source: lemon-0.x/src/work/edmonds_karp.hh @ 196:8a9b9360463e

#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 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), 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) {
        NodeIt n=t;
        Number augment_value=free.get(t);
        while (res_graph.valid(pred.get(n))) { 
          AugEdgeIt e=pred.get(n);
          res_graph.augment(e, augment_value); 
          //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, 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<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))) {
            if (dfs.isBNodeNewlyReached()) {
//            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)); 
              }
              if (w==tF) { 
                //std::cout << "AUGMENTATION"<<std::endl;
                __augment=true; 
                _augment=true;
                break; 
              }
              
            } else {
              F.erase(typename MutableGraph::OutEdgeIt(dfs));
            }
          } 
        }

        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);
            res_graph.augment(original_edge.get(e), augment_value); 
            //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;
    }
    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::EdgeIt EAugEdgeIt;

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

      //std::cout << "meg jo1" << std::endl;

      //typedef typename EAugGraph::NodeMap<bool> ReachedMap;
      BfsIterator4< 
        ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 
        ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt, 
        ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);
      
      //std::cout << "meg jo2" << std::endl;

      bfs.pushAndSetReached(s);
      //std::cout << "meg jo2.5" << std::endl;

      //typename EAugGraph::NodeMap<int> dist(res_graph); //filled up with 0's
      typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::
        NodeMap<int>& dist=res_graph.dist;
      //std::cout << "meg jo2.6" << std::endl;

      while ( !bfs.finished() ) {
        ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt e=bfs;
//      EAugOutEdgeIt e=/*AugOutEdgeIt*/(bfs);
        //if (res_graph.valid(e)) {
        //    std::cout<<"a:"<<res_graph.tail(e)<<"b:"<<res_graph.head(e)<<std::endl;
        //}
        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


      //std::cout << "meg jo3" << std::endl;

//       typedef typename EAugGraph::EachNodeIt EAugEachNodeIt;
//       for(EAugEachNodeIt n=res_graph.template first<EAugEachNodeIt>(); res_graph.valid(n); res_graph.next(n)) {
//      std::cout << "dist: " << dist.get(n) << std::endl;
//       }

      bool __augment=true;

      while (__augment) {
//      std::cout << "new iteration"<< std::endl;

        __augment=false;
        //computing blocking flow with dfs
        typedef typename EAugGraph::NodeMap<bool> BlockingReachedMap;
        DfsIterator4< EAugGraph, EAugOutEdgeIt, BlockingReachedMap > 
          dfs(res_graph);
        typename EAugGraph::NodeMap<EAugEdgeIt> pred(res_graph); //invalid iterators
        typename EAugGraph::NodeMap<Number> free(res_graph);

        dfs.pushAndSetReached(s);
        while (!dfs.finished()) {
          ++dfs;
          if (res_graph.valid(EAugOutEdgeIt(dfs))) { 
            if (dfs.isBNodeNewlyReached()) {
//            std::cout << "OutEdgeIt: " << dfs; 
//            std::cout << " aNode: " << res_graph.aNode(dfs); 
//            std::cout << " res cap: " << EAugOutEdgeIt(dfs).free(); 
//            std::cout << " bNode: " << res_graph.bNode(dfs) << " ";
          
              typename EAugGraph::NodeIt v=res_graph.aNode(dfs);
              typename EAugGraph::NodeIt w=res_graph.bNode(dfs);

              pred.set(w, EAugOutEdgeIt(dfs));

              //std::cout << EAugOutEdgeIt(dfs).free() << std::endl;
              if (res_graph.valid(pred.get(v))) {
                free.set(w, std::min(free.get(v), res_graph.free(/*EAugOutEdgeIt*/(dfs))));
              } else {
                free.set(w, res_graph.free(/*EAugOutEdgeIt*/(dfs))); 
              }
              
              if (w==t) { 
//              std::cout << "t is reached, AUGMENTATION"<<std::endl;
                __augment=true; 
                _augment=true;
                break; 
              }
            } else {
//            std::cout << "<<DELETE ";
//            std::cout << " aNode: " << res_graph.aNode(dfs); 
//            std::cout << " res cap: " << EAugOutEdgeIt(dfs).free(); 
//            std::cout << " bNode: " << res_graph.bNode(dfs) << " ";
//            std::cout << "DELETE>> ";

              res_graph.erase(dfs);
            }
          } 

        }

        if (__augment) {
          typename EAugGraph::NodeIt n=t;
          Number augment_value=free.get(t);
//        std::cout << "av:" << augment_value << std::endl;
          while (res_graph.valid(pred.get(n))) { 
            EAugEdgeIt e=pred.get(n);
            res_graph.augment(e, augment_value);
            //e.augment(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->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 ResGraphWrapper<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