#ifndef EDMONDS_KARP_HH

#define EDMONDS_KARP_HH

#include <algorithm>

#include <list>

#include <iterator>

#include <bfs_iterator.hh>

//#include <time_measure.h>

namespace hugo {

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

  class ResGraph {

  public:

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::EachNodeIt EachNodeIt;

  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 EdgeIt; 

    class OutEdgeIt; 

    friend class EdgeIt; 

    friend class OutEdgeIt; 

    class EdgeIt {

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

    protected:

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

      OldSymEdgeIt sym;

    public:

      EdgeIt() { } 

      //EdgeIt(const EdgeIt& 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 EdgeIt {

      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, NodeIt 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 getFirst(OutEdgeIt& e, NodeIt v) const { 

      e=OutEdgeIt(*this, v); 

    }

    void getFirst(EachNodeIt& v) const { G.getFirst(v); }

    template< typename It >

    It first() const { 

      It e;      

      getFirst(e);

      return e; 

    }

    template< typename It >

    It first(NodeIt v) const { 

      It e;

      getFirst(e, v);

      return e; 

    }

    NodeIt tail(EdgeIt e) const { return G.aNode(e.sym); }

    NodeIt head(EdgeIt e) const { return G.bNode(e.sym); }

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

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

    int id(NodeIt 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(NodeIt nit, S a) { node_map.set(nit, a); }

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

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

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

    };

  };

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

  class ResGraph2 {

  public:

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::EachNodeIt EachNodeIt;

  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 EdgeIt; 

    class OutEdgeIt; 

    friend class EdgeIt; 

    friend class OutEdgeIt; 

    class EdgeIt {

      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:

      EdgeIt() : 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 EdgeIt {

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

    public:

      OutEdgeIt() { }

    private:

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

	  NodeIt 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 getFirst(OutEdgeIt& e, NodeIt v) const { 

      e=OutEdgeIt(*this, v); 

    }

    void getFirst(EachNodeIt& v) const { G.getFirst(v); }

    template< typename It >

    It first() const { 

      It e;

      getFirst(e);

      return e; 

    }

    template< typename It >

    It first(NodeIt v) const { 

      It e;

      getFirst(e, v);

      return e; 

    }

    NodeIt tail(EdgeIt e) const { 

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

    NodeIt head(EdgeIt e) const { 

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

    NodeIt aNode(OutEdgeIt e) const { 

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

    NodeIt bNode(OutEdgeIt e) const { 

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

    int id(NodeIt 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(NodeIt nit, S a) { node_map.set(nit, a); }

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

    };

  };

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

  class MaxFlow {

  public:

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::EdgeIt EdgeIt;

    typedef typename Graph::EachEdgeIt EachEdgeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

  private:

    const Graph* G;

    NodeIt s;

    NodeIt t;

    FlowMap* flow;

    const CapacityMap* capacity;

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

    typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

    typedef typename AugGraph::EdgeIt AugEdgeIt;

    //AugGraph res_graph;    

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

    //typename AugGraph::NodeMap<AugEdgeIt> pred; 

    //typename AugGraph::NodeMap<Number> free;

  public:

    MaxFlow(const Graph& _G, NodeIt _s, NodeIt _t, FlowMap& _flow, const CapacityMap& _capacity) : 

      G(&_G), s(_s), t(_t), flow(&_flow), capacity(&_capacity) //,  

      //res_graph(G, flow, capacity), pred(res_graph), free(res_graph) 

      { }

    bool augmentOnShortestPath() {

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

      bool _augment=false;

      typedef typename AugGraph::NodeMap<bool> ReachedMap;

      BfsIterator5< AugGraph, AugOutEdgeIt, ReachedMap > res_bfs(res_graph);

      res_bfs.pushAndSetReached(s);

      typename AugGraph::NodeMap<AugEdgeIt> pred(res_graph); 

      //filled up with invalid iterators

      //pred.set(s, AugEdgeIt());

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

      //searching for augmenting path

      while ( !res_bfs.finished() ) { 

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

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

	  NodeIt v=res_graph.tail(e);

	  NodeIt w=res_graph.head(e);

	  pred.set(w, e);

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

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

	  } else {

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

	  }

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

	}

	++res_bfs;

      } //end of searching augmenting path

      if (_augment) {

	NodeIt n=t;

	Number augment_value=free.get(t);

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

	  AugEdgeIt e=pred.get(n);

	  e.augment(augment_value); 

	  n=res_graph.tail(e);

	}

      }

      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);

      bfs.pushAndSetReached(s);

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

      while ( !bfs.finished() ) { 

	AugOutEdgeIt e=/*AugOutEdgeIt*/(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<NodeIt> res_graph_to_F(res_graph);

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

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

      }

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

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

      typename MutableGraph::EdgeMap<AugEdgeIt> 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::EachEdgeIt e=res_graph.template first<typename AugGraph::EachEdgeIt>(); res_graph.valid(e); res_graph.next(e)) {

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

	  typename MutableGraph::EdgeIt 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, e.free());

	} 

      }

      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<EdgeIt> pred(F); //invalid iterators

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

	dfs.pushAndSetReached(sF);      

	while (!dfs.finished()) {

	  ++dfs;

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

	    //std::cout << "OutEdgeIt: " << dfs; 

	    //std::cout << " aNode: " << F.aNode(dfs); 

	    //std::cout << " bNode: " << F.bNode(dfs) << " ";

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

	    typename MutableGraph::NodeIt 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)/*original_edge.get(dfs).free()*/); 

	    }

	    if (w==tF) { 

	      //std::cout << "AUGMENTATION"<<std::endl;

	      __augment=true; 

	      _augment=true;

	      break; 

	    }

	  } else { 

	    //std::cout << "OutEdgeIt: " << "invalid"; 

	    //std::cout << " aNode: " << dfs.aNode(); 

	    //std::cout << " bNode: " << "invalid" << " ";

	  }

	  if (dfs.isBNodeNewlyReached()) { 

	    //std::cout << "bNodeIsNewlyReached ";

	  } else { 

	    //std::cout << "bNodeIsNotNewlyReached ";

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

	      //std::cout << "DELETE ";

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

	    }

	  } 

	  //if (dfs.isANodeExamined()) { 

	    //std::cout << "aNodeIsExamined ";

	    //} else { 

	    //std::cout << "aNodeIsNotExamined ";

	    //} 

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

	}

	if (__augment) {

	  typename MutableGraph::NodeIt n=tF;

	  Number augment_value=free.get(tF);

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

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

	    original_edge.get(e).augment(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;

    }

    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->getFirst(e, s); 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::NodeIt NodeIt;

//     typedef typename Graph::EdgeIt EdgeIt;

//     typedef typename Graph::EachEdgeIt EachEdgeIt;

//     typedef typename Graph::OutEdgeIt OutEdgeIt;

//     typedef typename Graph::InEdgeIt InEdgeIt;

//   private:

//     const Graph& G;

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

//     std::list<NodeIt>& T;

//     FlowMap& flow;

//     const CapacityMap& capacity;

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

//     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

//     typedef typename AugGraph::EdgeIt AugEdgeIt;

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

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

//   public:

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

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

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

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

//       }

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

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

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

//       }

//     }

//     bool augment() {

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

//       bool _augment=false;

//       NodeIt reached_t_node;

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

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

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

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

// 	res_bfs.pushAndSetReached(*i);

//       }

//       //res_bfs.pushAndSetReached(s);

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

//       //filled up with invalid iterators

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

//       //searching for augmenting path

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

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

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

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

// 	  NodeIt 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; 

// 	  }

// 	}

// 	++res_bfs;

//       } //end of searching augmenting path

//       if (_augment) {

// 	NodeIt n=reached_t_node;

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

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

// 	  AugEdgeIt 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<NodeIt>::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 //EDMONDS_KARP_HH