source: lemon-0.x/src/hugo/max_flow.h @ 759:2d2d41010cb9

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

#include <vector>
#include <queue>

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

/// \file
/// \ingroup flowalgs

namespace hugo {

  /// \addtogroup flowalgs
  /// @{                                                   

  ///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 setSource, \ref setTarget, \ref setCap and
  ///\ref setFlow. Before any subsequent runs of any algorithm of
  ///the class \ref setFlow 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<Node> VecFirst;
    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 ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
    typedef typename ResGW::Edge ResGWEdge;
    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;

    // 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_FAST_AUGMENTING, 
      AFTER_PRE_FLOW_PHASE_1,      
      AFTER_PRE_FLOW_PHASE_2
    };

    /// Do 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) {
//      if (b)
//        map->set(n, *number_of_augmentations);
//      else 
//        map->set(n, *number_of_augmentations-1);
//       }
//       bool operator[](const Node& n) const { 
//      return (*map)[n]==*number_of_augmentations; 
//       }
//     };
    
    ///Constructor

    ///\todo Document, please.
    ///
    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) { }

    ///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.
    ///
    ///\todo NO_FLOW should be the default 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 not 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)
    {

      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

      VecFirst first(n, INVALID);
      NNMap next(*g, INVALID); //maybe INVALID is not needed

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

      preflowPreproc(fe, next, first, 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 ( !g->valid(first[b]) ) --b;
        else {
          end=false;
          Node w=first[b];
          first[b]=next[w];
          int newlevel=push(w, next, first);
          if ( excess[w] > 0 ) relabel(w, newlevel, next, first, 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;
    }


    ///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()
    {

      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

    
      VecFirst first(n, INVALID);
      NNMap next(*g, INVALID); //maybe INVALID is not needed
      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 ) {
              next.set(u,first[l]);
              first[l]=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 ) {
              next.set(u,first[l]);
              first[l]=u;
            }
          }
        }
      }
      b=n-2;

      while ( true ) {

        if ( b == 0 ) break;

        if ( !g->valid(first[b]) ) --b;
        else {

          Node w=first[b];
          first[b]=next[w];
          int newlevel=push(w,next, first/*active*/);

          //relabel
          if ( excess[w] > 0 ) {
            level.set(w,++newlevel);
            next.set(w,first[newlevel]);
            first[newlevel]=w;
            b=newlevel;
          }
        } 
      } // while(true)

      status=AFTER_PRE_FLOW_PHASE_2;
    }


    /// 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(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e];
      for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) 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:
      case AFTER_AUGMENTING:
      case AFTER_FAST_AUGMENTING:
        minMinCut(M);
        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); }

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

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

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

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

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

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

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

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


  private:

    int push(Node w, NNMap& next, VecFirst& first) {

      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 ) {
            next.set(v,first[level[v]]);
            first[level[v]]=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 ) {
              next.set(v,first[level[v]]);
              first[level[v]]=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, NNMap& next, VecFirst& first,
                        VecNode& level_list, NNMap& left, NNMap& right)
    {
      switch (fe) { //setting excess
        case NO_FLOW: 
        {
          EdgeIt e;
          for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0);
          
          NodeIt v;
          for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
          break;
        }
        case ZERO_FLOW: 
        {
          NodeIt v;
          for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
          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;
        }
        default: break;
      }

      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
      //setting each node to level n
      
      std::queue<Node> bfs_queue;


      switch (fe) {
      case NO_FLOW:   //flow is already set to const zero
      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 z=level_list[l];
                if ( g->valid(z) ) left.set(z,w);
                right.set(w,z);
                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 ) //putting into the stack
                  { 
                    next.set(w,first[level[w]]);
                    first[level[w]]=w;
                  }
                flow->set(e, c);
                excess.set(w, excess[w]+c);
              }
            }
          break;
        }

      case GEN_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 z=level_list[l];
                if ( g->valid(z) ) left.set(z,w);
                right.set(w,z);
                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 z=level_list[l];
                if ( g->valid(z) ) left.set(z,w);
                right.set(w,z);
                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 ) //putting into the stack
                  {
                    next.set(w,first[level[w]]);
                    first[level[w]]=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 )
                  {
                    next.set(w,first[level[w]]);
                    first[level[w]]=w;
                  }  
                excess.set(w, excess[w]+(*flow)[f]);
                flow->set(f, 0);
              }
            }
          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 z=level_list[l];
                if ( g->valid(z) ) left.set(z,w);
                right.set(w,z);
                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 z=level_list[l];
                if ( g->valid(z) ) left.set(z,w);
                right.set(w,z);
                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 ) {
                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 ) {
                excess.set(w, excess[w]+(*flow)[f]);
                flow->set(f, 0);
              }
            }
          
          NodeIt w; //computing the excess
          for(g->first(w); g->valid(w); g->next(w)) {
            Num exc=0;

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

            excess.set(w,exc);

            //putting the active nodes into the stack
            int lev=level[w];
            if ( exc > 0 && lev < n && w != t ) 
              {
                next.set(w,first[lev]);
                first[lev]=w;
              }
          }
          break;
        } //case PRE_FLOW
      }
    } //preflowPreproc


    void relabel(Node w, int newlevel, NNMap& next, VecFirst& first,
                 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 ) first[i]=INVALID;
        }

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

      } else {

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

    void printexcess() {////
      std::cout << "Excesses:" <<std::endl;

      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) {
        std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl; 
      }
    }

 void printlevel() {////
      std::cout << "Levels:" <<std::endl;

      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) {
        std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
      }
    }

void printactive() {////
      std::cout << "Levels:" <<std::endl;

      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) {
        std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
      }
    }


  };  //class MaxFlow
} //namespace hugo

#endif //HUGO_MAX_FLOW_H