#ifndef EDMONDS_KARP_HH
#define EDMONDS_KARP_HH

#include <algorithm>
#include <list>
#include <iterator>

#include <bfs_iterator.hh>

namespace marci {

  template<typename Graph, typename Number, 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, 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 {
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
    //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; //1, iff out
    public:
      EdgeIt() : out_or_in(1) { } 
      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 ResGraph3 {
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
    //typedef typename Graph::SymEdgeIt OldSymEdgeIt;
    typedef typename Graph::OutEdgeIt OldOutEdgeIt;
    typedef typename Graph::InEdgeIt OldInEdgeIt;
    
    const Graph& G;
    FlowMap& flow;
    const CapacityMap& capacity;
  public:
    ResGraph3(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 ResGraph3<Graph, Number, FlowMap, CapacityMap>;
    protected:
      //const ResGraph3<Graph, Number, FlowMap, CapacityMap>* resG;
      const Graph* G;
      FlowMap* flow;
      const CapacityMap* capacity;
      //OldSymEdgeIt sym;
      OldOutEdgeIt out;
      OldInEdgeIt in;
      bool out_or_in; //1, iff out
    public:
      EdgeIt() : out_or_in(1) { } 
      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 ResGraph3<Graph, Number, FlowMap, CapacityMap>;
    public:
      OutEdgeIt() { }
    private:
      OutEdgeIt(const Graph& _G, NodeIt v, FlowMap& _flow, const CapacityMap& _capacity) { 
      	G=&_G;
	flow=&_flow;
	capacity=&_capacity;
	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(G, v, flow, capacity); 
    }
    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 ResGraph3<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }
      NodeMap(const ResGraph3<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 {
    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 ResGraph3<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<int> 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 augment() {
      AugGraph res_graph(G, flow, capacity);
      bool _augment=false;
      
      typedef typename AugGraph::NodeMap<bool> ReachedMap;
      BfsIterator4< 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<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;
	Number 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()) { } 
    }
    Number flowValue() { 
      Number a=0;
      for(OutEdgeIt i=G.template first<OutEdgeIt>(s); i.valid(); ++i) {
	a+=flow.get(i);
      }
      return a;
    }
  };


/*
  template <typename Graph>
  class IteratorBoolNodeMap {
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
    class BoolItem {
    public:
      bool value;
      NodeIt prev;
      NodeIt next;
      BoolItem() : value(false), prev(), next() {}
    };
    NodeIt first_true;
    //NodeIt last_true;
    NodeIt first_false;
    //NodeIt last_false;
    const Graph& G; 
    typename Graph::NodeMap<BoolItem> container;
  public:
    typedef bool ValueType;
    typedef NodeIt KeyType;
    IteratorBoolNodeMap(const Graph& _G) : G(_G), container(G), first_true(NodeIt()) { 
      //for (EachNodeIt e=G.template first<EacNodeIt>(); e.valid(); ++e) {
      //BoolItem b=container.get(e);
      //b.me=e;
      //container.set(b);
      //} 
      G.getFirst(first_false);
      NodeIt e_prev;
      for (EachNodeIt e=G.template first<EacNodeIt>(); e.valid(); ++e) {
	container[e].prev=e_prev;
	if (e_prev.valid()) container[e_prev].next=e;
	e_prev=e;
      }
    }
    //NodeMap(const Graph& _G, T a) : 
    //  G(_G), container(G.node_id, a) { }
    //FIXME
    void set(NodeIt nit, T a) { container[G.id(nit)]=a; }
    T get(NodeIt nit) const { return container[G.id(nit)]; }
    //void resize() { container.resize(G.node_id); }
    //void resize(T a) { container.resize(G.node_id, a); }
  };
*/

  
  template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>
  class MaxFlow2 {
    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;
    std::list<NodeIt>& S;
    std::list<NodeIt>& T;
    FlowMap& flow;
    const CapacityMap& capacity;
    typedef ResGraph<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<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 (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 marci

#endif //EDMONDS_KARP_HH