#ifndef EDMONDS_KARP_HH

 #define EDMONDS_KARP_HH

 #include <algorithm>

 #include <bfs_iterator.hh>

 namespace marci {

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

   class ResGraph {

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::EachNodeIt EachNodeIt;

     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, T, FlowMap, CapacityMap>;

     protected:

       const ResGraph<Graph, T, FlowMap, CapacityMap>* 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(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, FlowMap, CapacityMap>;

     public:

       OutEdgeIt() { }

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

     private:

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

       NodeMap(const ResGraph<Graph, T, 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 T, typename FlowMap, typename CapacityMap>

   class MaxFlow {

     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;

     FlowMap& flow;

     const CapacityMap& capacity;

     typedef ResGraph<Graph, T, FlowMap, CapacityMap > AugGraph;

     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

     typedef typename AugGraph::EdgeIt AugEdgeIt;

   public:

     MaxFlow(const Graph& _G, NodeIt _s, NodeIt _t, FlowMap& _flow, const CapacityMap& _capacity) : G(_G), s(_s), t(_t), flow(_flow), capacity(_capacity) { }

     bool augment() {

       AugGraph res_graph(G, flow, capacity);

       bool _augment=false;

       typedef typename AugGraph::NodeMap<bool> ReachedMap;

       BfsIterator2< AugGraph, AugOutEdgeIt, ReachedMap > res_bfs(res_graph);

       res_bfs.pushAndSetReached(s);

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

       //filled with invalid iterators

       typename AugGraph::NodeMap<int> 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 (res_graph.head(e)==t) { _augment=true; break; }

 	}

 	++res_bfs;

       } //end of searching augmenting path

       if (_augment) {

 	NodeIt n=t;

 	T augment_value=free.get(t);

 	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()) { } 

     }

     T flowValue() { 

       T a=0;

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

 	a+=flow.get(i);

       }

       return a;

     }

   };

 } // namespace marci

 #endif //EDMONDS_KARP_HH