source: lemon-0.x/src/work/jacint/max_flow.h @ 647:19dd325da0e8

// -*- C++ -*-
#ifndef HUGO_MAX_FLOW_H
#define HUGO_MAX_FLOW_H

#include <vector>
#include <queue>
#include <stack>

#include <hugo/graph_wrapper.h>
#include <bfs_dfs.h>
#include <hugo/invalid.h>
#include <hugo/maps.h>
#include <hugo/for_each_macros.h>

/// \file
/// \brief Maximum flow algorithms.
/// \ingroup galgs

namespace hugo {

  /// \addtogroup galgs
  /// @{                                                                                                                                        
  ///Maximum flow algorithms class.

  ///This class provides various algorithms for finding a flow of
  ///maximum value in a directed graph. The \e source node, the \e
  ///target node, the \e capacity of the edges and the \e starting \e
  ///flow value of the edges should be passed to the algorithm through the
  ///constructor. It is possible to change these quantities using the
  ///functions \ref resetSource, \ref resetTarget, \ref resetCap and
  ///\ref resetFlow. Before any subsequent runs of any algorithm of
  ///the class \ref resetFlow should be called. 

  ///After running an algorithm of the class, the actual flow value 
  ///can be obtained by calling \ref flowValue(). The minimum
  ///value cut can be written into a \c node map of \c bools by
  ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
  ///the inclusionwise minimum and maximum of the minimum value
  ///cuts, resp.)                                                                                                                               
  ///\param Graph The directed graph type the algorithm runs on.
  ///\param Num The number type of the capacities and the flow values.
  ///\param CapMap The capacity map type.
  ///\param FlowMap The flow map type.                                                                                                           
  ///\author Marton Makai, Jacint Szabo 
  template <typename Graph, typename Num,
            typename CapMap=typename Graph::template EdgeMap<Num>,
            typename FlowMap=typename Graph::template EdgeMap<Num> >
  class MaxFlow {
  protected:
    typedef typename Graph::Node Node;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EdgeIt EdgeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;

    typedef typename std::vector<std::stack<Node> > VecStack;
    typedef typename Graph::template NodeMap<Node> NNMap;
    typedef typename std::vector<Node> VecNode;

    const Graph* g;
    Node s;
    Node t;
    const CapMap* capacity;
    FlowMap* flow;
    int n;      //the number of nodes of G
    typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
    typedef typename ResGW::Edge ResGWEdge;
    //typedef typename ResGW::template NodeMap<bool> ReachedMap;
    typedef typename Graph::template NodeMap<int> ReachedMap;


    //level works as a bool map in augmenting path algorithms and is
    //used by bfs for storing reached information.  In preflow, it
    //shows the levels of nodes.     
    ReachedMap level;

    //excess is needed only in preflow
    typename Graph::template NodeMap<Num> excess;

    //fixme    
//   protected:
    //     MaxFlow() { }
    //     void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
    //       FlowMap& _flow)
    //       {
    //  g=&_G;
    //  s=_s;
    //  t=_t;
    //  capacity=&_capacity;
    //  flow=&_flow;
    //  n=_G.nodeNum;
    //  level.set (_G); //kellene vmi ilyesmi fv
    //  excess(_G,0); //itt is
    //       }

    // constants used for heuristics
    static const int H0=20;
    static const int H1=1;

  public:

    ///Indicates the property of the starting flow.

    ///Indicates the property of the starting flow. The meanings are as follows:
    ///- \c ZERO_FLOW: constant zero flow
    ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
    ///the sum of the out-flows in every node except the \e source and
    ///the \e target.
    ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at 
    ///least the sum of the out-flows in every node except the \e source.
    ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be 
    ///set to the constant zero flow in the beginning of the algorithm in this case.
    enum FlowEnum{
      ZERO_FLOW,
      GEN_FLOW,
      PRE_FLOW,
      NO_FLOW
    };

    enum StatusEnum {
      AFTER_NOTHING,
      AFTER_AUGMENTING,
      AFTER_PRE_FLOW_PHASE_1,      
      AFTER_PRE_FLOW_PHASE_2
    };

    /// Don not needle this flag only if necessary.
    StatusEnum status;
    int number_of_augmentations;


    template<typename IntMap>
    class TrickyReachedMap {
    protected:
      IntMap* map;
      int* number_of_augmentations;
    public:
      TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : 
        map(&_map), number_of_augmentations(&_number_of_augmentations) { }
      void set(const Node& n, bool b) {
        map->set(n, *number_of_augmentations);
      }
      bool operator[](const Node& n) const { 
        return (*map)[n]==*number_of_augmentations; 
      }
    };
    
    MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
            FlowMap& _flow) :
      g(&_G), s(_s), t(_t), capacity(&_capacity),
      flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), 
      status(AFTER_NOTHING), number_of_augmentations(0) { }

    ///Runs a maximum flow algorithm.

    ///Runs a preflow algorithm, which is the fastest maximum flow
    ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
    ///\pre The starting flow must be
    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
    /// - an arbitary flow if \c fe is \c GEN_FLOW,
    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
    /// - any map if \c fe is NO_FLOW.
    void run(FlowEnum fe=ZERO_FLOW) {
      preflow(fe);
    }

                                                                              
    ///Runs a preflow algorithm.  

    ///Runs a preflow algorithm. The preflow algorithms provide the
    ///fastest way to compute a maximum flow in a directed graph.
    ///\pre The starting flow must be
    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
    /// - an arbitary flow if \c fe is \c GEN_FLOW,
    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
    /// - any map if \c fe is NO_FLOW.
    void preflow(FlowEnum fe) {
      preflowPhase1(fe);
      preflowPhase2();
    }
    // Heuristics:
    //   2 phase
    //   gap
    //   list 'level_list' on the nodes on level i implemented by hand
    //   stack 'active' on the active nodes on level i                                                                                    
    //   runs heuristic 'highest label' for H1*n relabels
    //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
    //   Parameters H0 and H1 are initialized to 20 and 1.

    ///Runs the first phase of the preflow algorithm.

    ///The preflow algorithm consists of two phases, this method runs the
    ///first phase. After the first phase the maximum flow value and a
    ///minimum value cut can already be computed, though a maximum flow
    ///is net yet obtained. So after calling this method \ref flowValue
    ///and \ref actMinCut gives proper results.
    ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
    ///give minimum value cuts unless calling \ref preflowPhase2.
    ///\pre The starting flow must be
    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
    /// - an arbitary flow if \c fe is \c GEN_FLOW,
    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
    /// - any map if \c fe is NO_FLOW.
    void preflowPhase1(FlowEnum fe);

    ///Runs the second phase of the preflow algorithm.

    ///The preflow algorithm consists of two phases, this method runs
    ///the second phase. After calling \ref preflowPhase1 and then
    ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
    ///\ref minMinCut and \ref maxMinCut give proper results.
    ///\pre \ref preflowPhase1 must be called before.
    void preflowPhase2();

    /// Starting from a flow, this method searches for an augmenting path
    /// according to the Edmonds-Karp algorithm
    /// and augments the flow on if any.
    /// The return value shows if the augmentation was succesful.
    bool augmentOnShortestPath();
    bool augmentOnShortestPath2();

    /// Starting from a flow, this method searches for an augmenting blocking
    /// flow according to Dinits' algorithm and augments the flow on if any.
    /// The blocking flow is computed in a physically constructed
    /// residual graph of type \c Mutablegraph.
    /// The return value show sif the augmentation was succesful.
    template<typename MutableGraph> bool augmentOnBlockingFlow();

    /// The same as \c augmentOnBlockingFlow<MutableGraph> but the
    /// residual graph is not constructed physically.
    /// The return value shows if the augmentation was succesful.
    bool augmentOnBlockingFlow2();

    /// Returns the maximum value of a flow.

    /// Returns the maximum value of a flow, by counting the 
    /// over-flow of the target node \ref t.
    /// It can be called already after running \ref preflowPhase1.
    Num flowValue() const {
      Num a=0;
      FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e];
      FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e];
      return a;
      //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan   
    }

    ///Returns a minimum value cut after calling \ref preflowPhase1.

    ///After the first phase of the preflow algorithm the maximum flow
    ///value and a minimum value cut can already be computed. This
    ///method can be called after running \ref preflowPhase1 for
    ///obtaining a minimum value cut.
    /// \warning Gives proper result only right after calling \ref
    /// preflowPhase1.
    /// \todo We have to make some status variable which shows the
    /// actual state
    /// of the class. This enables us to determine which methods are valid
    /// for MinCut computation
    template<typename _CutMap>
    void actMinCut(_CutMap& M) const {
      NodeIt v;
      switch (status) {
        case AFTER_PRE_FLOW_PHASE_1:
        for(g->first(v); g->valid(v); g->next(v)) {
          if (level[v] < n) {
            M.set(v, false);
          } else {
            M.set(v, true);
          }
        }
        break;
        case AFTER_PRE_FLOW_PHASE_2:
        case AFTER_NOTHING:
        minMinCut(M);
        break;
        case AFTER_AUGMENTING:
        for(g->first(v); g->valid(v); g->next(v)) {
          if (level[v]) {
            M.set(v, true);
          } else {
            M.set(v, false);
          }
        }
        break;
      }
    }

    ///Returns the inclusionwise minimum of the minimum value cuts.

    ///Sets \c M to the characteristic vector of the minimum value cut
    ///which is inclusionwise minimum. It is computed by processing
    ///a bfs from the source node \c s in the residual graph.
    ///\pre M should be a node map of bools initialized to false.
    ///\pre \c flow must be a maximum flow.
    template<typename _CutMap>
    void minMinCut(_CutMap& M) const {
      std::queue<Node> queue;

      M.set(s,true);
      queue.push(s);

      while (!queue.empty()) {
        Node w=queue.front();
        queue.pop();

        OutEdgeIt e;
        for(g->first(e,w) ; g->valid(e); g->next(e)) {
          Node v=g->head(e);
          if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
            queue.push(v);
            M.set(v, true);
          }
        }

        InEdgeIt f;
        for(g->first(f,w) ; g->valid(f); g->next(f)) {
          Node v=g->tail(f);
          if (!M[v] && (*flow)[f] > 0 ) {
            queue.push(v);
            M.set(v, true);
          }
        }
      }
    }

    ///Returns the inclusionwise maximum of the minimum value cuts.

    ///Sets \c M to the characteristic vector of the minimum value cut
    ///which is inclusionwise maximum. It is computed by processing a
    ///backward bfs from the target node \c t in the residual graph.
    ///\pre M should be a node map of bools initialized to false.
    ///\pre \c flow must be a maximum flow. 
    template<typename _CutMap>
    void maxMinCut(_CutMap& M) const {

      NodeIt v;
      for(g->first(v) ; g->valid(v); g->next(v)) {
        M.set(v, true);
      }

      std::queue<Node> queue;

      M.set(t,false);
      queue.push(t);

      while (!queue.empty()) {
        Node w=queue.front();
        queue.pop();

        InEdgeIt e;
        for(g->first(e,w) ; g->valid(e); g->next(e)) {
          Node v=g->tail(e);
          if (M[v] && (*flow)[e] < (*capacity)[e] ) {
            queue.push(v);
            M.set(v, false);
          }
        }

        OutEdgeIt f;
        for(g->first(f,w) ; g->valid(f); g->next(f)) {
          Node v=g->head(f);
          if (M[v] && (*flow)[f] > 0 ) {
            queue.push(v);
            M.set(v, false);
          }
        }
      }
    }

    ///Returns a minimum value cut.

    ///Sets \c M to the characteristic vector of a minimum value cut.
    ///\pre M should be a node map of bools initialized to false.
    ///\pre \c flow must be a maximum flow.    
    template<typename CutMap>
    void minCut(CutMap& M) const { minMinCut(M); }

    ///Resets the source node to \c _s.

    ///Resets the source node to \c _s.
    /// 
    void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; }

    ///Resets the target node to \c _t.

    ///Resets the target node to \c _t.
    ///
    void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; }

    /// Resets the edge map of the capacities to _cap.

    /// Resets the edge map of the capacities to _cap.
    /// 
    void resetCap(const CapMap& _cap) { capacity=&_cap; status=AFTER_NOTHING; }

    /// Resets the edge map of the flows to _flow.

    /// Resets the edge map of the flows to _flow.
    /// 
    void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; }


  private:

    int push(Node w, VecStack& active) {

      int lev=level[w];
      Num exc=excess[w];
      int newlevel=n;       //bound on the next level of w

      OutEdgeIt e;
      for(g->first(e,w); g->valid(e); g->next(e)) {

        if ( (*flow)[e] >= (*capacity)[e] ) continue;
        Node v=g->head(e);

        if( lev > level[v] ) { //Push is allowed now

          if ( excess[v]<=0 && v!=t && v!=s ) {
            int lev_v=level[v];
            active[lev_v].push(v);
          }

          Num cap=(*capacity)[e];
          Num flo=(*flow)[e];
          Num remcap=cap-flo;

          if ( remcap >= exc ) { //A nonsaturating push.

            flow->set(e, flo+exc);
            excess.set(v, excess[v]+exc);
            exc=0;
            break;

          } else { //A saturating push.
            flow->set(e, cap);
            excess.set(v, excess[v]+remcap);
            exc-=remcap;
          }
        } else if ( newlevel > level[v] ) newlevel = level[v];
      } //for out edges wv

      if ( exc > 0 ) {
        InEdgeIt e;
        for(g->first(e,w); g->valid(e); g->next(e)) {

          if( (*flow)[e] <= 0 ) continue;
          Node v=g->tail(e);

          if( lev > level[v] ) { //Push is allowed now

            if ( excess[v]<=0 && v!=t && v!=s ) {
              int lev_v=level[v];
              active[lev_v].push(v);
            }

            Num flo=(*flow)[e];

            if ( flo >= exc ) { //A nonsaturating push.

              flow->set(e, flo-exc);
              excess.set(v, excess[v]+exc);
              exc=0;
              break;
            } else {  //A saturating push.

              excess.set(v, excess[v]+flo);
              exc-=flo;
              flow->set(e,0);
            }
          } else if ( newlevel > level[v] ) newlevel = level[v];
        } //for in edges vw

      } // if w still has excess after the out edge for cycle

      excess.set(w, exc);

      return newlevel;
    }


    void preflowPreproc(FlowEnum fe, VecStack& active,
                        VecNode& level_list, NNMap& left, NNMap& right)
    {
      std::queue<Node> bfs_queue;

      switch (fe) {
      case NO_FLOW:   //flow is already set to const zero in this case
      case ZERO_FLOW:
        {
          //Reverse_bfs from t, to find the starting level.
          level.set(t,0);
          bfs_queue.push(t);

          while (!bfs_queue.empty()) {

            Node v=bfs_queue.front();
            bfs_queue.pop();
            int l=level[v]+1;

            InEdgeIt e;
            for(g->first(e,v); g->valid(e); g->next(e)) {
              Node w=g->tail(e);
              if ( level[w] == n && w != s ) {
                bfs_queue.push(w);
                Node first=level_list[l];
                if ( g->valid(first) ) left.set(first,w);
                right.set(w,first);
                level_list[l]=w;
                level.set(w, l);
              }
            }
          }

          //the starting flow
          OutEdgeIt e;
          for(g->first(e,s); g->valid(e); g->next(e))
            {
              Num c=(*capacity)[e];
              if ( c <= 0 ) continue;
              Node w=g->head(e);
              if ( level[w] < n ) {
                if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
                flow->set(e, c);
                excess.set(w, excess[w]+c);
              }
            }
          break;
        }

      case GEN_FLOW:
      case PRE_FLOW:
        {
          //Reverse_bfs from t in the residual graph,
          //to find the starting level.
          level.set(t,0);
          bfs_queue.push(t);

          while (!bfs_queue.empty()) {

            Node v=bfs_queue.front();
            bfs_queue.pop();
            int l=level[v]+1;

            InEdgeIt e;
            for(g->first(e,v); g->valid(e); g->next(e)) {
              if ( (*capacity)[e] <= (*flow)[e] ) continue;
              Node w=g->tail(e);
              if ( level[w] == n && w != s ) {
                bfs_queue.push(w);
                Node first=level_list[l];
                if ( g->valid(first) ) left.set(first,w);
                right.set(w,first);
                level_list[l]=w;
                level.set(w, l);
              }
            }

            OutEdgeIt f;
            for(g->first(f,v); g->valid(f); g->next(f)) {
              if ( 0 >= (*flow)[f] ) continue;
              Node w=g->head(f);
              if ( level[w] == n && w != s ) {
                bfs_queue.push(w);
                Node first=level_list[l];
                if ( g->valid(first) ) left.set(first,w);
                right.set(w,first);
                level_list[l]=w;
                level.set(w, l);
              }
            }
          }


          //the starting flow
          OutEdgeIt e;
          for(g->first(e,s); g->valid(e); g->next(e))
            {
              Num rem=(*capacity)[e]-(*flow)[e];
              if ( rem <= 0 ) continue;
              Node w=g->head(e);
              if ( level[w] < n ) {
                if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
                flow->set(e, (*capacity)[e]);
                excess.set(w, excess[w]+rem);
              }
            }

          InEdgeIt f;
          for(g->first(f,s); g->valid(f); g->next(f))
            {
              if ( (*flow)[f] <= 0 ) continue;
              Node w=g->tail(f);
              if ( level[w] < n ) {
                if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
                excess.set(w, excess[w]+(*flow)[f]);
                flow->set(f, 0);
              }
            }
          break;
        } //case PRE_FLOW
      }
    } //preflowPreproc



    void relabel(Node w, int newlevel, VecStack& active,
                 VecNode& level_list, NNMap& left,
                 NNMap& right, int& b, int& k, bool what_heur )
    {

      Num lev=level[w];

      Node right_n=right[w];
      Node left_n=left[w];

      //unlacing starts
      if ( g->valid(right_n) ) {
        if ( g->valid(left_n) ) {
          right.set(left_n, right_n);
          left.set(right_n, left_n);
        } else {
          level_list[lev]=right_n;
          left.set(right_n, INVALID);
        }
      } else {
        if ( g->valid(left_n) ) {
          right.set(left_n, INVALID);
        } else {
          level_list[lev]=INVALID;
        }
      }
      //unlacing ends

      if ( !g->valid(level_list[lev]) ) {

        //gapping starts
        for (int i=lev; i!=k ; ) {
          Node v=level_list[++i];
          while ( g->valid(v) ) {
            level.set(v,n);
            v=right[v];
          }
          level_list[i]=INVALID;
          if ( !what_heur ) {
            while ( !active[i].empty() ) {
              active[i].pop();    //FIXME: ezt szebben kene
            }
          }
        }

        level.set(w,n);
        b=lev-1;
        k=b;
        //gapping ends

      } else {

        if ( newlevel == n ) level.set(w,n);
        else {
          level.set(w,++newlevel);
          active[newlevel].push(w);
          if ( what_heur ) b=newlevel;
          if ( k < newlevel ) ++k;      //now k=newlevel
          Node first=level_list[newlevel];
          if ( g->valid(first) ) left.set(first,w);
          right.set(w,first);
          left.set(w,INVALID);
          level_list[newlevel]=w;
        }
      }

    } //relabel


    template<typename MapGraphWrapper>
    class DistanceMap {
    protected:
      const MapGraphWrapper* g;
      typename MapGraphWrapper::template NodeMap<int> dist;
    public:
      DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }
      void set(const typename MapGraphWrapper::Node& n, int a) {
        dist.set(n, a);
      }
      int operator[](const typename MapGraphWrapper::Node& n) const { 
        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 Graph, typename Num, typename CapMap, typename FlowMap>
  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1(FlowEnum fe)
  {

    int heur0=(int)(H0*n);  //time while running 'bound decrease'
    int heur1=(int)(H1*n);  //time while running 'highest label'
    int heur=heur1;         //starting time interval (#of relabels)
    int numrelabel=0;

    bool what_heur=1;
    //It is 0 in case 'bound decrease' and 1 in case 'highest label'

    bool end=false;
    //Needed for 'bound decrease', true means no active nodes are above bound
    //b.

    int k=n-2;  //bound on the highest level under n containing a node
    int b=k;    //bound on the highest level under n of an active node

    VecStack active(n);

    NNMap left(*g, INVALID);
    NNMap right(*g, INVALID);
    VecNode level_list(n,INVALID);
    //List of the nodes in level i<n, set to n.

    NodeIt v;
    for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
    //setting each node to level n

    if ( fe == NO_FLOW ) {
      EdgeIt e;
      for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0);
    }

    switch (fe) { //computing the excess
    case PRE_FLOW:
      {
        NodeIt v;
        for(g->first(v); g->valid(v); g->next(v)) {
          Num exc=0;

          InEdgeIt e;
          for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e];
          OutEdgeIt f;
          for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f];

          excess.set(v,exc);

          //putting the active nodes into the stack
          int lev=level[v];
          if ( exc > 0 && lev < n && v != t ) active[lev].push(v);
        }
        break;
      }
    case GEN_FLOW:
      {
        NodeIt v;
        for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);

        Num exc=0;
        InEdgeIt e;
        for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
        OutEdgeIt f;
        for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
        excess.set(t,exc);
        break;
      }
    case ZERO_FLOW:
    case NO_FLOW:
      {
        NodeIt v;
        for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
        break;
      }
    }

    preflowPreproc(fe, active, level_list, left, right);
    //End of preprocessing


    //Push/relabel on the highest level active nodes.
    while ( true ) {
      if ( b == 0 ) {
        if ( !what_heur && !end && k > 0 ) {
          b=k;
          end=true;
        } else break;
      }

      if ( active[b].empty() ) --b;
      else {
        end=false;
        Node w=active[b].top();
        active[b].pop();
        int newlevel=push(w,active);
        if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list,
                                     left, right, b, k, what_heur);

        ++numrelabel;
        if ( numrelabel >= heur ) {
          numrelabel=0;
          if ( what_heur ) {
            what_heur=0;
            heur=heur0;
            end=false;
          } else {
            what_heur=1;
            heur=heur1;
            b=k;
          }
        }
      }
    }

    status=AFTER_PRE_FLOW_PHASE_1;
  }



  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2()
  {

    int k=n-2;  //bound on the highest level under n containing a node
    int b=k;    //bound on the highest level under n of an active node

    VecStack active(n);
    level.set(s,0);
    std::queue<Node> bfs_queue;
    bfs_queue.push(s);

    while (!bfs_queue.empty()) {

      Node v=bfs_queue.front();
      bfs_queue.pop();
      int l=level[v]+1;

      InEdgeIt e;
      for(g->first(e,v); g->valid(e); g->next(e)) {
        if ( (*capacity)[e] <= (*flow)[e] ) continue;
        Node u=g->tail(e);
        if ( level[u] >= n ) {
          bfs_queue.push(u);
          level.set(u, l);
          if ( excess[u] > 0 ) active[l].push(u);
        }
      }

      OutEdgeIt f;
      for(g->first(f,v); g->valid(f); g->next(f)) {
        if ( 0 >= (*flow)[f] ) continue;
        Node u=g->head(f);
        if ( level[u] >= n ) {
          bfs_queue.push(u);
          level.set(u, l);
          if ( excess[u] > 0 ) active[l].push(u);
        }
      }
    }
    b=n-2;

    while ( true ) {

      if ( b == 0 ) break;

      if ( active[b].empty() ) --b;
      else {
        Node w=active[b].top();
        active[b].pop();
        int newlevel=push(w,active);

        //relabel
        if ( excess[w] > 0 ) {
          level.set(w,++newlevel);
          active[newlevel].push(w);
          b=newlevel;
        }
      }  // if stack[b] is nonempty
    } // while(true)

    status=AFTER_PRE_FLOW_PHASE_2;
  }



  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath()
  {
    ResGW res_graph(*g, *capacity, *flow);
    bool _augment=false;

    //ReachedMap level(res_graph);
    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
    bfs.pushAndSetReached(s);

    typename ResGW::template NodeMap<ResGWEdge> pred(res_graph);
    pred.set(s, INVALID);

    typename ResGW::template NodeMap<Num> 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;
      Num 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);
      }
    }

    status=AFTER_AUGMENTING;
    return _augment;
  }


  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath2()
  {
    ResGW res_graph(*g, *capacity, *flow);
    bool _augment=false;

    if (status!=AFTER_AUGMENTING) {
      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, -1); 
      number_of_augmentations=0;
    } else {
      ++number_of_augmentations;
    }
    TrickyReachedMap<ReachedMap> 
      tricky_reached_map(level, number_of_augmentations);
    //ReachedMap level(res_graph);
//    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, TrickyReachedMap<ReachedMap> > 
      bfs(res_graph, tricky_reached_map);
    bfs.pushAndSetReached(s);

    typename ResGW::template NodeMap<ResGWEdge> pred(res_graph);
    pred.set(s, INVALID);

    typename ResGW::template NodeMap<Num> 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;
      Num 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);
      }
    }

    status=AFTER_AUGMENTING;
    return _augment;
  }


  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  template<typename MutableGraph>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow()
  {
    typedef MutableGraph MG;
    bool _augment=false;

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

    //bfs for distances on the residual graph
    //ReachedMap level(res_graph);
    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
    bfs.pushAndSetReached(s);
    typename ResGW::template 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::template 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::template EdgeMap<ResGWEdge> original_edge(F);
    typename MG::template EdgeMap<Num> 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
      DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
      typename MG::template NodeMap<typename MG::Edge> pred(F);
      pred.set(sF, INVALID);
      //invalid iterators for sources

      typename MG::template NodeMap<Num> 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;
        Num 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);
        }
      }

    }

    status=AFTER_AUGMENTING;
    return _augment;
  }




  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2()
  {
    bool _augment=false;

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

    //ReachedMap level(res_graph);
    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

    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::template 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::
      template 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
      DfsIterator< ErasingResGW,
        typename ErasingResGW::template NodeMap<bool> >
        dfs(erasing_res_graph);
      typename ErasingResGW::
        template NodeMap<typename ErasingResGW::OutEdgeIt>
        pred(erasing_res_graph);
      pred.set(s, INVALID);
      //invalid iterators for sources

      typename ErasingResGW::template NodeMap<Num>
        free1(erasing_res_graph);

      dfs.pushAndSetReached
        ///\bug hugo 0.2
        (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<Num> a(res_graph);
        //        typename ResGW::Node b;
        //        Num j=a[b];
        //        typename FilterResGW::NodeMap<Num> a1(filter_res_graph);
        //        typename FilterResGW::Node b1;
        //        Num j1=a1[b1];
        //        typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph);
        //        typename ErasingResGW::Node b2;
        //        Num j2=a2[b2];
        Num 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)

    status=AFTER_AUGMENTING;
    return _augment;
  }


} //namespace hugo

#endif //HUGO_MAX_FLOW_H