// -*- 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>

#include <for_each_macros.h>

namespace hugo {

  template <typename Graph, typename Num, 

	    typename CapMap, typename FlowMap>

  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;

    const CapMap* capacity;

    FlowMap* flow;

    typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;

    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;

    typedef typename ResGW::Edge ResGWEdge;

    //typedef typename ResGW::template NodeMap<bool> ReachedMap;

    typedef typename Graph::template NodeMap<bool> ReachedMap;

    ReachedMap level;

    //reached is called level because of compatibility with preflow

  public:

    MaxFlow(const Graph& _g, Node _s, Node _t, const CapMap& _capacity, 

	    FlowMap& _flow) : 

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

    bool augmentOnShortestPath() {

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

      bool _augment=false;

      //ReachedMap level(res_graph);

      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);

      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

      bfs.pushAndSetReached(s);

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

      pred.set(s, INVALID);

      typename ResGW::template NodeMap<Num> 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;

	Num 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::template NodeMap<int> dist; 

    public:

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

      void set(const typename MapGraphWrapper::Node& n, int a) { 

	dist.set(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, *capacity, *flow);

      //ReachedMap level(res_graph);

      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);

      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

      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::template 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::template EdgeMap<ResGWEdge> original_edge(F);

      typename MG::template EdgeMap<Num> 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

	DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);

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

	pred.set(sF, INVALID);

	//invalid iterators for sources

	typename MG::template NodeMap<Num> 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;

	  Num 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, *capacity, *flow);

      //bfs for distances on the residual graph

      //ReachedMap level(res_graph);

      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);

      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

      bfs.pushAndSetReached(s);

      typename ResGW::template 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::template 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::template EdgeMap<ResGWEdge> original_edge(F);

      typename MG::template EdgeMap<Num> 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

	DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);

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

	pred.set(sF, INVALID);

	//invalid iterators for sources

	typename MG::template NodeMap<Num> 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;

	  Num 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, *capacity, *flow);

      //ReachedMap level(res_graph);

      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);

      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

      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::template 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::

	template 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

  	DfsIterator< ErasingResGW, 

	  typename ErasingResGW::template NodeMap<bool> > 

  	  dfs(erasing_res_graph);

 	typename ErasingResGW::

	  template NodeMap<typename ErasingResGW::OutEdgeIt> 

	  pred(erasing_res_graph); 

 	pred.set(s, INVALID);

  	//invalid iterators for sources

  	typename ErasingResGW::template NodeMap<Num> 

	  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<Num> a(res_graph);

// 	  typename ResGW::Node b;

// 	  Num j=a[b];

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

// 	  typename FilterResGW::Node b1;

// 	  Num j1=a1[b1];

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

// 	  typename ErasingResGW::Node b2;

// 	  Num j2=a2[b2];

 	  Num 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;

      } 

    }

    Num flowValue() { 

      Num a=0;

      OutEdgeIt e;

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

	a+=(*flow)[e];

      }

      return a;

    }

  };

//   template <typename Graph, typename Num, typename FlowMap, typename CapMap>

//   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 CapMap* capacity;

//     typedef ResGraphWrapper<Graph, Num, FlowMap, CapMap > 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 CapMap& _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;

//       BfsIterator< 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) ) {

// 	  //Num 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<Num> 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) ) { 

// 	    //Num 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

// 	Num 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)) {

// // 	  Num 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<Num> 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<Num> 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;

// // 	  Num 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, Num, FlowMap, CapMap> EAugGraph;

//       typedef FilterGraphWrapper< ErasingResGraphWrapper<Graph, Num, FlowMap, CapMap> > EAugGraph;

//       typedef typename EAugGraph::OutEdgeIt EAugOutEdgeIt;

//       typedef typename EAugGraph::Edge EAugEdge;

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

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

//       BfsIterator< 

// 	ErasingResGraphWrapper<Graph, Num, FlowMap, CapMap>, 

// 	/*typename ErasingResGraphWrapper<Graph, Num, FlowMap, CapMap>::OutEdgeIt,*/ 

// 	ErasingResGraphWrapper<Graph, Num, FlowMap, CapMap>::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)) {

// 	  Num 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, Num, FlowMap, CapMap>::

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

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

// 	typename ErasingResGraphWrapper<Graph, Num, FlowMap, CapMap>::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;

// 	DfsIterator< 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<Num> 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)) {

// 	  Num 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)) {

// 		Num 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;

// 	  Num 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;

// //       } 

// //     } 

//     Num flowValue() { 

//       Num 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 Num, typename FlowMap, typename CapMap>

// //   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 CapMap& capacity;

// //     typedef ResGraphWrapper<Graph, Num, FlowMap, CapMap > 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 CapMap& _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<Num> 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;

// // 	Num 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()) { } 

// //     }

// //     Num flowValue() { 

// //       Num 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