// -*- c++ -*-

 #ifndef HUGO_EDMONDS_KARP_H

 #define HUGO_EDMONDS_KARP_H

 #include <algorithm>

 #include <list>

 #include <iterator>

 #include <bfs_iterator.h>

 #include <invalid.h>

 #include <graph_wrapper.h>

 #include <maps.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 Graph, typename Number, typename FlowMap, typename CapacityMap>

   class MaxFlow {

   protected:

     typedef typename Graph::Node Node;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::InEdgeIt InEdgeIt;

     const Graph* g;

     Node s;

     Node t;

     FlowMap* flow;

     const CapacityMap* capacity;

     typedef ResGraphWrapper<const Graph, Number, FlowMap, CapacityMap > ResGW;

     typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;

     typedef typename ResGW::Edge ResGWEdge;

   public:

     MaxFlow(const Graph& _g, Node _s, Node _t, FlowMap& _flow, const CapacityMap& _capacity) : 

       g(&_g), s(_s), t(_t), flow(&_flow), capacity(&_capacity) { }

     bool augmentOnShortestPath() {

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

       bool _augment=false;

       BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > 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[v])) {

 	    free.set(w, std::min(free[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[t];

 	while (res_graph.valid(pred[n])) { 

 	  ResGWEdge e=pred[n];

 	  res_graph.augment(e, augment_value); 

 	  n=res_graph.tail(e);

 	}

       }

       return _augment;

     }

     template<typename MapGraphWrapper> 

     class DistanceMap {

     protected:

       const MapGraphWrapper* g;

       typename MapGraphWrapper::NodeMap<int> dist; 

     public:

       DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }

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

       int operator[](const typename MapGraphWrapper::Node& n) 

 	{ return dist[n]; }

 //       int get(const typename MapGraphWrapper::Node& n) const { 

 // 	return dist[n]; }

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

 // 	return (dist.get(g->tail(e))<dist.get(g->head(e))); }

       bool operator[](const typename MapGraphWrapper::Edge& e) const { 

 	return (dist[g->tail(e)]<dist[g->head(e)]); 

       }

     };

     template<typename MutableGraph> bool augmentOnBlockingFlow() {      

       typedef MutableGraph MG;

       bool _augment=false;

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

       BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > 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[res_graph.tail(e)]+1);

 	}

 	++bfs;

       } //computing distances from s in the residual graph

       MG F;

       ConstMap<typename ResGW::Node, bool> true_map(true);

       typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 

 	DistanceMap<ResGW> > FilterResGW;

       FilterResGW filter_res_graph(res_graph, true_map, 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[s];

       typename MG::Node tF=res_graph_to_F[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[res_graph.tail(e)], res_graph_to_F[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

 	DfsIterator5< MG, typename MG::NodeMap<bool> > 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[v])) {

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

 	      } else {

 		free.set(w, residual_capacity[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[tF];

 	  while (F.valid(pred[n])) { 

 	    typename MG::Edge e=pred[n];

 	    res_graph.augment(original_edge[e], augment_value); 

 	    n=F.tail(e);

 	    if (residual_capacity[e]==augment_value) 

 	      F.erase(e); 

 	    else 

 	      residual_capacity.set(e, residual_capacity[e]-augment_value);

 	  }

 	}

       }

       return _augment;

     }

     template<typename MutableGraph> bool augmentOnBlockingFlow1() {      

       typedef MutableGraph MG;

       bool _augment=false;

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

       //bfs for distances on the residual graph

       BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > 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[s];

       typename MG::Node tF=res_graph_to_F[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[res_graph.tail(e)]+1);

 	    typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[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[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {

 	      typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[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

 	DfsIterator5< MG, typename MG::NodeMap<bool> > 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[v])) {

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

 	      } else {

 		free.set(w, residual_capacity[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[tF];

 	  while (F.valid(pred[n])) { 

 	    typename MG::Edge e=pred[n];

 	    res_graph.augment(original_edge[e], augment_value); 

 	    n=F.tail(e);

 	    if (residual_capacity[e]==augment_value) 

 	      F.erase(e); 

 	    else 

 	      residual_capacity.set(e, residual_capacity[e]-augment_value);

 	  }

 	}

       }

       return _augment;

     }

     bool augmentOnBlockingFlow2() {

       bool _augment=false;

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

       BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > 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[res_graph.tail(e)]+1);

  	}

 	++bfs;

       } //computing distances from s in the residual graph

       //Subgraph containing the edges on some shortest paths

       ConstMap<typename ResGW::Node, bool> true_map(true);

       typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 

 	DistanceMap<ResGW> > FilterResGW;

       FilterResGW filter_res_graph(res_graph, true_map, 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

   	DfsIterator5< ErasingResGW, typename ErasingResGW::NodeMap<bool> > 

   	  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> free1(erasing_res_graph);

  	dfs.pushAndSetReached(

 	  typename ErasingResGW::Node(

 	    typename FilterResGW::Node(

 	      typename ResGW::Node(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[v])) {

  		free1.set(w, std::min(free1[v], res_graph.resCap(

 				       typename ErasingResGW::OutEdgeIt(dfs))));

  	      } else {

  		free1.set(w, res_graph.resCap(

 			   typename ErasingResGW::OutEdgeIt(dfs))); 

  	      }

  	      if (w==t) { 

  		__augment=true; 

  		_augment=true;

  		break; 

  	      }

  	    } else {

  	      erasing_res_graph.erase(dfs);

 	    }

 	  }

 	}	

   	if (__augment) {

    	  typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t));

 // 	  typename ResGW::NodeMap<Number> a(res_graph);

 // 	  typename ResGW::Node b;

 // 	  Number j=a[b];

 // 	  typename FilterResGW::NodeMap<Number> a1(filter_res_graph);

 // 	  typename FilterResGW::Node b1;

 // 	  Number j1=a1[b1];

 // 	  typename ErasingResGW::NodeMap<Number> a2(erasing_res_graph);

 // 	  typename ErasingResGW::Node b2;

 // 	  Number j2=a2[b2];

  	  Number augment_value=free1[n];

  	  while (erasing_res_graph.valid(pred[n])) { 

  	    typename ErasingResGW::OutEdgeIt e=pred[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;

     }

     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(g->first(e, s); g->valid(e); g->next(e)) {

 	a+=(*flow)[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);

 //       //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 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, INVALID); 

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

 // 	//invalid iterators for sources

 // 	typename EAugGraph::NodeMap<Number> free(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) {

 // 	    dfs.pushAndSetReached(s);

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

 // 	  }

 // 	}

 //       }

 //       //dfs.pushAndSetReached(s);

 //       typename EAugGraph::Node n;

 // 	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)); 

 // 	      }

 // 	      n=w;

 // 	      if (T->get(w)) {

 // 		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; 

 // 		  _augment=true;

 // 		  break; 

 // 		}

 // 	      }

 // 	    } else {

 // 	      res_graph.erase(dfs);

 // 	    }

 // 	  } 

 // 	}

 // 	if (__augment) {

 // 	  // typename EAugGraph::Node n=t;

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

 // 	  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;

 //       EdgeIt e;

 //       for(G->/*getF*/first(e); G->valid(e); G->next(e)) {

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

 //       }

 //       return a;

 //     }

 //   };

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

 // //   class MaxFlow2 {

 // //   public:

 // //     typedef typename Graph::Node Node;

 // //     typedef typename Graph::Edge Edge;

 // //     typedef typename Graph::EdgeIt EdgeIt;

 // //     typedef typename Graph::OutEdgeIt OutEdgeIt;

 // //     typedef typename Graph::InEdgeIt InEdgeIt;

 // //   private:

 // //     const Graph& G;

 // //     std::list<Node>& S;

 // //     std::list<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<bool> SMap;

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

 // //   public:

 // //     MaxFlow2(const Graph& _G, std::list<Node>& _S, std::list<Node>& _T, FlowMap& _flow, const CapacityMap& _capacity) : G(_G), S(_S), T(_T), flow(_flow), capacity(_capacity), SMap(_G), TMap(_G) { 

 // //       for(typename std::list<Node>::const_iterator i=S.begin(); 

 // // 	  i!=S.end(); ++i) { 

 // // 	SMap.set(*i, true); 

 // //       }

 // //       for (typename std::list<Node>::const_iterator i=T.begin(); 

 // // 	   i!=T.end(); ++i) { 

 // // 	TMap.set(*i, true); 

 // //       }

 // //     }

 // //     bool augment() {

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

 // //       bool _augment=false;

 // //       Node reached_t_node;

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

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

 // //       for(typename std::list<Node>::const_iterator i=S.begin(); 

 // // 	  i!=S.end(); ++i) {

 // // 	bfs.pushAndSetReached(*i);

 // //       }

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

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

 // //       //filled up with invalid iterators

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

 // //       //searching for augmenting path

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

 // // 	AugOutEdgeIt e=/*AugOutEdgeIt*/(bfs);

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

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

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

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

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

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

 // // 	  } else {

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

 // // 	  }

 // // 	  if (TMap.get(res_graph.head(e))) { 

 // // 	    _augment=true; 

 // // 	    reached_t_node=res_graph.head(e);

 // // 	    break; 

 // // 	  }

 // // 	}

 // // 	++bfs;

 // //       } //end of searching augmenting path

 // //       if (_augment) {

 // // 	Node n=reached_t_node;

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

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

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

 // // 	  e.augment(augment_value); 

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

 // // 	}

 // //       }

 // //       return _augment;

 // //     }

 // //     void run() {

 // //       while (augment()) { } 

 // //     }

 // //     Number flowValue() { 

 // //       Number a=0;

 // //       for(typename std::list<Node>::const_iterator i=S.begin(); 

 // // 	  i!=S.end(); ++i) { 

 // // 	for(OutEdgeIt e=G.template first<OutEdgeIt>(*i); e.valid(); ++e) {

 // // 	  a+=flow.get(e);

 // // 	}

 // // 	for(InEdgeIt e=G.template first<InEdgeIt>(*i); e.valid(); ++e) {

 // // 	  a-=flow.get(e);

 // // 	}

 // //       }

 // //       return a;

 // //     }

 // //   };

 } // namespace hugo

 #endif //HUGO_EDMONDS_KARP_H