#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 {

public:

    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;

private:

    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