// -*- c++ -*-
#ifndef EDMONDS_KARP_H
#define EDMONDS_KARP_H

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

#include <bfs_iterator.h>
#include <invalid.h>

namespace hugo {

  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>
  class ResGraph {
  public:
    typedef typename Graph::Node Node;
    typedef typename Graph::NodeIt NodeIt;
  private:
    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 Edge; 
    class OutEdgeIt; 
    friend class Edge; 
    friend class OutEdgeIt; 

    class Edge {
      friend class ResGraph<Graph, Number, FlowMap, CapacityMap>;
    protected:
      const ResGraph<Graph, Number, FlowMap, CapacityMap>* resG;
      OldSymEdgeIt sym;
    public:
      Edge() { } 
      //Edge(const Edge& 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 Edge {
      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, Node 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 /*getF*/first(OutEdgeIt& e, Node v) const { 
      e=OutEdgeIt(*this, v); 
    }
    void /*getF*/first(NodeIt& v) const { G./*getF*/first(v); }
    
    template< typename It >
    It first() const { 
      It e;      
      /*getF*/first(e);
      return e; 
    }

    template< typename It >
    It first(Node v) const { 
      It e;
      /*getF*/first(e, v);
      return e; 
    }

    Node tail(Edge e) const { return G.aNode(e.sym); }
    Node head(Edge e) const { return G.bNode(e.sym); }

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

    int id(Node 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(Node nit, S a) { node_map.set(nit, a); }
      S get(Node nit) const { return node_map.get(nit); }
      S& operator[](Node nit) { return node_map[nit]; } 
      const S& operator[](Node nit) const { return node_map[nit]; } 
    };

  };


  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>
  class ResGraph2 {
  public:
    typedef typename Graph::Node Node;
    typedef typename Graph::NodeIt NodeIt;
  private:
    //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 Edge; 
    class OutEdgeIt; 
    friend class Edge; 
    friend class OutEdgeIt; 

    class Edge {
      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; //true, iff out
    public:
      Edge() : out_or_in(true) { } 
      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 Edge {
      friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;
    public:
      OutEdgeIt() { }
    private:
      OutEdgeIt(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _resG, Node 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) {
	  Node 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 /*getF*/first(OutEdgeIt& e, Node v) const { 
      e=OutEdgeIt(*this, v); 
    }
    void /*getF*/first(NodeIt& v) const { G./*getF*/first(v); }
    
    template< typename It >
    It first() const { 
      It e;
      /*getF*/first(e);
      return e; 
    }

    template< typename It >
    It first(Node v) const { 
      It e;
      /*getF*/first(e, v);
      return e; 
    }

    Node tail(Edge e) const { 
      return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }
    Node head(Edge e) const { 
      return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

    Node aNode(OutEdgeIt e) const { 
      return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }
    Node bNode(OutEdgeIt e) const { 
      return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

    int id(Node 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(Node nit, S a) { node_map.set(nit, a); }
      S get(Node nit) const { return node_map.get(nit); }
    };
  };


  template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>
  class MaxFlow {
  public:
    typedef typename Graph::Node Node;
    typedef typename Graph::Edge Edge;
    typedef typename Graph::EdgeIt EdgeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;

  private:
    const Graph* G;
    Node s;
    Node t;
    FlowMap* flow;
    const CapacityMap* capacity;
    typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;
    typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;
    typedef typename AugGraph::Edge AugEdge;

  public:
    MaxFlow(const Graph& _G, Node _s, Node _t, FlowMap& _flow, const CapacityMap& _capacity) : 
      G(&_G), s(_s), t(_t), flow(&_flow), capacity(&_capacity) { }
    bool augmentOnShortestPath() {
      AugGraph res_graph(*G, *flow, *capacity);
      bool _augment=false;
      
      typedef typename AugGraph::NodeMap<bool> ReachedMap;
      BfsIterator5< AugGraph, /*AugOutEdgeIt,*/ ReachedMap > res_bfs(res_graph);
      res_bfs.pushAndSetReached(s);
	
      typename AugGraph::NodeMap<AugEdge> pred(res_graph); 
      pred.set(s, AugEdge(INVALID));
      
      typename AugGraph::NodeMap<Number> free(res_graph);
	
      //searching for augmenting path
      while ( !res_bfs.finished() ) { 
	AugOutEdgeIt e=res_bfs;
	if (res_graph.valid(e) && res_bfs.isBNodeNewlyReached()) {
	  Node v=res_graph.tail(e);
	  Node w=res_graph.head(e);
	  pred.set(w, e);
	  if (res_graph.valid(pred.get(v))) {
	    free.set(w, std::min(free.get(v), res_graph.free(e)));
	  } else {
	    free.set(w, res_graph.free(e)); 
	  }
	  if (res_graph.head(e)==t) { _augment=true; break; }
	}
	
	++res_bfs;
      } //end of searching augmenting path

      if (_augment) {
	Node n=t;
	Number augment_value=free.get(t);
	while (res_graph.valid(pred.get(n))) { 
	  AugEdge e=pred.get(n);
	  res_graph.augment(e, augment_value); 
	  n=res_graph.tail(e);
	}
      }

      return _augment;
    }

    template<typename MutableGraph> bool augmentOnBlockingFlow() {      
      bool _augment=false;

      AugGraph res_graph(*G, *flow, *capacity);

      typedef typename AugGraph::NodeMap<bool> ReachedMap;
      BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > bfs(res_graph);

      bfs.pushAndSetReached(s);
      typename AugGraph::NodeMap<int> dist(res_graph); //filled up with 0's
      while ( !bfs.finished() ) { 
	AugOutEdgeIt e=bfs;
	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);
	}
	
	++bfs;
      } //computing distances from s in the residual graph

      MutableGraph F;
      typename AugGraph::NodeMap<typename MutableGraph::Node> 
	res_graph_to_F(res_graph);
      for(typename AugGraph::NodeIt n=res_graph.template first<typename AugGraph::NodeIt>(); res_graph.valid(n); res_graph.next(n)) {
	res_graph_to_F.set(n, F.addNode());
      }
      
      typename MutableGraph::Node sF=res_graph_to_F.get(s);
      typename MutableGraph::Node tF=res_graph_to_F.get(t);

      typename MutableGraph::EdgeMap<AugEdge> original_edge(F);
      typename MutableGraph::EdgeMap<Number> residual_capacity(F);

      //Making F to the graph containing the edges of the residual graph 
      //which are in some shortest paths
      for(typename AugGraph::EdgeIt e=res_graph.template first<typename AugGraph::EdgeIt>(); res_graph.valid(e); res_graph.next(e)) {
	if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {
	  typename MutableGraph::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));
	  original_edge.update();
	  original_edge.set(f, e);
	  residual_capacity.update();
	  residual_capacity.set(f, res_graph.free(e));
	} 
      }

      bool __augment=true;

      while (__augment) {
	__augment=false;
	//computing blocking flow with dfs
	typedef typename MutableGraph::NodeMap<bool> BlockingReachedMap;
	DfsIterator4< MutableGraph, typename MutableGraph::OutEdgeIt, BlockingReachedMap > dfs(F);
	typename MutableGraph::NodeMap<typename MutableGraph::Edge> pred(F);
	pred.set(sF, typename MutableGraph::Edge(INVALID));
	//invalid iterators for sources

	typename MutableGraph::NodeMap<Number> free(F);

	dfs.pushAndSetReached(sF);      
	while (!dfs.finished()) {
	  ++dfs;
	  if (F.valid(typename MutableGraph::OutEdgeIt(dfs))) {
	    if (dfs.isBNodeNewlyReached()) {
	      typename MutableGraph::Node v=F.aNode(dfs);
	      typename MutableGraph::Node w=F.bNode(dfs);
	      pred.set(w, dfs);
	      if (F.valid(pred.get(v))) {
		free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));
	      } else {
		free.set(w, residual_capacity.get(dfs)); 
	      }
	      if (w==tF) { 
		__augment=true; 
		_augment=true;
		break; 
	      }
	      
	    } else {
	      F.erase(typename MutableGraph::OutEdgeIt(dfs));
	    }
	  } 
	}

	if (__augment) {
	  typename MutableGraph::Node n=tF;
	  Number augment_value=free.get(tF);
	  while (F.valid(pred.get(n))) { 
	    typename MutableGraph::Edge e=pred.get(n);
	    res_graph.augment(original_edge.get(e), augment_value); 
	    n=F.tail(e);
	    if (residual_capacity.get(e)==augment_value) 
	      F.erase(e); 
	    else 
	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);
	  }
	}
	
      }
            
      return _augment;
    }
    bool augmentOnBlockingFlow2() {
      bool _augment=false;

      //typedef ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> EAugGraph;
      typedef FilterGraphWrapper< ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> > EAugGraph;
      typedef typename EAugGraph::OutEdgeIt EAugOutEdgeIt;
      typedef typename EAugGraph::Edge EAugEdge;

      EAugGraph res_graph(*G, *flow, *capacity);

      //typedef typename EAugGraph::NodeMap<bool> ReachedMap;
      BfsIterator4< 
	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 
	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt, 
	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);
      
      bfs.pushAndSetReached(s);

      typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::
	NodeMap<int>& dist=res_graph.dist;

      while ( !bfs.finished() ) {
	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt e=bfs;
	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);
	}
	++bfs;	
      } //computing distances from s in the residual graph

      bool __augment=true;

      while (__augment) {

	__augment=false;
	//computing blocking flow with dfs
	typedef typename EAugGraph::NodeMap<bool> BlockingReachedMap;
	DfsIterator4< EAugGraph, EAugOutEdgeIt, BlockingReachedMap > 
	  dfs(res_graph);
	typename EAugGraph::NodeMap<EAugEdge> pred(res_graph); 
	pred.set(s, EAugEdge(INVALID));
	//invalid iterators for sources

	typename EAugGraph::NodeMap<Number> free(res_graph);

	dfs.pushAndSetReached(s);
	while (!dfs.finished()) {
	  ++dfs;
	  if (res_graph.valid(EAugOutEdgeIt(dfs))) { 
	    if (dfs.isBNodeNewlyReached()) {
	  
	      typename EAugGraph::Node v=res_graph.aNode(dfs);
	      typename EAugGraph::Node w=res_graph.bNode(dfs);

	      pred.set(w, EAugOutEdgeIt(dfs));
	      if (res_graph.valid(pred.get(v))) {
		free.set(w, std::min(free.get(v), res_graph.free(dfs)));
	      } else {
		free.set(w, res_graph.free(dfs)); 
	      }
	      
	      if (w==t) { 
		__augment=true; 
		_augment=true;
		break; 
	      }
	    } else {
	      res_graph.erase(dfs);
	    }
	  } 

	}

	if (__augment) {
	  typename EAugGraph::Node n=t;
	  Number augment_value=free.get(t);
	  while (res_graph.valid(pred.get(n))) { 
	    EAugEdge e=pred.get(n);
	    res_graph.augment(e, augment_value);
	    n=res_graph.tail(e);
	    if (res_graph.free(e)==0)
	      res_graph.erase(e);
	  }
	}
      
      }
            
      return _augment;
    }
    void run() {
      //int num_of_augmentations=0;
      while (augmentOnShortestPath()) { 
	//while (augmentOnBlockingFlow<MutableGraph>()) { 
	//std::cout << ++num_of_augmentations << " ";
	//std::cout<<std::endl;
      } 
    }
    template<typename MutableGraph> void run() {
      //int num_of_augmentations=0;
      //while (augmentOnShortestPath()) { 
	while (augmentOnBlockingFlow<MutableGraph>()) { 
	//std::cout << ++num_of_augmentations << " ";
	//std::cout<<std::endl;
      } 
    }
    Number flowValue() { 
      Number a=0;
      OutEdgeIt e;
      for(G->/*getF*/first(e, s); G->valid(e); G->next(e)) {
	a+=flow->get(e);
      }
      return a;
    }
  };

  
//   template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>
//   class MaxFlow2 {
//   public:
//     typedef typename Graph::Node Node;
//     typedef typename Graph::Edge Edge;
//     typedef typename Graph::EdgeIt EdgeIt;
//     typedef typename Graph::OutEdgeIt OutEdgeIt;
//     typedef typename Graph::InEdgeIt InEdgeIt;
//   private:
//     const Graph& G;
//     std::list<Node>& S;
//     std::list<Node>& T;
//     FlowMap& flow;
//     const CapacityMap& capacity;
//     typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;
//     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;
//     typedef typename AugGraph::Edge AugEdge;
//     typename Graph::NodeMap<bool> SMap;
//     typename Graph::NodeMap<bool> TMap;
//   public:
//     MaxFlow2(const Graph& _G, std::list<Node>& _S, std::list<Node>& _T, FlowMap& _flow, const CapacityMap& _capacity) : G(_G), S(_S), T(_T), flow(_flow), capacity(_capacity), SMap(_G), TMap(_G) { 
//       for(typename std::list<Node>::const_iterator i=S.begin(); 
// 	  i!=S.end(); ++i) { 
// 	SMap.set(*i, true); 
//       }
//       for (typename std::list<Node>::const_iterator i=T.begin(); 
// 	   i!=T.end(); ++i) { 
// 	TMap.set(*i, true); 
//       }
//     }
//     bool augment() {
//       AugGraph res_graph(G, flow, capacity);
//       bool _augment=false;
//       Node reached_t_node;
      
//       typedef typename AugGraph::NodeMap<bool> ReachedMap;
//       BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > res_bfs(res_graph);
//       for(typename std::list<Node>::const_iterator i=S.begin(); 
// 	  i!=S.end(); ++i) {
// 	res_bfs.pushAndSetReached(*i);
//       }
//       //res_bfs.pushAndSetReached(s);
	
//       typename AugGraph::NodeMap<AugEdge> pred(res_graph); 
//       //filled up with invalid iterators
      
//       typename AugGraph::NodeMap<Number> free(res_graph);
	
//       //searching for augmenting path
//       while ( !res_bfs.finished() ) { 
// 	AugOutEdgeIt e=/*AugOutEdgeIt*/(res_bfs);
// 	if (e.valid() && res_bfs.isBNodeNewlyReached()) {
// 	  Node v=res_graph.tail(e);
// 	  Node 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) {
// 	Node n=reached_t_node;
// 	Number augment_value=free.get(reached_t_node);
// 	while (pred.get(n).valid()) { 
// 	  AugEdge 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<Node>::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 hugo

#endif //EDMONDS_KARP_H