#ifndef MARCI_MAX_FLOW_HH
#define MARCI_MAX_FLOW_HH

#include <algorithm>

#include <bfs_iterator.hh>

namespace marci {

  template<typename Graph, typename T>
  class ResGraph {
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
    typedef typename Graph::SymEdgeIt OldSymEdgeIt;
    const Graph& G;
    typename Graph::EdgeMap<T>& flow;
    const typename Graph::EdgeMap<T>& capacity;
  public:
    ResGraph(const Graph& _G, typename Graph::EdgeMap<T>& _flow, 
	     const typename Graph::EdgeMap<T>& _capacity) : 
      G(_G), flow(_flow), capacity(_capacity) { }

    class EdgeIt; 
    class OutEdgeIt; 
    friend class EdgeIt; 
    friend class OutEdgeIt; 

    class EdgeIt {
      friend class ResGraph<Graph, T>;
    protected:
      const ResGraph<Graph, T>* resG;
      OldSymEdgeIt sym;
    public:
      EdgeIt() { } 
      //EdgeIt(const EdgeIt& e) : resG(e.resG), sym(e.sym) { }
      T 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(const T a) const {
	if (resG->G.aNode(sym)==resG->G.tail(sym)) { 
	  resG->flow.set(sym, resG->flow.get(sym)+a);
	} else { 
	  resG->flow.set(sym, resG->flow.get(sym)-a);
	}
      }
    };

    class OutEdgeIt : public EdgeIt {
      friend class ResGraph<Graph, T>;
    public:
      OutEdgeIt() { }
      //OutEdgeIt(const OutEdgeIt& e) { resG=e.resG; sym=e.sym; }
    private:
      OutEdgeIt(const ResGraph<Graph, T>& _resG, const 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, const 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(const NodeIt v) const { 
      It e;
      getFirst(e, v);
      return e; 
    }

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

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

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

    template <typename ValueType>
    class NodeMap {
      //const ResGraph<Graph, T>& G; 
      typename Graph::NodeMap<ValueType> node_map; 
    public:
      NodeMap(const ResGraph<Graph, T>& _G) : node_map(_G.G)/*: G(_G)*/ { }
      NodeMap(const ResGraph<Graph, T>& _G, const ValueType a) : node_map(_G.G, a) /*: G(_G)*/ { }
      void set(const NodeIt nit, const ValueType a) { node_map.set(nit, a); }
      ValueType get(const NodeIt nit) const { return node_map.get(nit); }
    };

  };

  template <typename Graph, typename T>
  struct max_flow_type {
    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;
    const Graph& G;
    NodeIt s;
    NodeIt t;
    typename Graph::EdgeMap<T> flow;
    const typename Graph::EdgeMap<T>& capacity;

    max_flow_type(const Graph& _G, NodeIt _s, NodeIt _t, const typename Graph::EdgeMap<T>& _capacity) : G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) { }
    void run() {
      typedef ResGraph<Graph, T> AugGraph;
      AugGraph res_graph(G, flow, capacity);

      bool augment;
      do {
	augment=false;

	typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;
	typedef typename AugGraph::EdgeIt AugEdgeIt;
	typedef std::queue<AugOutEdgeIt> BfsQueue;
	BfsQueue bfs_queue;
	bfs_queue.push(res_graph.template first<AugOutEdgeIt>(s));

	typedef typename AugGraph::NodeMap<bool> ReachedMap;
	ReachedMap reached(res_graph, false);
	reached.set(s, true); 
	
	bfs_iterator1< AugGraph, ReachedMap > 
	res_bfs(res_graph, bfs_queue, reached);

	typedef typename AugGraph::NodeMap<AugEdgeIt> PredMap;
	PredMap pred(res_graph);
	//typename AugGraph::EdgeIt a; //invalid
	//a.makeInvalid();
	//pred.set(s, a);

	typedef typename AugGraph::NodeMap<int> FreeMap;
	FreeMap free(res_graph);
	
	//searching for augmenting path
	while ( res_bfs.valid() ) { 
	  //std::cout<<"KULSO ciklus itt jar: "<<G.id(res_graph.tail(res_bfs))<<"->"<<G.id(res_graph.head(res_bfs))<<std::endl;
	  if (res_bfs.newly_reached()) {
	    AugOutEdgeIt e=AugOutEdgeIt(res_bfs);
	    NodeIt v=res_graph.tail(e);
	    NodeIt w=res_graph.head(e);
	    //std::cout<<G.id(v)<<"->"<<G.id(w)<<", "<<G.id(w)<<" is newly reached";
	    pred.set(w, e);
	    if (pred.get(v).valid()) {
	      free.set(w, std::min(free.get(v), e.free()));
	      //std::cout <<" nem elso csucs: ";
	      //std::cout <<"szabad kap eddig: "<< free.get(w) << " ";
	    } else {
	      free.set(w, e.free()); 
	      //std::cout <<" elso csucs: ";
	      //std::cout <<"szabad kap eddig: "<< free.get(w) << " ";
	    }
	    //std::cout<<std::endl;
	  }
	
	  if (res_graph.head(res_bfs)==t) break;
	  ++res_bfs;
	} //end searching augmenting path
	if (reached.get(t)) {
	  augment=true;
	  NodeIt n=t;
	  T augment_value=free.get(t);
	  std::cout<<"augmentation: ";
	  while (pred.get(n).valid()) { 
	    AugEdgeIt e=pred.get(n);
	    e.augment(augment_value); 
	    std::cout<<"("<<res_graph.tail(e)<< "->"<<res_graph.head(e)<<") ";
	    n=res_graph.tail(e);
	  }
	  std::cout<<std::endl;
	}

	std::cout << "actual flow: "<< std::endl;
	for(EachEdgeIt e=G.template first<EachEdgeIt>(); e.valid(); ++e) { 
	  std::cout<<"("<<G.tail(e)<< "-"<<flow.get(e)<<"->"<<G.head(e)<<") ";
	}
	std::cout<<std::endl;

      } while (augment);
    }
  };

} // namespace marci

#endif //MARCI_MAX_FLOW_HH