#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