// -*- c++ -*-

#ifndef HUGO_EDMONDS_KARP_H

#define HUGO_EDMONDS_KARP_H

#include <algorithm>

#include <list>

#include <iterator>

#include <bfs_iterator.h>

#include <invalid.h>

namespace hugo {

  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>

  class ResGraph {

  public:

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

  private:

    typedef typename Graph::SymEdgeIt OldSymEdgeIt;

    const Graph& G;

    FlowMap& flow;

    const CapacityMap& capacity;

  public:

    ResGraph(const Graph& _G, FlowMap& _flow, 

	     const CapacityMap& _capacity) : 

      G(_G), flow(_flow), capacity(_capacity) { }

    class Edge; 

    class OutEdgeIt; 

    friend class Edge; 

    friend class OutEdgeIt; 

    class Edge {

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

    protected:

      const ResGraph<Graph, Number, FlowMap, CapacityMap>* resG;

      OldSymEdgeIt sym;

    public:

      Edge() { } 

      //Edge(const Edge& e) : resG(e.resG), sym(e.sym) { }

      Number free() const { 

	if (resG->G.aNode(sym)==resG->G.tail(sym)) { 

	  return (resG->capacity.get(sym)-resG->flow.get(sym)); 

	} else { 

	  return (resG->flow.get(sym)); 

	}

      }

      bool valid() const { return sym.valid(); }

      void augment(Number a) const {

	if (resG->G.aNode(sym)==resG->G.tail(sym)) { 

	  resG->flow.set(sym, resG->flow.get(sym)+a);

	  //resG->flow[sym]+=a;

	} else { 

	  resG->flow.set(sym, resG->flow.get(sym)-a);

	  //resG->flow[sym]-=a;

	}

      }

    };

    class OutEdgeIt : public Edge {

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

    public:

      OutEdgeIt() { }

      //OutEdgeIt(const OutEdgeIt& e) { resG=e.resG; sym=e.sym; }

    private:

      OutEdgeIt(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _resG, Node v) { 

      	resG=&_resG;

	sym=resG->G.template first<OldSymEdgeIt>(v);

	while( sym.valid() && !(free()>0) ) { ++sym; }

      }

    public:

      OutEdgeIt& operator++() { 

	++sym; 

	while( sym.valid() && !(free()>0) ) { ++sym; }

	return *this; 

      }

    };

    void /*getF*/first(OutEdgeIt& e, Node v) const { 

      e=OutEdgeIt(*this, v); 

    }

    void /*getF*/first(NodeIt& v) const { G./*getF*/first(v); }

    template< typename It >

    It first() const { 

      It e;      

      /*getF*/first(e);

      return e; 

    }

    template< typename It >

    It first(Node v) const { 

      It e;

      /*getF*/first(e, v);

      return e; 

    }

    Node tail(Edge e) const { return G.aNode(e.sym); }

    Node head(Edge e) const { return G.bNode(e.sym); }

    Node aNode(OutEdgeIt e) const { return G.aNode(e.sym); }

    Node bNode(OutEdgeIt e) const { return G.bNode(e.sym); }

    int id(Node v) const { return G.id(v); }

    template <typename S>

    class NodeMap {

      typename Graph::NodeMap<S> node_map; 

    public:

      NodeMap(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }

      NodeMap(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _G, S a) : node_map(_G.G, a) { }

      void set(Node nit, S a) { node_map.set(nit, a); }

      S get(Node nit) const { return node_map.get(nit); }

      S& operator[](Node nit) { return node_map[nit]; } 

      const S& operator[](Node nit) const { return node_map[nit]; } 

    };

  };

  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>

  class ResGraph2 {

  public:

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

  private:

    //typedef typename Graph::SymEdgeIt OldSymEdgeIt;

    typedef typename Graph::OutEdgeIt OldOutEdgeIt;

    typedef typename Graph::InEdgeIt OldInEdgeIt;

    const Graph& G;

    FlowMap& flow;

    const CapacityMap& capacity;

  public:

    ResGraph2(const Graph& _G, FlowMap& _flow, 

	     const CapacityMap& _capacity) : 

      G(_G), flow(_flow), capacity(_capacity) { }

    class Edge; 

    class OutEdgeIt; 

    friend class Edge; 

    friend class OutEdgeIt; 

    class Edge {

      friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;

    protected:

      const ResGraph2<Graph, Number, FlowMap, CapacityMap>* resG;

      //OldSymEdgeIt sym;

      OldOutEdgeIt out;

      OldInEdgeIt in;

      bool out_or_in; //true, iff out

    public:

      Edge() : out_or_in(true) { } 

      Number free() const { 

	if (out_or_in) { 

	  return (resG->capacity.get(out)-resG->flow.get(out)); 

	} else { 

	  return (resG->flow.get(in)); 

	}

      }

      bool valid() const { 

	return out_or_in && out.valid() || in.valid(); }

      void augment(Number a) const {

	if (out_or_in) { 

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

	} else { 

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

	}

      }

    };

    class OutEdgeIt : public Edge {

      friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;

    public:

      OutEdgeIt() { }

    private:

      OutEdgeIt(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _resG, Node v) { 

      	resG=&_resG;

	out=resG->G.template first<OldOutEdgeIt>(v);

	while( out.valid() && !(free()>0) ) { ++out; }

	if (!out.valid()) {

	  out_or_in=0;

	  in=resG->G.template first<OldInEdgeIt>(v);

	  while( in.valid() && !(free()>0) ) { ++in; }

	}

      }

    public:

      OutEdgeIt& operator++() { 

	if (out_or_in) {

	  Node v=resG->G.aNode(out);

	  ++out;

	  while( out.valid() && !(free()>0) ) { ++out; }

	  if (!out.valid()) {

	    out_or_in=0;

	    in=resG->G.template first<OldInEdgeIt>(v);

	    while( in.valid() && !(free()>0) ) { ++in; }

	  }

	} else {

	  ++in;

	  while( in.valid() && !(free()>0) ) { ++in; } 

	}

	return *this; 

      }

    };

    void /*getF*/first(OutEdgeIt& e, Node v) const { 

      e=OutEdgeIt(*this, v); 

    }

    void /*getF*/first(NodeIt& v) const { G./*getF*/first(v); }

    template< typename It >

    It first() const { 

      It e;

      /*getF*/first(e);

      return e; 

    }

    template< typename It >

    It first(Node v) const { 

      It e;

      /*getF*/first(e, v);

      return e; 

    }

    Node tail(Edge e) const { 

      return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }

    Node head(Edge e) const { 

      return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

    Node aNode(OutEdgeIt e) const { 

      return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }

    Node bNode(OutEdgeIt e) const { 

      return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

    int id(Node v) const { return G.id(v); }

    template <typename S>

    class NodeMap {

      typename Graph::NodeMap<S> node_map; 

    public:

      NodeMap(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }

      NodeMap(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _G, S a) : node_map(_G.G, a) { }

      void set(Node nit, S a) { node_map.set(nit, a); }

      S get(Node nit) const { return node_map.get(nit); }

    };

  };

  template <typename GraphWrapper, typename Number, typename FlowMap, typename CapacityMap>

  class MaxFlow {

  protected:

    typedef GraphWrapper GW;

    typedef typename GW::Node Node;

    typedef typename GW::Edge Edge;

    typedef typename GW::EdgeIt EdgeIt;

    typedef typename GW::OutEdgeIt OutEdgeIt;

    typedef typename GW::InEdgeIt InEdgeIt;

    //const Graph* G;

    GW gw;

    Node s;

    Node t;

    FlowMap* flow;

    const CapacityMap* capacity;

    typedef ResGraphWrapper<GW, Number, FlowMap, CapacityMap > ResGW;

    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;

    typedef typename ResGW::Edge ResGWEdge;

  public:

    MaxFlow(const GW& _gw, Node _s, Node _t, FlowMap& _flow, const CapacityMap& _capacity) : 

      gw(_gw), s(_s), t(_t), flow(&_flow), capacity(&_capacity) { }

    bool augmentOnShortestPath() {

      ResGW res_graph(gw, *flow, *capacity);

      bool _augment=false;

      typedef typename ResGW::NodeMap<bool> ReachedMap;

      BfsIterator5< ResGW, ReachedMap > bfs(res_graph);

      bfs.pushAndSetReached(s);

      typename ResGW::NodeMap<ResGWEdge> pred(res_graph); 

      pred.set(s, INVALID);

      typename ResGW::NodeMap<Number> free(res_graph);

      //searching for augmenting path

      while ( !bfs.finished() ) { 

	ResGWOutEdgeIt e=bfs;

	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

	  Node v=res_graph.tail(e);

	  Node w=res_graph.head(e);

	  pred.set(w, e);

	  if (res_graph.valid(pred.get(v))) {

	    free.set(w, std::min(free.get(v), res_graph.resCap(e)));

	  } else {

	    free.set(w, res_graph.resCap(e)); 

	  }

	  if (res_graph.head(e)==t) { _augment=true; break; }

	}

	++bfs;

      } //end of searching augmenting path

      if (_augment) {

	Node n=t;

	Number augment_value=free.get(t);

	while (res_graph.valid(pred.get(n))) { 

	  ResGWEdge e=pred.get(n);

	  res_graph.augment(e, augment_value); 

	  n=res_graph.tail(e);

	}

      }

      return _augment;

    }

    template<typename MapGraphWrapper> 

    class DistanceMap {

    protected:

      MapGraphWrapper gw;

      typename MapGraphWrapper::NodeMap<int> dist; 

    public:

      DistanceMap(MapGraphWrapper& _gw) : gw(_gw), dist(_gw, _gw.nodeNum()) { }

      void set(const typename MapGraphWrapper::Node& n, int a) { dist[n]=a; }

      int get(const typename MapGraphWrapper::Node& n) const { return dist[n]; }

      bool get(const typename MapGraphWrapper::Edge& e) const { 

	return (dist.get(gw.tail(e))<dist.get(gw.head(e))); 

      }

    };

    template<typename MutableGraph> bool augmentOnBlockingFlow() {      

      typedef MutableGraph MG;

      bool _augment=false;

      ResGW res_graph(gw, *flow, *capacity);

      typedef typename ResGW::NodeMap<bool> ReachedMap;

      BfsIterator5< ResGW, ReachedMap > bfs(res_graph);

      bfs.pushAndSetReached(s);

      //typename ResGW::NodeMap<int> dist(res_graph); //filled up with 0's

      DistanceMap<ResGW> dist(res_graph);

      while ( !bfs.finished() ) { 

	ResGWOutEdgeIt e=bfs;

	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

	}

	++bfs;

      } //computing distances from s in the residual graph

      MG F;

      typedef SubGraphWrapper<ResGW, DistanceMap<ResGW> > FilterResGW;

      FilterResGW filter_res_graph(res_graph, dist);

      typename ResGW::NodeMap<typename MG::Node> res_graph_to_F(res_graph);

      {

	typename ResGW::NodeIt n;

	for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {

	  res_graph_to_F.set(n, F.addNode());

	}

      }

      typename MG::Node sF=res_graph_to_F.get(s);

      typename MG::Node tF=res_graph_to_F.get(t);

      typename MG::EdgeMap<ResGWEdge> original_edge(F);

      typename MG::EdgeMap<Number> residual_capacity(F);

      //Making F to the graph containing the edges of the residual graph 

      //which are in some shortest paths

      {

	typename FilterResGW::EdgeIt e;

	for(filter_res_graph.first(e); filter_res_graph.valid(e); filter_res_graph.next(e)) {

	  //if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {

	  typename MG::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

	  original_edge.update();

	  original_edge.set(f, e);

	  residual_capacity.update();

	  residual_capacity.set(f, res_graph.resCap(e));

	  //} 

	}

      }

      bool __augment=true;

      while (__augment) {

	__augment=false;

	//computing blocking flow with dfs

	typedef typename TrivGraphWrapper<MG>::NodeMap<bool> BlockingReachedMap;

	DfsIterator5< TrivGraphWrapper<MG>, BlockingReachedMap > dfs(F);

	typename MG::NodeMap<typename MG::Edge> pred(F);

	pred.set(sF, INVALID);

	//invalid iterators for sources

	typename MG::NodeMap<Number> free(F);

	dfs.pushAndSetReached(sF);      

	while (!dfs.finished()) {

	  ++dfs;

	  if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {

	    if (dfs.isBNodeNewlyReached()) {

	      typename MG::Node v=F.aNode(dfs);

	      typename MG::Node w=F.bNode(dfs);

	      pred.set(w, dfs);

	      if (F.valid(pred.get(v))) {

		free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));

	      } else {

		free.set(w, residual_capacity.get(dfs)); 

	      }

	      if (w==tF) { 

		__augment=true; 

		_augment=true;

		break; 

	      }

	    } else {

	      F.erase(/*typename MG::OutEdgeIt*/(dfs));

	    }

	  } 

	}

	if (__augment) {

	  typename MG::Node n=tF;

	  Number augment_value=free.get(tF);

	  while (F.valid(pred.get(n))) { 

	    typename MG::Edge e=pred.get(n);

	    res_graph.augment(original_edge.get(e), augment_value); 

	    n=F.tail(e);

	    if (residual_capacity.get(e)==augment_value) 

	      F.erase(e); 

	    else 

	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);

	  }

	}

      }

      return _augment;

    }

    template<typename MutableGraph> bool augmentOnBlockingFlow1() {      

      typedef MutableGraph MG;

      bool _augment=false;

      ResGW res_graph(gw, *flow, *capacity);

      //bfs for distances on the residual graph

      typedef typename ResGW::NodeMap<bool> ReachedMap;

      BfsIterator5< ResGW, ReachedMap > bfs(res_graph);

      bfs.pushAndSetReached(s);

      typename ResGW::NodeMap<int> dist(res_graph); //filled up with 0's

      //F will contain the physical copy of the residual graph

      //with the set of edges which are on shortest paths

      MG F;

      typename ResGW::NodeMap<typename MG::Node> res_graph_to_F(res_graph);

      {

	typename ResGW::NodeIt n;

	for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {

	  res_graph_to_F.set(n, F.addNode());

	}

      }

      typename MG::Node sF=res_graph_to_F.get(s);

      typename MG::Node tF=res_graph_to_F.get(t);

      typename MG::EdgeMap<ResGWEdge> original_edge(F);

      typename MG::EdgeMap<Number> residual_capacity(F);

      while ( !bfs.finished() ) { 

	ResGWOutEdgeIt e=bfs;

	if (res_graph.valid(e)) {

	  if (bfs.isBNodeNewlyReached()) {

	    dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

	    typename MG::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

	    original_edge.update();

	    original_edge.set(f, e);

	    residual_capacity.update();

	    residual_capacity.set(f, res_graph.resCap(e));

	  } else {

	    if (dist.get(res_graph.head(e))==(dist.get(res_graph.tail(e))+1)) {

	      typename MG::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

	      original_edge.update();

	      original_edge.set(f, e);

	      residual_capacity.update();

	      residual_capacity.set(f, res_graph.resCap(e));

	    }

	  }

	}

	++bfs;

      } //computing distances from s in the residual graph

      bool __augment=true;

      while (__augment) {

	__augment=false;

	//computing blocking flow with dfs

	typedef typename TrivGraphWrapper<MG>::NodeMap<bool> BlockingReachedMap;

	DfsIterator5< TrivGraphWrapper<MG>, BlockingReachedMap > dfs(F);

	typename MG::NodeMap<typename MG::Edge> pred(F);

	pred.set(sF, INVALID);

	//invalid iterators for sources

	typename MG::NodeMap<Number> free(F);

	dfs.pushAndSetReached(sF);      

	while (!dfs.finished()) {

	  ++dfs;

	  if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {

	    if (dfs.isBNodeNewlyReached()) {

	      typename MG::Node v=F.aNode(dfs);

	      typename MG::Node w=F.bNode(dfs);

	      pred.set(w, dfs);

	      if (F.valid(pred.get(v))) {

		free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));

	      } else {

		free.set(w, residual_capacity.get(dfs)); 

	      }

	      if (w==tF) { 

		__augment=true; 

		_augment=true;

		break; 

	      }

	    } else {

	      F.erase(/*typename MG::OutEdgeIt*/(dfs));

	    }

	  } 

	}

	if (__augment) {

	  typename MG::Node n=tF;

	  Number augment_value=free.get(tF);

	  while (F.valid(pred.get(n))) { 

	    typename MG::Edge e=pred.get(n);

	    res_graph.augment(original_edge.get(e), augment_value); 

	    n=F.tail(e);

	    if (residual_capacity.get(e)==augment_value) 

	      F.erase(e); 

	    else 

	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);

	  }

	}

      }

      return _augment;

    }

    bool augmentOnBlockingFlow2() {

      bool _augment=false;

      ResGW res_graph(gw, *flow, *capacity);

      typedef typename ResGW::NodeMap<bool> ReachedMap;

      BfsIterator5< ResGW, ReachedMap > bfs(res_graph);

      bfs.pushAndSetReached(s);

      DistanceMap<ResGW> dist(res_graph);

      while ( !bfs.finished() ) { 

 	ResGWOutEdgeIt e=bfs;

 	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

 	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

 	}

	++bfs;

      } //computing distances from s in the residual graph

      //Subgraph containing the edges on some shortest paths

      typedef SubGraphWrapper<ResGW, DistanceMap<ResGW> > FilterResGW;

      FilterResGW filter_res_graph(res_graph, dist);

      //Subgraph, which is able to delete edges which are already 

      //met by the dfs

      typename FilterResGW::NodeMap<typename FilterResGW::OutEdgeIt> 

 	first_out_edges(filter_res_graph);

      typename FilterResGW::NodeIt v;

      for(filter_res_graph.first(v); filter_res_graph.valid(v); 

 	  filter_res_graph.next(v)) 

      {

 	typename FilterResGW::OutEdgeIt e;

 	filter_res_graph.first(e, v);

 	first_out_edges.set(v, e);

      }

      typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::

	NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;

      ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);

      bool __augment=true;

      while (__augment) {

 	__augment=false;

 	//computing blocking flow with dfs

	typedef typename ErasingResGW::NodeMap<bool> BlockingReachedMap;

 	DfsIterator5< ErasingResGW, BlockingReachedMap > 

 	  dfs(erasing_res_graph);

 	typename ErasingResGW::NodeMap<typename ErasingResGW::OutEdgeIt> 

 	  pred(erasing_res_graph); 

 	pred.set(s, INVALID);

 	//invalid iterators for sources

 	typename ErasingResGW::NodeMap<Number> free(erasing_res_graph);

 	dfs.pushAndSetReached(s);

 	while (!dfs.finished()) {

 	  ++dfs;

 	  if (erasing_res_graph.valid(

 		/*typename ErasingResGW::OutEdgeIt*/(dfs))) 

 	  { 

 	    if (dfs.isBNodeNewlyReached()) {

 	      typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);

 	      typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);

 	      pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));

 	      if (erasing_res_graph.valid(pred.get(v))) {

 		free.set(w, std::min(free.get(v), res_graph.resCap(dfs)));

 	      } else {

 		free.set(w, res_graph.resCap(dfs)); 

 	      }

 	      if (w==t) { 

 		__augment=true; 

 		_augment=true;

 		break; 

 	      }

	    } else {

	      erasing_res_graph.erase(dfs);

	    }

	  }

	}	

 	if (__augment) {

 	  typename ErasingResGW::Node n=t;

 	  Number augment_value=free.get(n);

 	  while (erasing_res_graph.valid(pred.get(n))) { 

 	    typename ErasingResGW::OutEdgeIt e=pred.get(n);

 	    res_graph.augment(e, augment_value);

 	    n=erasing_res_graph.tail(e);

 	    if (res_graph.resCap(e)==0)

 	      erasing_res_graph.erase(e);

 	  }

 	}

      } //while (__augment) 

      return _augment;

    }

//     bool augmentOnBlockingFlow2() {

//       bool _augment=false;

//       //typedef ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> EAugGraph;

//       typedef FilterGraphWrapper< ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> > EAugGraph;

//       typedef typename EAugGraph::OutEdgeIt EAugOutEdgeIt;

//       typedef typename EAugGraph::Edge EAugEdge;

//       EAugGraph res_graph(*G, *flow, *capacity);

//       //typedef typename EAugGraph::NodeMap<bool> ReachedMap;

//       BfsIterator5< 

// 	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 

// 	/*typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt,*/ 

// 	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);

//       bfs.pushAndSetReached(s);

//       typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::

// 	NodeMap<int>& dist=res_graph.dist;

//       while ( !bfs.finished() ) {

// 	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt e=bfs;

// 	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

// 	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

// 	}

// 	++bfs;	

//       } //computing distances from s in the residual graph

//       bool __augment=true;

//       while (__augment) {

// 	__augment=false;

// 	//computing blocking flow with dfs

// 	typedef typename EAugGraph::NodeMap<bool> BlockingReachedMap;

// 	DfsIterator5< EAugGraph/*, EAugOutEdgeIt*/, BlockingReachedMap > 

// 	  dfs(res_graph);

// 	typename EAugGraph::NodeMap<EAugEdge> pred(res_graph); 

// 	pred.set(s, EAugEdge(INVALID));

// 	//invalid iterators for sources

// 	typename EAugGraph::NodeMap<Number> free(res_graph);

// 	dfs.pushAndSetReached(s);

// 	while (!dfs.finished()) {

// 	  ++dfs;

// 	  if (res_graph.valid(EAugOutEdgeIt(dfs))) { 

// 	    if (dfs.isBNodeNewlyReached()) {

// 	      typename EAugGraph::Node v=res_graph.aNode(dfs);

// 	      typename EAugGraph::Node w=res_graph.bNode(dfs);

// 	      pred.set(w, EAugOutEdgeIt(dfs));

// 	      if (res_graph.valid(pred.get(v))) {

// 		free.set(w, std::min(free.get(v), res_graph.free(dfs)));

// 	      } else {

// 		free.set(w, res_graph.free(dfs)); 

// 	      }

// 	      if (w==t) { 

// 		__augment=true; 

// 		_augment=true;

// 		break; 

// 	      }

// 	    } else {

// 	      res_graph.erase(dfs);

// 	    }

// 	  } 

// 	}

// 	if (__augment) {

// 	  typename EAugGraph::Node n=t;

// 	  Number augment_value=free.get(t);

// 	  while (res_graph.valid(pred.get(n))) { 

// 	    EAugEdge e=pred.get(n);

// 	    res_graph.augment(e, augment_value);

// 	    n=res_graph.tail(e);

// 	    if (res_graph.free(e)==0)

// 	      res_graph.erase(e);

// 	  }

// 	}

//       }

//       return _augment;

//     }

    void run() {

      //int num_of_augmentations=0;

      while (augmentOnShortestPath()) { 

	//while (augmentOnBlockingFlow<MutableGraph>()) { 

	//std::cout << ++num_of_augmentations << " ";

	//std::cout<<std::endl;

      } 

    }

    template<typename MutableGraph> void run() {

      //int num_of_augmentations=0;

      //while (augmentOnShortestPath()) { 

	while (augmentOnBlockingFlow<MutableGraph>()) { 

	//std::cout << ++num_of_augmentations << " ";

	//std::cout<<std::endl;

      } 

    }

    Number flowValue() { 

      Number a=0;

      OutEdgeIt e;

      for(gw.first(e, s); gw.valid(e); gw.next(e)) {

	a+=flow->get(e);

      }

      return a;

    }

  };

//   template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>

//   class MaxMatching {

//   public:

//     typedef typename Graph::Node Node;

//     typedef typename Graph::NodeIt NodeIt;

//     typedef typename Graph::Edge Edge;

//     typedef typename Graph::EdgeIt EdgeIt;

//     typedef typename Graph::OutEdgeIt OutEdgeIt;

//     typedef typename Graph::InEdgeIt InEdgeIt;

//     typedef typename Graph::NodeMap<bool> SMap;

//     typedef typename Graph::NodeMap<bool> TMap;

//   private:

//     const Graph* G;

//     SMap* S;

//     TMap* T;

//     //Node s;

//     //Node t;

//     FlowMap* flow;

//     const CapacityMap* capacity;

//     typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;

//     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

//     typedef typename AugGraph::Edge AugEdge;

//     typename Graph::NodeMap<int> used; //0

//   public:

//     MaxMatching(const Graph& _G, SMap& _S, TMap& _T, FlowMap& _flow, const CapacityMap& _capacity) : 

//       G(&_G), S(&_S), T(&_T), flow(&_flow), capacity(&_capacity), used(_G) { }

//     bool augmentOnShortestPath() {

//       AugGraph res_graph(*G, *flow, *capacity);

//       bool _augment=false;

//       typedef typename AugGraph::NodeMap<bool> ReachedMap;

//       BfsIterator5< AugGraph, /*AugOutEdgeIt,*/ ReachedMap > bfs(res_graph);

//       typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

//       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {

// 	if ((S->get(s)) && (used.get(s)<1) ) {

// 	  //Number u=0;

// 	  //for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))

// 	  //u+=flow->get(e);

// 	  //if (u<1) {

// 	    bfs.pushAndSetReached(s);

// 	    pred.set(s, AugEdge(INVALID));

// 	    //}

// 	}

//       }

//       typename AugGraph::NodeMap<Number> free(res_graph);

//       Node n;

//       //searching for augmenting path

//       while ( !bfs.finished() ) { 

// 	AugOutEdgeIt e=bfs;

// 	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

// 	  Node v=res_graph.tail(e);

// 	  Node w=res_graph.head(e);

// 	  pred.set(w, e);

// 	  if (res_graph.valid(pred.get(v))) {

// 	    free.set(w, std::min(free.get(v), res_graph.free(e)));

// 	  } else {

// 	    free.set(w, res_graph.free(e)); 

// 	  }

// 	  n=res_graph.head(e);

// 	  if (T->get(n) && (used.get(n)<1) ) { 

// 	    //Number u=0;

// 	    //for(InEdgeIt f=G->template first<InEdgeIt>(n); G->valid(f); G->next(f))

// 	    //u+=flow->get(f);

// 	    //if (u<1) {

// 	      _augment=true; 

// 	      break; 

// 	      //}

// 	  }

// 	}

// 	++bfs;

//       } //end of searching augmenting path

//       if (_augment) {

// 	//Node n=t;

// 	used.set(n, 1); //mind2 vegen jav

// 	Number augment_value=free.get(n);

// 	while (res_graph.valid(pred.get(n))) { 

// 	  AugEdge e=pred.get(n);

// 	  res_graph.augment(e, augment_value); 

// 	  n=res_graph.tail(e);

// 	}

// 	used.set(n, 1); //mind2 vegen jav

//       }

//       return _augment;

//     }

// //     template<typename MutableGraph> bool augmentOnBlockingFlow() {      

// //       bool _augment=false;

// //       AugGraph res_graph(*G, *flow, *capacity);

// //       typedef typename AugGraph::NodeMap<bool> ReachedMap;

// //       BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > bfs(res_graph);

// //       //typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

// //       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {

// // 	if (S->get(s)) {

// // 	  Number u=0;

// // 	  for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))

// // 	    u+=flow->get(e);

// // 	  if (u<1) {

// // 	    bfs.pushAndSetReached(s);

// // 	    //pred.set(s, AugEdge(INVALID));

// // 	  }

// // 	}

// //       }

// //       //bfs.pushAndSetReached(s);

// //       typename AugGraph::NodeMap<int> dist(res_graph); //filled up with 0's

// //       while ( !bfs.finished() ) { 

// // 	AugOutEdgeIt e=bfs;

// // 	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

// // 	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

// // 	}

// // 	++bfs;

// //       } //computing distances from s in the residual graph

// //       MutableGraph F;

// //       typename AugGraph::NodeMap<typename MutableGraph::Node> 

// // 	res_graph_to_F(res_graph);

// //       for(typename AugGraph::NodeIt n=res_graph.template first<typename AugGraph::NodeIt>(); res_graph.valid(n); res_graph.next(n)) {

// // 	res_graph_to_F.set(n, F.addNode());

// //       }

// //       typename MutableGraph::Node sF=res_graph_to_F.get(s);

// //       typename MutableGraph::Node tF=res_graph_to_F.get(t);

// //       typename MutableGraph::EdgeMap<AugEdge> original_edge(F);

// //       typename MutableGraph::EdgeMap<Number> residual_capacity(F);

// //       //Making F to the graph containing the edges of the residual graph 

// //       //which are in some shortest paths

// //       for(typename AugGraph::EdgeIt e=res_graph.template first<typename AugGraph::EdgeIt>(); res_graph.valid(e); res_graph.next(e)) {

// // 	if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {

// // 	  typename MutableGraph::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

// // 	  original_edge.update();

// // 	  original_edge.set(f, e);

// // 	  residual_capacity.update();

// // 	  residual_capacity.set(f, res_graph.free(e));

// // 	} 

// //       }

// //       bool __augment=true;

// //       while (__augment) {

// // 	__augment=false;

// // 	//computing blocking flow with dfs

// // 	typedef typename MutableGraph::NodeMap<bool> BlockingReachedMap;

// // 	DfsIterator4< MutableGraph, typename MutableGraph::OutEdgeIt, BlockingReachedMap > dfs(F);

// // 	typename MutableGraph::NodeMap<typename MutableGraph::Edge> pred(F);

// // 	pred.set(sF, typename MutableGraph::Edge(INVALID));

// // 	//invalid iterators for sources

// // 	typename MutableGraph::NodeMap<Number> free(F);

// // 	dfs.pushAndSetReached(sF);      

// // 	while (!dfs.finished()) {

// // 	  ++dfs;

// // 	  if (F.valid(typename MutableGraph::OutEdgeIt(dfs))) {

// // 	    if (dfs.isBNodeNewlyReached()) {

// // 	      typename MutableGraph::Node v=F.aNode(dfs);

// // 	      typename MutableGraph::Node w=F.bNode(dfs);

// // 	      pred.set(w, dfs);

// // 	      if (F.valid(pred.get(v))) {

// // 		free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));

// // 	      } else {

// // 		free.set(w, residual_capacity.get(dfs)); 

// // 	      }

// // 	      if (w==tF) { 

// // 		__augment=true; 

// // 		_augment=true;

// // 		break; 

// // 	      }

// // 	    } else {

// // 	      F.erase(typename MutableGraph::OutEdgeIt(dfs));

// // 	    }

// // 	  } 

// // 	}

// // 	if (__augment) {

// // 	  typename MutableGraph::Node n=tF;

// // 	  Number augment_value=free.get(tF);

// // 	  while (F.valid(pred.get(n))) { 

// // 	    typename MutableGraph::Edge e=pred.get(n);

// // 	    res_graph.augment(original_edge.get(e), augment_value); 

// // 	    n=F.tail(e);

// // 	    if (residual_capacity.get(e)==augment_value) 

// // 	      F.erase(e); 

// // 	    else 

// // 	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);

// // 	  }

// // 	}

// //       }

// //       return _augment;

// //     }

//     bool augmentOnBlockingFlow2() {

//       bool _augment=false;

//       //typedef ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> EAugGraph;

//       typedef FilterGraphWrapper< ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> > EAugGraph;

//       typedef typename EAugGraph::OutEdgeIt EAugOutEdgeIt;

//       typedef typename EAugGraph::Edge EAugEdge;

//       EAugGraph res_graph(*G, *flow, *capacity);

//       //typedef typename EAugGraph::NodeMap<bool> ReachedMap;

//       BfsIterator5< 

// 	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 

// 	/*typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt,*/ 

// 	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);