgeIt(const Invalid& i) : e(i) { }

      InEdgeIt(const GraphWrapper<Graph>& _G, const Node& _n) : 

	e(*(_G.graph), typename Graph::Node(_n)) { }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    //typedef typename Graph::SymEdgeIt SymEdgeIt;

    class EdgeIt { 

      friend class GraphWrapper<Graph>;

      typename Graph::EdgeIt e;

    public:

      EdgeIt() { }

      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }

      EdgeIt(const Invalid& i) : e(i) { }

      EdgeIt(const GraphWrapper<Graph>& _G) : e(*(_G.graph)) { }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    NodeIt& first(NodeIt& i) const { 

      i=NodeIt(*this); return i;

    }

    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const { 

      i=OutEdgeIt(*this, p); return i;

    }

    InEdgeIt& first(InEdgeIt& i, const Node& p) const { 

      i=InEdgeIt(*this, p); return i;

    }

    EdgeIt& first(EdgeIt& i) const { 

      i=EdgeIt(*this); return i;

    }

    NodeIt& next(NodeIt& i) const { graph->next(i.n); return i; }

    OutEdgeIt& next(OutEdgeIt& i) const { graph->next(i.e); return i; }

    InEdgeIt& next(InEdgeIt& i) const { graph->next(i.e); return i; }

    EdgeIt& next(EdgeIt& i) const { graph->next(i.e); return i; }    

    Node tail(const Edge& e) const { 

      return Node(graph->tail(static_cast<typename Graph::Edge>(e))); }

    Node head(const Edge& e) const { 

      return Node(graph->head(static_cast<typename Graph::Edge>(e))); }

    bool valid(const Node& n) const { 

      return graph->valid(static_cast<typename Graph::Node>(n)); }

    bool valid(const Edge& e) const { 

      return graph->valid(static_cast<typename Graph::Edge>(e)); }

    int nodeNum() const { return graph->nodeNum(); }

    int edgeNum() const { return graph->edgeNum(); }

    Node aNode(const OutEdgeIt& e) const { return Node(graph->aNode(e.e)); }

    Node aNode(const InEdgeIt& e) const { return Node(graph->aNode(e.e)); }

    Node bNode(const OutEdgeIt& e) const { return Node(graph->bNode(e.e)); }

    Node bNode(const InEdgeIt& e) const { return Node(graph->bNode(e.e)); }

    Node addNode() const { return Node(graph->addNode()); }

    Edge addEdge(const Node& tail, const Node& head) const { 

      return Edge(graph->addEdge(tail, head)); }

    void erase(const Node& i) const { graph->erase(i); }

    void erase(const Edge& i) const { graph->erase(i); }

    void clear() const { graph->clear(); }

    template<typename T> class NodeMap : public Graph::template NodeMap<T> { 

      typedef typename Graph::template NodeMap<T> Parent;

    public:

      NodeMap(const GraphWrapper<Graph>& _G) :  Parent(*(_G.graph)) { }

      NodeMap(const GraphWrapper<Graph>& _G, T a) : Parent(*(_G.graph), a) { }

    };

    template<typename T> class EdgeMap : public Graph::template EdgeMap<T> { 

      typedef typename Graph::template EdgeMap<T> Parent;

    public:

      EdgeMap(const GraphWrapper<Graph>& _G) : Parent(*(_G.graph)) { }

      EdgeMap(const GraphWrapper<Graph>& _G, T a) : Parent(*(_G.graph), a) { }

    };

  };

  /// A graph wrapper which reverses the orientation of the edges.

  /// A graph wrapper which reverses the orientation of the edges.

  ///

  ///\author Marton Makai

  template<typename Graph>

  class RevGraphWrapper : public GraphWrapper<Graph> {

  protected:

    RevGraphWrapper() : GraphWrapper<Graph>(0) { }

  public:

    RevGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { }  

    typedef typename GraphWrapper<Graph>::Node Node;

    typedef typename GraphWrapper<Graph>::Edge Edge;

    //If Graph::OutEdgeIt is not defined

    //and we do not want to use RevGraphWrapper::InEdgeIt,

    //the typdef techinque does not work.

    //Unfortunately all the typedefs are instantiated in templates.

    //typedef typename GraphWrapper<Graph>::OutEdgeIt InEdgeIt;

    //typedef typename GraphWrapper<Graph>::InEdgeIt OutEdgeIt;

    class OutEdgeIt { 

      friend class GraphWrapper<Graph>;

      friend class RevGraphWrapper<Graph>;

      typename Graph::InEdgeIt e;

    public:

      OutEdgeIt() { }

      OutEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }

      OutEdgeIt(const Invalid& i) : e(i) { }

      OutEdgeIt(const RevGraphWrapper<Graph>& _G, const Node& _n) : 

	e(*(_G.graph), typename Graph::Node(_n)) { }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    class InEdgeIt { 

      friend class GraphWrapper<Graph>;

      friend class RevGraphWrapper<Graph>;

      typename Graph::OutEdgeIt e;

    public:

      InEdgeIt() { }

      InEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }

      InEdgeIt(const Invalid& i) : e(i) { }

      InEdgeIt(const RevGraphWrapper<Graph>& _G, const Node& _n) : 

	e(*(_G.graph), typename Graph::Node(_n)) { }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    using GraphWrapper<Graph>::first;

    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const { 

      i=OutEdgeIt(*this, p); return i;

    }

    InEdgeIt& first(InEdgeIt& i, const Node& p) const { 

      i=InEdgeIt(*this, p); return i;

    }

    using GraphWrapper<Graph>::next;

    OutEdgeIt& next(OutEdgeIt& i) const { this->graph->next(i.e); return i; }

    InEdgeIt& next(InEdgeIt& i) const { this->graph->next(i.e); return i; }

    Node aNode(const OutEdgeIt& e) const { 

      return Node(this->graph->aNode(e.e)); }

    Node aNode(const InEdgeIt& e) const { 

      return Node(this->graph->aNode(e.e)); }

    Node bNode(const OutEdgeIt& e) const { 

      return Node(this->graph->bNode(e.e)); }

    Node bNode(const InEdgeIt& e) const { 

      return Node(this->graph->bNode(e.e)); }

    Node tail(const Edge& e) const { 

      return GraphWrapper<Graph>::head(e); }

    Node head(const Edge& e) const { 

      return GraphWrapper<Graph>::tail(e); }

  };

  /// Wrapper for hiding nodes and edges from a graph.

  /// This wrapper shows a graph with filtered node-set and 

  /// edge-set. The quick brown fox iterator jumps over 

  /// the lazy dog nodes or edges if the values for them are false 

  /// in the bool maps. 

  ///

  ///\author Marton Makai

  template<typename Graph, typename NodeFilterMap, 

	   typename EdgeFilterMap>

  class SubGraphWrapper : public GraphWrapper<Graph> {

  protected:

    NodeFilterMap* node_filter_map;

    EdgeFilterMap* edge_filter_map;

    SubGraphWrapper() : GraphWrapper<Graph>(0), 

			node_filter_map(0), edge_filter_map(0) { }

    void setNodeFilterMap(NodeFilterMap& _node_filter_map) {

      node_filter_map=&_node_filter_map;

    }

    void setEdgeFilterMap(EdgeFilterMap& _edge_filter_map) {

      edge_filter_map=&_edge_filter_map;

    }

  public:

    SubGraphWrapper(Graph& _graph, NodeFilterMap& _node_filter_map, 

		    EdgeFilterMap& _edge_filter_map) : 

      GraphWrapper<Graph>(_graph), node_filter_map(&_node_filter_map), 

      edge_filter_map(&_edge_filter_map) { }  

    typedef typename GraphWrapper<Graph>::Node Node;

    class NodeIt { 

      friend class GraphWrapper<Graph>;

      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;

      typename Graph::NodeIt n;

     public:

      NodeIt() { }

      NodeIt(const typename Graph::NodeIt& _n) : n(_n) { }

      NodeIt(const Invalid& i) : n(i) { }

      NodeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G) : 

	n(*(_G.graph)) { 

	while (_G.graph->valid(n) && !(*(_G.node_filter_map))[n]) 

	  _G.graph->next(n);

      }

      operator Node() const { return Node(typename Graph::Node(n)); }

    };

    typedef typename GraphWrapper<Graph>::Edge Edge;

    class OutEdgeIt { 

      friend class GraphWrapper<Graph>;

      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;

      typename Graph::OutEdgeIt e;

    public:

      OutEdgeIt() { }

      OutEdgeIt(const typename Graph::OutEdgeIt& _e) : e(_e) { }

      OutEdgeIt(const Invalid& i) : e(i) { }

      OutEdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G, 

		const Node& _n) : 

	e(*(_G.graph), typename Graph::Node(_n)) { 

      	while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e]) 

	  _G.graph->next(e);

      }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    class InEdgeIt { 

      friend class GraphWrapper<Graph>;

      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;

      typename Graph::InEdgeIt e;

    public:

      InEdgeIt() { }

      InEdgeIt(const typename Graph::InEdgeIt& _e) : e(_e) { }

      InEdgeIt(const Invalid& i) : e(i) { }

      InEdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G, 

	       const Node& _n) : 

	e(*(_G.graph), typename Graph::Node(_n)) { 

      	while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e]) 

	  _G.graph->next(e);

      }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    //typedef typename Graph::SymEdgeIt SymEdgeIt;

    class EdgeIt { 

      friend class GraphWrapper<Graph>;

      friend class SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>;

      typename Graph::EdgeIt e;

    public:

      EdgeIt() { }

      EdgeIt(const typename Graph::EdgeIt& _e) : e(_e) { }

      EdgeIt(const Invalid& i) : e(i) { }

      EdgeIt(const SubGraphWrapper<Graph, NodeFilterMap, EdgeFilterMap>& _G) : 

	e(*(_G.graph)) { 

      	while (_G.graph->valid(e) && !(*(_G.edge_filter_map))[e]) 

	  _G.graph->next(e);

      }

      operator Edge() const { return Edge(typename Graph::Edge(e)); }

    };

    NodeIt& first(NodeIt& i) const { 

      i=NodeIt(*this); return i;

    }

    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const { 

      i=OutEdgeIt(*this, p); return i;

    }

    InEdgeIt& first(InEdgeIt& i, const Node& p) const { 

      i=InEdgeIt(*this, p); return i;

    }

    EdgeIt& first(EdgeIt& i) const { 

      i=EdgeIt(*this); return i;

    }

    NodeIt& next(NodeIt& i) const {

      this->graph->next(i.n); 

      while (this->graph->valid(i) && !(*node_filter_map)[i.n]) { 

	this->graph->next(i.n); }

      return i;

    }

    OutEdgeIt& next(OutEdgeIt& i) const {

      this->graph->next(i.e); 

      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) { 

	this->graph->next(i.e); }

      return i;

    }

    InEdgeIt& next(InEdgeIt& i) const {

      this->graph->next(i.e); 

      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) { 

	this->graph->next(i.e); }

      return i;

    }

    EdgeIt& next(EdgeIt& i) const {

      this->graph->next(i.e); 

      while (this->graph->valid(i) && !(*edge_filter_map)[i.e]) { 

	this->graph->next(i.e); }

      return i;

    }

    Node aNode(const OutEdgeIt& e) const { 

      return Node(this->graph->aNode(e.e)); }

    Node aNode(const InEdgeIt& e) const { 

      return Node(this->graph->aNode(e.e)); }

    Node bNode(const OutEdgeIt& e) const { 

      return Node(this->graph->bNode(e.e)); }

    Node bNode(const InEdgeIt& e) const { 

      return Node(this->graph->bNode(e.e)); }

    /// This function hides \c n in the graph, i.e. the iteration 

    /// jumps over it. This is done by simply setting the value of \c n  

    /// to be false in the corresponding node-map.

    void hide(const Node& n) const { node_filter_map->set(n, false); }

    /// This function hides \c e in the graph, i.e. the iteration 

    /// jumps over it. This is done by simply setting the value of \c e  

    /// to be false in the corresponding edge-map.

    void hide(const Edge& e) const { edge_filter_map->set(e, false); }

    /// The value of \c n is set to be true in the node-map which stores 

    /// hide information. If \c n was hidden previuosly, then it is shown 

    /// again

     void unHide(const Node& n) const { node_filter_map->set(n, true); }

    /// The value of \c e is set to be true in the edge-map which stores 

    /// hide information. If \c e was hidden previuosly, then it is shown 

    /// again

    void unHide(const Edge& e) const { edge_filter_map->set(e, true); }

    /// Returns true if \c n is hidden.

    bool hidden(const Node& n) const { return !(*node_filter_map)[n]; }

    /// Returns true if \c n is hidden.

    bool hidden(const Edge& e) const { return !(*edge_filter_map)[e]; }

  };

  /// A wrapper for forgetting the orientation of a graph.

  /// A wrapper for getting an undirected graph by forgetting

  /// the orientation of a directed one.

  template<typename Graph>

  class UndirGraphWrapper : public GraphWrapper<Graph> {

  protected:

    UndirGraphWrapper() : GraphWrapper<Graph>() { }

  public:

    typedef typename GraphWrapper<Graph>::Node Node;

    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;

    typedef typename GraphWrapper<Graph>::Edge Edge;

    typedef typename GraphWrapper<Graph>::EdgeIt EdgeIt;

    UndirGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { }  

    class OutEdgeIt {

      friend class UndirGraphWrapper<Graph>;

      bool out_or_in; //true iff out

      typename Graph::OutEdgeIt out;

      typename Graph::InEdgeIt in;

    public:

      OutEdgeIt() { }

      OutEdgeIt(const Invalid& i) : Edge(i) { }

      OutEdgeIt(const UndirGraphWrapper<Graph>& _G, const Node& _n) {

	out_or_in=true; _G.graph->first(out, _n);

	if (!(_G.graph->valid(out))) { out_or_in=false; _G.graph->first(in, _n);	}

      } 

      operator Edge() const { 

	if (out_or_in) return Edge(out); else return Edge(in); 

      }

    };

//FIXME InEdgeIt

    typedef OutEdgeIt InEdgeIt; 

    using GraphWrapper<Graph>::first;

//     NodeIt& first(NodeIt& i) const { 

//       i=NodeIt(*this); return i;

//     }

    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const { 

      i=OutEdgeIt(*this, p); return i;

    }

//FIXME

//     InEdgeIt& first(InEdgeIt& i, const Node& p) const { 

//       i=InEdgeIt(*this, p); return i;

//     }

//     EdgeIt& first(EdgeIt& i) const { 

//       i=EdgeIt(*this); return i;

//     }

    using GraphWrapper<Graph>::next;

//     NodeIt& next(NodeIt& n) const {

//       GraphWrapper<Graph>::next(n);

//       return n;

//     }

    OutEdgeIt& next(OutEdgeIt& e) const {

      if (e.out_or_in) {

	typename Graph::Node n=this->graph->tail(e.out);

	this->graph->next(e.out);

	if (!this->graph->valid(e.out)) { 

	  e.out_or_in=false; this->graph->first(e.in, n); }

      } else {

	this->graph->next(e.in);

      }

      return e;

    }

    //FIXME InEdgeIt

//     EdgeIt& next(EdgeIt& e) const {

//       GraphWrapper<Graph>::next(n);

// //      graph->next(e.e);

//       return e;

//     }

    Node aNode(const OutEdgeIt& e) const { 

      if (e.out_or_in) return this->graph->tail(e); else 

	return this->graph->head(e); }

    Node bNode(const OutEdgeIt& e) const { 

      if (e.out_or_in) return this->graph->head(e); else 

	return this->graph->tail(e); }

  };

  /// An undirected graph template

  template<typename Graph>

  class UndirGraph : public UndirGraphWrapper<Graph> {

    typedef UndirGraphWrapper<Graph> Parent;

  protected:

    Graph gr;

  public:

    UndirGraph() : UndirGraphWrapper<Graph>() { 

      Parent::setGraph(gr); 

    }

  };

  /// A wrapper for composing bidirected graph from a directed one. 

  /// experimental, for fezso's sake.

  /// A wrapper for composing bidirected graph from a directed one. 

  /// experimental, for fezso's sake.

  template<typename Graph>

  class BidirGraphWrapper : public GraphWrapper<Graph> {

  protected:

    //const CapacityMap* capacity;

    //FlowMap* flow;

    BidirGraphWrapper() : GraphWrapper<Graph>()/*, 

						 capacity(0), flow(0)*/ { }

//     void setCapacityMap(const CapacityMap& _capacity) {

//       capacity=&_capacity;

//     }

//     void setFlowMap(FlowMap& _flow) {

//       flow=&_flow;

//     }

  public:

    BidirGraphWrapper(Graph& _graph/*, const CapacityMap& _capacity, 

				     FlowMap& _flow*/) : 

      GraphWrapper<Graph>(_graph)/*, capacity(&_capacity), flow(&_flow)*/ { }

    class Edge; 

    class OutEdgeIt; 

    friend class Edge; 

    friend class OutEdgeIt; 

    typedef typename GraphWrapper<Graph>::Node Node;

    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;

    class Edge : public Graph::Edge {

      friend class BidirGraphWrapper<Graph>;

    protected:

      bool backward; //true, iff backward

//      typename Graph::Edge e;

    public:

      Edge() { }

      Edge(const typename Graph::Edge& _e, bool _backward) : 

	Graph::Edge(_e), backward(_backward) { }

      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }

//the unique invalid iterator

      friend bool operator==(const Edge& u, const Edge& v) { 

	return (v.backward==u.backward && 

		static_cast<typename Graph::Edge>(u)==

		static_cast<typename Graph::Edge>(v));

      } 

      friend bool operator!=(const Edge& u, const Edge& v) { 

	return (v.backward!=u.backward || 

		static_cast<typename Graph::Edge>(u)!=

		static_cast<typename Graph::Edge>(v));

      } 

    };

    class OutEdgeIt {

      friend class BidirGraphWrapper<Graph>;

    protected:

      typename Graph::OutEdgeIt out;

      typename Graph::InEdgeIt in;

      bool backward;

    public:

      OutEdgeIt() { }

      //FIXME

//      OutEdgeIt(const Edge& e) : Edge(e) { }

      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }

//the unique invalid iterator

      OutEdgeIt(const BidirGraphWrapper<Graph>& _G, Node v) { 

	backward=false;

	_G.graph->first(out, v);

	while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }

	if (!_G.graph->valid(out)) {

	  backward=true;

	  _G.graph->first(in, v);

	  while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }

	}

      }

      operator Edge() const { 

//	Edge e;

//	e.forward=this->forward;

//	if (this->forward) e=out; else e=in;

//	return e;

	if (this->backward) 

	  return Edge(in, this->backward); 

	else 

	  return Edge(out, this->backward);

      }

    };

    class InEdgeIt {

      friend class BidirGraphWrapper<Graph>;

    protected:

      typename Graph::OutEdgeIt out;

      typename Graph::InEdgeIt in;

      bool backward;

    public:

      InEdgeIt() { }

      //FIXME

//      OutEdgeIt(const Edge& e) : Edge(e) { }

      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }

//the unique invalid iterator

      InEdgeIt(const BidirGraphWrapper<Graph>& _G, Node v) { 

	backward=false;

	_G.graph->first(in, v);

	while(_G.graph->valid(in) && !_G.enabled(*this)) { _G.graph->next(in); }

	if (!_G.graph->valid(in)) {

	  backward=true;

	  _G.graph->first(out, v);

	  while(_G.graph->valid(out) && !_G.enabled(*this)) { _G.graph->next(out); }

	}

      }

      operator Edge() const { 

//	Edge e;

//	e.forward=this->forward;

//	if (this->forward) e=out; else e=in;

//	return e;

	if (this->backward) 

	  return Edge(out, this->backward); 

	else 

	  return Edge(in, this->backward);

      }

    };

    class EdgeIt {

      friend class BidirGraphWrapper<Graph>;

    protected:

      typename Graph::EdgeIt e;

      bool backward;

    public:

      EdgeIt() { }

      EdgeIt(const Invalid& i) : e(i), backward(true) { }

      EdgeIt(const BidirGraphWrapper<Graph>& _G) { 

	backward=false;

	_G.graph->first(e);

	while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);

	if (!_G.graph->valid(e)) {

	  backward=true;

	  _G.graph->first(e);

	  while (_G.graph->valid(e) && !_G.enabled(*this)) _G.graph->next(e);

	}

      }

      operator Edge() const { 

	return Edge(e, this->backward);

      }

    };

    using GraphWrapper<Graph>::first;

//     NodeIt& first(NodeIt& i) const { 

//       i=NodeIt(*this); return i;

//     }

    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const { 

      i=OutEdgeIt(*this, p); return i;

    }

//    FIXME not tested

    InEdgeIt& first(InEdgeIt& i, const Node& p) const { 

      i=InEdgeIt(*this, p); return i;

    }

    EdgeIt& first(EdgeIt& i) const { 

      i=EdgeIt(*this); return i;

    }

    using GraphWrapper<Graph>::next;

//    NodeIt& next(NodeIt& n) const { GraphWrapper<Graph>::next(n); return n; }

    OutEdgeIt& next(OutEdgeIt& e) const { 

      if (!e.backward) {

	Node v=this->graph->aNode(e.out);

	this->graph->next(e.out);

	while(this->graph->valid(e.out) && !enabled(e)) { 

	  this->graph->next(e.out); }

	if (!this->graph->valid(e.out)) {

	  e.backward=true;

	  this->graph->first(e.in, v); 

	  while(this->graph->valid(e.in) && !enabled(e)) { 

	    this->graph->next(e.in); }

	}

      } else {

	this->graph->next(e.in);

	while(this->graph->valid(e.in) && !enabled(e)) { 

	  this->graph->next(e.in); } 

      }

      return e;

    }

//     FIXME Not tested

    InEdgeIt& next(InEdgeIt& e) const { 

      if (!e.backward) {

	Node v=this->graph->aNode(e.in);

	this->graph->next(e.in);

	while(this->graph->valid(e.in) && !enabled(e)) { 

	  this->graph->next(e.in); }

	if (!this->graph->valid(e.in)) {

	  e.backward=true;

	  this->graph->first(e.out, v); 

	  while(this->graph->valid(e.out) && !enabled(e)) { 

	    this->graph->next(e.out); }

	}

      } else {

	this->graph->next(e.out);

	while(this->graph->valid(e.out) && !enabled(e)) { 

	  this->graph->next(e.out); } 

      }

      return e;

    }

    EdgeIt& next(EdgeIt& e) const {

      if (!e.backward) {

	this->graph->next(e.e);

	while(this->graph->valid(e.e) && !enabled(e)) { 

	  this->graph->next(e.e); }

	if (!this->graph->valid(e.e)) {

	  e.backward=true;

	  this->graph->first(e.e); 

	  while(this->graph->valid(e.e) && !enabled(e)) { 

	    this->graph->next(e.e); }

	}

      } else {

	this->graph->next(e.e);

	while(this->graph->valid(e.e) && !enabled(e)) { 

	  this->graph->next(e.e); } 

      }

      return e;

    }

    Node tail(Edge e) const { 

      return ((!e.backward) ? this->graph->tail(e) : this->graph->head(e)); }

    Node head(Edge e) const { 

      return ((!e.backward) ? this->graph->head(e) : this->graph->tail(e)); }

    Node aNode(OutEdgeIt e) const { 

      return ((!e.backward) ? this->graph->aNode(e.out) : 

	      this->graph->aNode(e.in)); }

    Node bNode(OutEdgeIt e) const { 

      return ((!e.backward) ? this->graph->bNode(e.out) : 

	      this->graph->bNode(e.in)); }

    Node aNode(InEdgeIt e) const { 

      return ((!e.backward) ? this->graph->aNode(e.in) : 

	      this->graph->aNode(e.out)); }

    Node bNode(InEdgeIt e) const { 

      return ((!e.backward) ? this->graph->bNode(e.in) : 

	      this->graph->bNode(e.out)); }

    /// Gives back the opposite edge.

    Edge opposite(const Edge& e) const { 

      Edge f=e;

      f.backward=!f.backward;

      return f;

    }

//    int nodeNum() const { return graph->nodeNum(); }

    //FIXME

    void edgeNum() const { }

    //int edgeNum() const { return graph->edgeNum(); }

//    int id(Node v) const { return graph->id(v); }

    bool valid(Node n) const { return GraphWrapper<Graph>::valid(n); }

    bool valid(Edge e) const { 

      return this->graph->valid(e);

	//return e.forward ? graph->valid(e.out) : graph->valid(e.in); 

    }

    bool forward(const Edge& e) const { return !e.backward; }

    bool backward(const Edge& e) const { return e.backward; }

//     void augment(const Edge& e, Number a) const {

//       if (!e.backward)  

// // 	flow->set(e.out, flow->get(e.out)+a);

// 	flow->set(e, (*flow)[e]+a);

//       else  

// // 	flow->set(e.in, flow->get(e.in)-a);

// 	flow->set(e, (*flow)[e]-a);

//     }

    bool enabled(const Edge& e) const { 

      if (!e.backward) 

//	return (capacity->get(e.out)-flow->get(e.out)); 

	//return ((*capacity)[e]-(*flow)[e]);

	return true;

      else 

//	return (flow->get(e.in)); 

	//return ((*flow)[e]); 

	return true;

    }

//     Number enabled(typename Graph::OutEdgeIt out) const { 

// //      return (capacity->get(out)-flow->get(out)); 

//       return ((*capacity)[out]-(*flow)[out]); 

//     }

//     Number enabled(typename Graph::InEdgeIt in) const { 

// //      return (flow->get(in)); 

//       return ((*flow)[in]); 

//     }

    template <typename T>

    class EdgeMap {

      typename Graph::template EdgeMap<T> forward_map, backward_map; 

    public:

      EdgeMap(const BidirGraphWrapper<Graph>& _G) : forward_map(*(_G.graph)), backward_map(*(_G.graph)) { }

      EdgeMap(const BidirGraphWrapper<Graph>& _G, T a) : forward_map(*(_G.graph), a), backward_map(*(_G.graph), a) { }

      void set(Edge e, T a) { 

	if (!e.backward) 

	  forward_map.set(e.out, a); 

	else 

	  backward_map.set(e.in, a); 

      }

      T operator[](Edge e) const { 

	if (!e.backward) 

	  return forward_map[e.out]; 

	else 

	  return backward_map[e.in]; 

      }

//       T get(Edge e) const { 

// 	if (e.out_or_in) 

// 	  return forward_map.get(e.out); 

// 	else 

// 	  return backward_map.get(e.in); 

//       }

    };

  };

  /// A wrapper for composing the residual graph for directed flow and circulation problems.

  /// A wrapper for composing the residual graph for directed flow and circulation problems.

  template<typename Graph, typename Number, 

	   typename CapacityMap, typename FlowMap>

  class ResGraphWrapper : public GraphWrapper<Graph> {

  protected:

    const CapacityMap* capacity;

    FlowMap* flow;

    ResGraphWrapper() : GraphWrapper<Graph>(0), 

			capacity(0), flow(0) { }

    void setCapacityMap(const CapacityMap& _capacity) {

      capacity=&_capacity;

    }

    void setFlowMap(FlowMap& _flow) {

      flow=&_flow;

    }

  public:

    ResGraphWrapper(Graph& _graph, const CapacityMap& _capacity, 

		    FlowMap& _flow) : 

      GraphWrapper<Graph>(_graph), capacity(&_capacity), flow(&_flow) { }

    class Edge; 

    class OutEdgeIt; 

    friend class Edge; 

    friend class OutEdgeIt; 

    typedef typename GraphWrapper<Graph>::Node Node;

    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;

    class Edge : public Graph::Edge {

      friend class ResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;

    protected:

      bool backward; //true, iff backward

//      typename Graph::Edge e;

    public:

      Edge() { }

      Edge(const typename Graph::Edge& _e, bool _backward) : 

	Graph::Edge(_e), backward(_backward) { }

      Edge(const Invalid& i) : Graph::Edge(i), backward(true) { }

//the unique invalid iterator

      friend bool operator==(const Edge& u, const Edge& v) { 

	return (v.backward==u.backward && 

		static_cast<typename Graph::Edge>(u)==

		static_cast<typename Graph::Edge>(v));

      } 

      friend bool operator!=(const Edge& u, const Edge& v) { 

	return (v.backward!=u.backward || 

		static_cast<typename Graph::Edge>(u)!=

		static_cast<typename Graph::Edge>(v));

      } 

    };

    class OutEdgeIt {

      friend class ResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;

    protected:

      typename Graph::OutEdgeIt out;

      typename Graph::InEdgeIt in;

      bool backward;

    public:

      OutEdgeIt() { }

      //FIXME

//      OutEdgeIt(const Edge& e) : Edge(e) { }

      OutEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }

//the unique invalid iterator

      OutEdgeIt(const ResGraphWrapper<Graph, Number, CapacityMap, FlowMap>& _G, Node v) { 

	backward=false;

	_G.graph->first(out, v);

	while( _G.graph->valid(out) && !(_G.resCap(*this)>0) ) { _G.graph->next(out); }

	if (!_G.graph->valid(out)) {

	  backward=true;

	  _G.graph->first(in, v);

	  while( _G.graph->valid(in) && !(_G.resCap(*this)>0) ) { _G.graph->next(in); }

	}

      }

      operator Edge() const { 

//	Edge e;

//	e.forward=this->forward;

//	if (this->forward) e=out; else e=in;

//	return e;

	if (this->backward) 

	  return Edge(in, this->backward); 

	else 

	  return Edge(out, this->backward);

      }

    };

    class InEdgeIt {

      friend class ResGraphWrapper<Graph, Number, CapacityMap, FlowMap>;

    protected:

      typename Graph::OutEdgeIt out;

      typename Graph::InEdgeIt in;

      bool backward;

    public:

      InEdgeIt() { }

      //FIXME

//      OutEdgeIt(const Edge& e) : Edge(e) { }

      InEdgeIt(const Invalid& i) : out(i), in(i), backward(true) { }