source: lemon-0.x/src/work/edmonds_karp.hh @ 148:004fdf703abb

#ifndef EDMONDS_KARP_HH
#define EDMONDS_KARP_HH

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

#include <bfs_iterator.hh>
//#include <time_measure.h>

namespace hugo {

  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>
  class ResGraph {
  public:
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
  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 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 {
  public:
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
  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 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; //true, iff out
    public:
      EdgeIt() : 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 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 ResGraphWrapper {
  public:
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
  private:
    typedef typename Graph::OutEdgeIt OldOutEdgeIt;
    typedef typename Graph::InEdgeIt OldInEdgeIt;
    const Graph* G;
    FlowMap* flow;
    const CapacityMap* capacity;
  public:
    ResGraphWrapper(const Graph& _G, FlowMap& _flow, 
             const CapacityMap& _capacity) : 
      G(&_G), flow(&_flow), capacity(&_capacity) { }
//     ResGraphWrapper(const ResGraphWrapper& res_graph_wrapper) : 
//       G(res_graph_wrapper.G), flow(res_graph_wrapper.flow), capacity(res_graph_wrapper.capacity) { }
    class EdgeIt; 
    class OutEdgeIt; 
    friend class EdgeIt; 
    friend class OutEdgeIt; 

    class EdgeIt {
      friend class ResGraphWrapper<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; //true, iff out
    public:
      EdgeIt() : out_or_in(true) { } 
      EdgeIt(const Graph& _G, FlowMap& _flow, const CapacityMap& _capacity) : 
        G(&_G), flow(&_flow), capacity(&_capacity), out_or_in(true) { }
      //EdgeIt(const EdgeIt& e) : G(e.G), flow(e.flow), capacity(e.capacity), out(e.out), in(e.in), out_or_in(e.out_or_in) { }
      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);
        }
      }
      void print() { 
        if (out_or_in) {
          std::cout << "out "; 
          if (out.valid()) 
            std::cout << G->id(G->tail(out)) << "--"<< G->id(out) <<"->"<< G->id(G->head(out)); 
          else 
            std::cout << "invalid"; 
        }
        else {
          std::cout << "in "; 
          if (in.valid()) 
            std::cout << G->id(G->head(in)) << "<-"<< G->id(in) <<"--"<< G->id(G->tail(in)); 
          else 
            std::cout << "invalid"; 
        }
        std::cout << std::endl;
      }
    };

    Number free(OldOutEdgeIt out) const { 
      return (/*resG->*/capacity->get(out)-/*resG->*/flow->get(out)); 
    }
    Number free(OldInEdgeIt in) const { 
      return (/*resG->*/flow->get(in)); 
    }

    class OutEdgeIt : public EdgeIt {
      friend class ResGraphWrapper<Graph, Number, FlowMap, CapacityMap>;
    public:
      OutEdgeIt() { }
    private:
      OutEdgeIt(const Graph& _G, NodeIt v, FlowMap& _flow, const CapacityMap& _capacity) : EdgeIt(_G, _flow, _capacity) { 
        //out=/*resG->*/G->template first<OldOutEdgeIt>(v);
        G->getFirst(out, v);
        while( out.valid() && !(EdgeIt::free()>0) ) { ++out; }
        if (!out.valid()) {
          out_or_in=0;
          //in=/*resG->*/G->template first<OldInEdgeIt>(v);
          G->getFirst(in, v);
          while( in.valid() && !(EdgeIt::free()>0) ) { ++in; }
        }
      }
    public:
      OutEdgeIt& operator++() { 
        if (out_or_in) {
          NodeIt v=/*resG->*/G->aNode(out);
          ++out;
          while( out.valid() && !(EdgeIt::free()>0) ) { ++out; }
          if (!out.valid()) {
            out_or_in=0;
            G->getFirst(in, v); //=/*resG->*/G->template first<OldInEdgeIt>(v);
            while( in.valid() && !(EdgeIt::free()>0) ) { ++in; }
          }
        } else {
          ++in;
          while( in.valid() && !(EdgeIt::free()>0) ) { ++in; } 
        }
        return *this; 
      }
    };

    class EachEdgeIt : public EdgeIt {
      friend class ResGraphWrapper<Graph, Number, FlowMap, CapacityMap>;
      typename Graph::EachNodeIt v;
    public:
      EachEdgeIt() { }
      //EachEdgeIt(const EachEdgeIt& e) : EdgeIt(e), v(e.v) { }
      EachEdgeIt(const Graph& _G, FlowMap& _flow, const CapacityMap& _capacity) : EdgeIt(_G, _flow, _capacity) { 
        out_or_in=true;
        G->getFirst(v);
        if (v.valid()) G->getFirst(out, v); else out=OldOutEdgeIt();
        while (out.valid() && !(EdgeIt::free()>0) ) { ++out; }
        while (v.valid() && !out.valid()) { 
          ++v; 
          if (v.valid()) G->getFirst(out, v); 
          while (out.valid() && !(EdgeIt::free()>0) ) { ++out; }
        }
        if (!out.valid()) {
          out_or_in=0;
          G->getFirst(v);
          if (v.valid()) G->getFirst(in, v); else in=OldInEdgeIt();
          while (in.valid() && !(EdgeIt::free()>0) ) { ++in; }
          while (v.valid() && !in.valid()) { 
            ++v; 
            if (v.valid()) G->getFirst(in, v); 
            while (in.valid() && !(EdgeIt::free()>0) ) { ++in; }
          }
        }
      }
      EachEdgeIt& operator++() { 
        if (out_or_in) {
          ++out;
          while (out.valid() && !(EdgeIt::free()>0) ) { ++out; }
          while (v.valid() && !out.valid()) { 
            ++v; 
            if (v.valid()) G->getFirst(out, v); 
            while (out.valid() && !(EdgeIt::free()>0) ) { ++out; }
          }
          if (!out.valid()) {
            out_or_in=0;
            G->getFirst(v);
            if (v.valid()) G->getFirst(in, v); else in=OldInEdgeIt();
            while (in.valid() && !(EdgeIt::free()>0) ) { ++in; }
            while (v.valid() && !in.valid()) { 
              ++v; 
              if (v.valid()) G->getFirst(in, v); 
              while (in.valid() && !(EdgeIt::free()>0) ) { ++in; }
            }  
          }
        } else {
          ++in;
          while (in.valid() && !(EdgeIt::free()>0) ) { ++in; }
          while (v.valid() && !in.valid()) { 
            ++v; 
            if (v.valid()) G->getFirst(in, v); 
            while (in.valid() && !(EdgeIt::free()>0) ) { ++in; }
          }
        }
        return *this;
      }
    };

    void getFirst(EachNodeIt& v) const { G->getFirst(v); }
    void getFirst(OutEdgeIt& e, NodeIt v) const { 
      e=OutEdgeIt(*G, v, *flow, *capacity); 
    }
    void getFirst(EachEdgeIt& e) const { 
      e=EachEdgeIt(*G, *flow, *capacity); 
    }
   
    EachNodeIt& next(EachNodeIt& n) const { return G->next(n); }

    OutEdgeIt& next(OutEdgeIt& e) const { 
      if (e.out_or_in) {
        NodeIt v=G->aNode(e.out);
        ++(e.out);
        while( G->valid(e.out) && !(e.free()>0) ) { ++(e.out); }
        if (!G->valid(e.out)) {
          e.out_or_in=0;
          G->getFirst(e.in, v); //=/*resG->*/G->template first<OldInEdgeIt>(v);
          while( G->valid(e.in) && !(e.free()>0) ) { ++(e.in); }
        }
      } else {
        ++(e.in);
        while( G->valid(e.in) && !(e.free()>0) ) { ++(e.in); } 
      }
      return e;
    }

    EachEdgeIt& next(EachEdgeIt& e) const { 
      if (e.out_or_in) {
        ++(e.out);
        while (G->valid(e.out) && !(e.free()>0) ) { ++(e.out); }
          while (G->valid(e.v) && !G->valid(e.out)) { 
            ++(e.v); 
            if (G->valid(e.v)) G->getFirst(e.out, e.v); 
            while (G->valid(e.out) && !(e.free()>0) ) { ++(e.out); }
          }
          if (!G->valid(e.out)) {
            e.out_or_in=0;
            G->getFirst(e.v);
            if (G->valid(e.v)) G->getFirst(e.in, e.v); else e.in=OldInEdgeIt();
            while (G->valid(e.in) && !(e.free()>0) ) { ++(e.in); }
            while (G->valid(e.v) && !G->valid(e.in)) { 
              ++(e.v); 
              if (G->valid(e.v)) G->getFirst(e.in, e.v); 
              while (G->valid(e.in) && !(e.free()>0) ) { ++(e.in); }
            }  
          }
        } else {
          ++(e.in);
          while (G->valid(e.in) && !(e.free()>0) ) { ++(e.in); }
          while (G->valid(e.v) && !G->valid(e.in)) { 
            ++(e.v); 
            if (G->valid(e.v)) G->getFirst(e.in, e.v); 
            while (G->valid(e.in) && !(e.free()>0) ) { ++(e.in); }
          }
        }
        return e;
      }
    

    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); }

    bool valid(NodeIt n) const { return G->valid(n); }
    bool valid(EdgeIt e) const { 
      return e.out_or_in ? G->valid(e.out) : G->valid(e.in); }

    template <typename T>
    class NodeMap {
      typename Graph::NodeMap<T> node_map; 
    public:
      NodeMap(const ResGraphWrapper<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(*(_G.G)) { }
      NodeMap(const ResGraphWrapper<Graph, Number, FlowMap, CapacityMap>& _G, T a) : node_map(*(_G.G), a) { }
      void set(NodeIt nit, T a) { node_map.set(nit, a); }
      T get(NodeIt nit) const { return node_map.get(nit); }
    };

    template <typename T>
    class EdgeMap {
      typename Graph::EdgeMap<T> forward_map, backward_map; 
    public:
      EdgeMap(const ResGraphWrapper<Graph, Number, FlowMap, CapacityMap>& _G) : forward_map(*(_G.G)), backward_map(*(_G.G)) { }
      EdgeMap(const ResGraphWrapper<Graph, Number, FlowMap, CapacityMap>& _G, T a) : forward_map(*(_G.G), a), backward_map(*(_G.G), a) { }
      void set(EdgeIt e, T a) { 
        if (e.out_or_in) 
          forward_map.set(e.out, a); 
        else 
          backward_map.set(e.in, a); 
      }
      T get(EdgeIt e) { 
        if (e.out_or_in) 
          return forward_map.get(e.out); 
        else 
          return backward_map.get(e.in); 
      }
    };

  };

  template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>
  class MaxFlow {
  public:
    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;

  private:
    const Graph* G;
    NodeIt s;
    NodeIt t;
    FlowMap* flow;
    const CapacityMap* capacity;
    typedef ResGraphWrapper<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<Number> 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 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<AugEdgeIt> pred(res_graph); 
      //filled up with invalid iterators
      //pred.set(s, AugEdgeIt());
      
      typename AugGraph::NodeMap<Number> free(res_graph);
        
      //searching for augmenting path
      while ( !res_bfs.finished() ) { 
        AugOutEdgeIt e=/*AugOutEdgeIt*/(res_bfs);
        if (res_graph.valid(e) && res_bfs.isBNodeNewlyReached()) {
          NodeIt v=res_graph.tail(e);
          NodeIt w=res_graph.head(e);
          pred.set(w, e);
          if (res_graph.valid(pred.get(v))) {
            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 (res_graph.valid(pred.get(n))) { 
          AugEdgeIt e=pred.get(n);
          e.augment(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=/*AugOutEdgeIt*/(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<NodeIt> res_graph_to_F(res_graph);
      for(typename AugGraph::EachNodeIt n=res_graph.template first<typename AugGraph::EachNodeIt>(); res_graph.valid(n); res_graph.next(n)) {
        res_graph_to_F.set(n, F.addNode());
      }
      
      typename MutableGraph::NodeIt sF=res_graph_to_F.get(s);
      typename MutableGraph::NodeIt tF=res_graph_to_F.get(t);

      typename MutableGraph::EdgeMap<AugEdgeIt> 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::EachEdgeIt e=res_graph.template first<typename AugGraph::EachEdgeIt>(); res_graph.valid(e); res_graph.next(e)) {
        if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {
          typename MutableGraph::EdgeIt 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, e.free());
        } 
      }

      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<EdgeIt> pred(F); //invalid iterators
        typename MutableGraph::NodeMap<Number> free(F);

        dfs.pushAndSetReached(sF);      
        while (!dfs.finished()) {
          ++dfs;
          if (F.valid(typename MutableGraph::OutEdgeIt(dfs))) {
            //std::cout << "OutEdgeIt: " << dfs; 
            //std::cout << " aNode: " << F.aNode(dfs); 
            //std::cout << " bNode: " << F.bNode(dfs) << " ";
          
            typename MutableGraph::NodeIt v=F.aNode(dfs);
            typename MutableGraph::NodeIt 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)/*original_edge.get(dfs).free()*/); 
            }
            if (w==tF) { 
              //std::cout << "AUGMENTATION"<<std::endl;
              __augment=true; 
              _augment=true;
              break; 
            }
          } else { 
            //std::cout << "OutEdgeIt: " << "invalid"; 
            //std::cout << " aNode: " << dfs.aNode(); 
            //std::cout << " bNode: " << "invalid" << " ";
          }
          if (dfs.isBNodeNewlyReached()) { 
            //std::cout << "bNodeIsNewlyReached ";
          } else { 
            //std::cout << "bNodeIsNotNewlyReached ";
            if (typename MutableGraph::OutEdgeIt(dfs).valid()) {
              //std::cout << "DELETE ";
              F.erase(typename MutableGraph::OutEdgeIt(dfs));
            }
          } 
          //if (dfs.isANodeExamined()) { 
            //std::cout << "aNodeIsExamined ";
            //} else { 
            //std::cout << "aNodeIsNotExamined ";
            //} 
          //std::cout<<std::endl;
        }

        if (__augment) {
          typename MutableGraph::NodeIt n=tF;
          Number augment_value=free.get(tF);
          while (F.valid(pred.get(n))) { 
            typename MutableGraph::EdgeIt e=pred.get(n);
            original_edge.get(e).augment(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;
    }
    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->getFirst(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::NodeIt NodeIt;
    typedef typename Graph::EdgeIt EdgeIt;
    typedef typename Graph::EachEdgeIt EachEdgeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;
  private:
    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<Number> 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 hugo

#endif //EDMONDS_KARP_HH