source: lemon-0.x/src/work/marci/edmonds_karp.h @ 347:e4ab32225f1c

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

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

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

namespace hugo {

//   template<typename Graph, typename Number, typename CapacityMap, typename FlowMap>
//   class ResGraph {
//   public:
//     typedef typename Graph::Node Node;
//     typedef typename Graph::NodeIt NodeIt;
//   private:
//     typedef typename Graph::SymEdgeIt OldSymEdgeIt;
//     const Graph& G;
//     const CapacityMap& capacity;
//     FlowMap& flow;
//   public:
//     ResGraph(const Graph& _G, const CapacityMap& _capacity, FlowMap& _flow) : 
//       G(_G), capacity(_capacity), flow(_flow) { }

//     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 CapacityMap, typename FlowMap>
  class MaxFlow {
  protected:
    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;
    const Graph* g;
    Node s;
    Node t;
    const CapacityMap* capacity;
    FlowMap* flow;
    typedef ResGraphWrapper<const Graph, Number, CapacityMap, FlowMap> ResGW;
    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
    typedef typename ResGW::Edge ResGWEdge;
  public:

    MaxFlow(const Graph& _g, Node _s, Node _t, const CapacityMap& _capacity, 
            FlowMap& _flow) : 
      g(&_g), s(_s), t(_t), capacity(&_capacity), flow(&_flow) { }

    bool augmentOnShortestPath() {
      ResGW res_graph(*g, *capacity, *flow);
      bool _augment=false;
      
      BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > bfs(res_graph);
      bfs.pushAndSetReached(s);
        
      typename ResGW::NodeMap<ResGWEdge> pred(res_graph); 
      pred.set(s, INVALID);
      
      typename ResGW::NodeMap<Number> free(res_graph);
        
      //searching for augmenting path
      while ( !bfs.finished() ) { 
        ResGWOutEdgeIt e=bfs;
        if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
          Node v=res_graph.tail(e);
          Node w=res_graph.head(e);
          pred.set(w, e);
          if (res_graph.valid(pred[v])) {
            free.set(w, std::min(free[v], res_graph.resCap(e)));
          } else {
            free.set(w, res_graph.resCap(e)); 
          }
          if (res_graph.head(e)==t) { _augment=true; break; }
        }
        
        ++bfs;
      } //end of searching augmenting path

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

      return _augment;
    }

    template<typename MapGraphWrapper> 
    class DistanceMap {
    protected:
      const MapGraphWrapper* g;
      typename MapGraphWrapper::NodeMap<int> dist; 
    public:
      DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }
      void set(const typename MapGraphWrapper::Node& n, int a) { dist[n]=a; }
      int operator[](const typename MapGraphWrapper::Node& n) 
        { return dist[n]; }
//       int get(const typename MapGraphWrapper::Node& n) const { 
//      return dist[n]; }
//       bool get(const typename MapGraphWrapper::Edge& e) const { 
//      return (dist.get(g->tail(e))<dist.get(g->head(e))); }
      bool operator[](const typename MapGraphWrapper::Edge& e) const { 
        return (dist[g->tail(e)]<dist[g->head(e)]); 
      }
    };

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

      ResGW res_graph(*g, *capacity, *flow);

      BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > bfs(res_graph);

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

      MG F;
      ConstMap<typename ResGW::Node, bool> true_map(true);
      typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 
        DistanceMap<ResGW> > FilterResGW;
      FilterResGW filter_res_graph(res_graph, true_map, dist);
      typename ResGW::NodeMap<typename MG::Node> res_graph_to_F(res_graph);
      {
        typename ResGW::NodeIt n;
        for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
          res_graph_to_F.set(n, F.addNode());
        }
      }

      typename MG::Node sF=res_graph_to_F[s];
      typename MG::Node tF=res_graph_to_F[t];
      typename MG::EdgeMap<ResGWEdge> original_edge(F);
      typename MG::EdgeMap<Number> residual_capacity(F);

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

      bool __augment=true;

      while (__augment) {
        __augment=false;
        //computing blocking flow with dfs

        DfsIterator5< MG, typename MG::NodeMap<bool> > dfs(F);
        typename MG::NodeMap<typename MG::Edge> pred(F);
        pred.set(sF, INVALID);
        //invalid iterators for sources

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

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

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

    template<typename MutableGraph> bool augmentOnBlockingFlow1() {      
      typedef MutableGraph MG;
      bool _augment=false;

      ResGW res_graph(*g, *capacity, *flow);

      //bfs for distances on the residual graph
      BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > bfs(res_graph);
      bfs.pushAndSetReached(s);
      typename ResGW::NodeMap<int> dist(res_graph); //filled up with 0's

      //F will contain the physical copy of the residual graph
      //with the set of edges which are on shortest paths
      MG F;
      typename ResGW::NodeMap<typename MG::Node> res_graph_to_F(res_graph);
      {
        typename ResGW::NodeIt n;
        for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
          res_graph_to_F.set(n, F.addNode());
        }
      }

      typename MG::Node sF=res_graph_to_F[s];
      typename MG::Node tF=res_graph_to_F[t];
      typename MG::EdgeMap<ResGWEdge> original_edge(F);
      typename MG::EdgeMap<Number> residual_capacity(F);

      while ( !bfs.finished() ) { 
        ResGWOutEdgeIt e=bfs;
        if (res_graph.valid(e)) {
          if (bfs.isBNodeNewlyReached()) {
            dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
            typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
            original_edge.update();
            original_edge.set(f, e);
            residual_capacity.update();
            residual_capacity.set(f, res_graph.resCap(e));
          } else {
            if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
              typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
              original_edge.update();
              original_edge.set(f, e);
              residual_capacity.update();
              residual_capacity.set(f, res_graph.resCap(e));
            }
          }
        }
        ++bfs;
      } //computing distances from s in the residual graph

      bool __augment=true;

      while (__augment) {
        __augment=false;
        //computing blocking flow with dfs
        DfsIterator5< MG, typename MG::NodeMap<bool> > dfs(F);
        typename MG::NodeMap<typename MG::Edge> pred(F);
        pred.set(sF, INVALID);
        //invalid iterators for sources

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

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

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

    bool augmentOnBlockingFlow2() {
      bool _augment=false;

      ResGW res_graph(*g, *capacity, *flow);

      BfsIterator5< ResGW, typename ResGW::NodeMap<bool> > bfs(res_graph);

      bfs.pushAndSetReached(s);
      DistanceMap<ResGW> dist(res_graph);
      while ( !bfs.finished() ) { 
        ResGWOutEdgeIt e=bfs;
        if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
          dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
        }
        ++bfs;
      } //computing distances from s in the residual graph

      //Subgraph containing the edges on some shortest paths
      ConstMap<typename ResGW::Node, bool> true_map(true);
      typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 
        DistanceMap<ResGW> > FilterResGW;
      FilterResGW filter_res_graph(res_graph, true_map, dist);

      //Subgraph, which is able to delete edges which are already 
      //met by the dfs
      typename FilterResGW::NodeMap<typename FilterResGW::OutEdgeIt> 
        first_out_edges(filter_res_graph);
      typename FilterResGW::NodeIt v;
      for(filter_res_graph.first(v); filter_res_graph.valid(v); 
          filter_res_graph.next(v)) 
      {
        typename FilterResGW::OutEdgeIt e;
        filter_res_graph.first(e, v);
        first_out_edges.set(v, e);
      }
      typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
        NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;
      ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);

      bool __augment=true;

      while (__augment) {

        __augment=false;
        //computing blocking flow with dfs
        DfsIterator5< ErasingResGW, typename ErasingResGW::NodeMap<bool> > 
          dfs(erasing_res_graph);
        typename ErasingResGW::NodeMap<typename ErasingResGW::OutEdgeIt> 
          pred(erasing_res_graph); 
        pred.set(s, INVALID);
        //invalid iterators for sources

        typename ErasingResGW::NodeMap<Number> free1(erasing_res_graph);

        dfs.pushAndSetReached(
          typename ErasingResGW::Node(
            typename FilterResGW::Node(
              typename ResGW::Node(s)
              )
            )
          );
        while (!dfs.finished()) {
          ++dfs;
          if (erasing_res_graph.valid(
                typename ErasingResGW::OutEdgeIt(dfs))) 
          { 
            if (dfs.isBNodeNewlyReached()) {
          
              typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);
              typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);

              pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));
              if (erasing_res_graph.valid(pred[v])) {
                free1.set(w, std::min(free1[v], res_graph.resCap(
                                       typename ErasingResGW::OutEdgeIt(dfs))));
              } else {
                free1.set(w, res_graph.resCap(
                           typename ErasingResGW::OutEdgeIt(dfs))); 
              }
              
              if (w==t) { 
                __augment=true; 
                _augment=true;
                break; 
              }
            } else {
              erasing_res_graph.erase(dfs);
            }
          }
        }       

        if (__augment) {
          typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t));
//        typename ResGW::NodeMap<Number> a(res_graph);
//        typename ResGW::Node b;
//        Number j=a[b];
//        typename FilterResGW::NodeMap<Number> a1(filter_res_graph);
//        typename FilterResGW::Node b1;
//        Number j1=a1[b1];
//        typename ErasingResGW::NodeMap<Number> a2(erasing_res_graph);
//        typename ErasingResGW::Node b2;
//        Number j2=a2[b2];
          Number augment_value=free1[n];
          while (erasing_res_graph.valid(pred[n])) { 
            typename ErasingResGW::OutEdgeIt e=pred[n];
            res_graph.augment(e, augment_value);
            n=erasing_res_graph.tail(e);
            if (res_graph.resCap(e)==0)
              erasing_res_graph.erase(e);
        }
      }
      
      } //while (__augment) 
            
      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->first(e, s); g->valid(e); g->next(e)) {
        a+=(*flow)[e];
      }
      return a;
    }

  };


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

//     typedef typename Graph::NodeMap<bool> SMap;
//     typedef typename Graph::NodeMap<bool> TMap;
//   private:
//     const Graph* G;
//     SMap* S;
//     TMap* T;
//     //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;
//     typename Graph::NodeMap<int> used; //0

//   public:
//     MaxMatching(const Graph& _G, SMap& _S, TMap& _T, FlowMap& _flow, const CapacityMap& _capacity) : 
//       G(&_G), S(&_S), T(&_T), flow(&_flow), capacity(&_capacity), used(_G) { }
//     bool augmentOnShortestPath() {
//       AugGraph res_graph(*G, *flow, *capacity);
//       bool _augment=false;
      
//       typedef typename AugGraph::NodeMap<bool> ReachedMap;
//       BfsIterator5< AugGraph, /*AugOutEdgeIt,*/ ReachedMap > bfs(res_graph);
//       typename AugGraph::NodeMap<AugEdge> pred(res_graph); 
//       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {
//      if ((S->get(s)) && (used.get(s)<1) ) {
//        //Number u=0;
//        //for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))
//        //u+=flow->get(e);
//        //if (u<1) {
//          bfs.pushAndSetReached(s);
//          pred.set(s, AugEdge(INVALID));
//          //}
//      }
//       }
      
//       typename AugGraph::NodeMap<Number> free(res_graph);
        
//       Node n;
//       //searching for augmenting path
//       while ( !bfs.finished() ) { 
//      AugOutEdgeIt e=bfs;
//      if (res_graph.valid(e) && 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)); 
//        }
//        n=res_graph.head(e);
//        if (T->get(n) && (used.get(n)<1) ) { 
//          //Number u=0;
//          //for(InEdgeIt f=G->template first<InEdgeIt>(n); G->valid(f); G->next(f))
//          //u+=flow->get(f);
//          //if (u<1) {
//            _augment=true; 
//            break; 
//            //}
//        }
//      }
        
//      ++bfs;
//       } //end of searching augmenting path

//       if (_augment) {
//      //Node n=t;
//      used.set(n, 1); //mind2 vegen jav
//      Number augment_value=free.get(n);
//      while (res_graph.valid(pred.get(n))) { 
//        AugEdge e=pred.get(n);
//        res_graph.augment(e, augment_value); 
//        n=res_graph.tail(e);
//      }
//      used.set(n, 1); //mind2 vegen jav
//       }

//       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);





// //       //typename AugGraph::NodeMap<AugEdge> pred(res_graph); 
// //       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {
// //   if (S->get(s)) {
// //     Number u=0;
// //     for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))
// //       u+=flow->get(e);
// //     if (u<1) {
// //       bfs.pushAndSetReached(s);
// //       //pred.set(s, AugEdge(INVALID));
// //     }
// //   }
// //       }




// //       //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;
//       BfsIterator5< 
//      ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 
//      /*typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt,*/ 
//      ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);


//       //typename AugGraph::NodeMap<AugEdge> pred(res_graph); 
//       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {
//      if (S->get(s)) {
//        Number u=0;
//        for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))
//          u+=flow->get(e);
//        if (u<1) {
//          bfs.pushAndSetReached(s);
//          //pred.set(s, AugEdge(INVALID));
//        }
//      }
//       }

      
//       //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;
//      DfsIterator5< EAugGraph/*, EAugOutEdgeIt*/, BlockingReachedMap > 
//        dfs(res_graph);
//      typename EAugGraph::NodeMap<EAugEdge> pred(res_graph, INVALID); 
//      //pred.set(s, EAugEdge(INVALID));
//      //invalid iterators for sources

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


//      //typename AugGraph::NodeMap<AugEdge> pred(res_graph); 
//       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {
//      if (S->get(s)) {
//        Number u=0;
//        for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))
//          u+=flow->get(e);
//        if (u<1) {
//          dfs.pushAndSetReached(s);
//          //pred.set(s, AugEdge(INVALID));
//        }
//      }
//       }



//       //dfs.pushAndSetReached(s);
//       typename EAugGraph::Node n;
//      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)); 
//            }
             
//            n=w;
//            if (T->get(w)) {
//              Number u=0;
//              for(InEdgeIt f=G->template first<InEdgeIt>(n); G->valid(f); G->next(f))
//                u+=flow->get(f);
//              if (u<1) {
//                __augment=true; 
//                _augment=true;
//                break; 
//              }
//            }
//          } else {
//            res_graph.erase(dfs);
//          }
//        } 

//      }

//      if (__augment) {
//        // typename EAugGraph::Node n=t;
//        Number augment_value=free.get(n);
//        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;
//       EdgeIt e;
//       for(G->/*getF*/first(e); 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 > bfs(res_graph);
// //       for(typename std::list<Node>::const_iterator i=S.begin(); 
// //     i!=S.end(); ++i) {
// //   bfs.pushAndSetReached(*i);
// //       }
// //       //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 ( !bfs.finished() ) { 
// //   AugOutEdgeIt e=/*AugOutEdgeIt*/(bfs);
// //   if (e.valid() && 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; 
// //     }
// //   }
        
// //   ++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 //HUGO_EDMONDS_KARP_H