# HG changeset patch
# User jacint
# Date 1095083833 0
# Node ID f8549e3f6c5a9b2a951e75ff497062f51cfc73df
# Parent  eb9587f09b424e82924a0f636f9e49c9cfd60731
preflow last changes

diff -r eb9587f09b42 -r f8549e3f6c5a src/hugo/max_flow.h
--- a/src/hugo/max_flow.h	Mon Sep 13 11:24:35 2004 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,903 +0,0 @@
-// -*- 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 ( first[b]==INVALID ) --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;
-
-	for(InEdgeIt e(*g,v); e!=INVALID; ++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;
-	    }
-	  }
-	}
-
-	for(OutEdgeIt e(*g,v); e!=INVALID; ++e) {
-	  if ( 0 >= (*flow)[e] ) continue;
-	  Node u=g->head(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;
-	    }
-	  }
-	}
-      }
-      b=n-2;
-
-      while ( true ) {
-
-	if ( b == 0 ) break;
-
-	if ( first[b]==INVALID ) --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 value of the maximum flow.
-
-    /// Returns the excess of the target node \ref t. 
-    /// After running \ref preflowPhase1, this is the value of 
-    /// the maximum flow.
-    /// 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;
-      return excess[t];
-      //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 {
-      switch (status) {
-	case AFTER_PRE_FLOW_PHASE_1:
-	for(NodeIt v(*g); v!=INVALID; ++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();
-
-	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
-	  Node v=g->head(e);
-	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
-	    queue.push(v);
-	    M.set(v, true);
-	  }
-	}
-
-	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
-	  Node v=g->tail(e);
-	  if (!M[v] && (*flow)[e] > 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 {
-
-      for(NodeIt v(*g) ; v!=INVALID; ++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();
-
-	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
-	  Node v=g->tail(e);
-	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
-	    queue.push(v);
-	    M.set(v, false);
-	  }
-	}
-
-	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
-	  Node v=g->head(e);
-	  if (M[v] && (*flow)[e] > 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
-
-      for(OutEdgeIt e(*g,w) ; e!=INVALID; ++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 ) {
-	for(InEdgeIt e(*g,w) ; e!=INVALID; ++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: 
-	for(EdgeIt e(*g); e!=INVALID; ++e) flow->set(e,0);
-	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
-	break;
-	case ZERO_FLOW: 
-	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
-	break;
-	case GEN_FLOW:
-	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
-	{
-	  Num exc=0;
-	  for(InEdgeIt e(*g,t) ; e!=INVALID; ++e) exc+=(*flow)[e];
-	  for(OutEdgeIt e(*g,t) ; e!=INVALID; ++e) exc-=(*flow)[e];
-	  excess.set(t,exc);
-	}
-	break;
-	default:
-	break;
-      }
-      
-      for(NodeIt v(*g); v!=INVALID; ++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;
-	  
-	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
-	    Node w=g->tail(e);
-	    if ( level[w] == n && w != s ) {
-	      bfs_queue.push(w);
-	      Node z=level_list[l];
-	      if ( z!=INVALID ) left.set(z,w);
-	      right.set(w,z);
-	      level_list[l]=w;
-	      level.set(w, l);
-	    }
-	  }
-	}
-	
-	//the starting flow
-	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++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;
-	  
-	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++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 ( z!=INVALID ) left.set(z,w);
-	      right.set(w,z);
-	      level_list[l]=w;
-	      level.set(w, l);
-	    }
-	  }
-	  
-	  for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
-	    if ( 0 >= (*flow)[e] ) continue;
-	    Node w=g->head(e);
-	    if ( level[w] == n && w != s ) {
-	      bfs_queue.push(w);
-	      Node z=level_list[l];
-	      if ( z!=INVALID ) left.set(z,w);
-	      right.set(w,z);
-	      level_list[l]=w;
-	      level.set(w, l);
-	    }
-	  }
-	}
-	
-	//the starting flow
-	for(OutEdgeIt e(*g,s); e!=INVALID; ++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);
-	    }
-	  }
-	
-	for(InEdgeIt e(*g,s); e!=INVALID; ++e)
-	  {
-	    if ( (*flow)[e] <= 0 ) continue;
-	    Node w=g->tail(e);
-	    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)[e]);
-	      flow->set(e, 0);
-	    }
-	  }
-	break;
-      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;
-	  
-	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++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 ( z!=INVALID ) left.set(z,w);
-	      right.set(w,z);
-	      level_list[l]=w;
-	      level.set(w, l);
-	    }
-	  }
-	  
-	  for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
-	    if ( 0 >= (*flow)[e] ) continue;
-	    Node w=g->head(e);
-	    if ( level[w] == n && w != s ) {
-	      bfs_queue.push(w);
-	      Node z=level_list[l];
-	      if ( z!=INVALID ) left.set(z,w);
-	      right.set(w,z);
-	      level_list[l]=w;
-	      level.set(w, l);
-	    }
-	  }
-	}
-	
-	
-	//the starting flow
-	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++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);
-	  }
-	}
-	
-	for(InEdgeIt e(*g,s) ; e!=INVALID; ++e) {
-	  if ( (*flow)[e] <= 0 ) continue;
-	  Node w=g->tail(e);
-	  if ( level[w] < n ) {
-	    excess.set(w, excess[w]+(*flow)[e]);
-	    flow->set(e, 0);
-	  }
-	}
-	
-	//computing the excess
-	for(NodeIt w(*g); w!=INVALID; ++w) {
-	  Num exc=0;
-	  
-	  for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) exc+=(*flow)[e];
-	  for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) exc-=(*flow)[e];
-	  
-	  excess.set(w,exc);
-	  
-	  //putting the active nodes into the stack
-	  int lev=level[w];
-	    if ( exc > 0 && lev < n && Node(w) != t ) 
-	      ///\bug	    if ( exc > 0 && lev < n && w != t ) temporarily for working with wrappers. 
-	    {
-	      next.set(w,first[lev]);
-	      first[lev]=w;
-	    }
-	}
-	break;
-      } //switch
-    } //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 )
-    {
-
-      int lev=level[w];
-
-      Node right_n=right[w];
-      Node left_n=left[w];
-
-      //unlacing starts
-      if ( right_n!=INVALID ) {
-	if ( left_n!=INVALID ) {
-	  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 ( left_n!=INVALID ) {
-	  right.set(left_n, INVALID);
-	} else {
-	  level_list[lev]=INVALID;
-	}
-      }
-      //unlacing ends
-
-      if ( level_list[lev]==INVALID ) {
-
-	//gapping starts
-	for (int i=lev; i!=k ; ) {
-	  Node v=level_list[++i];
-	  while ( v!=INVALID ) {
-	    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 ( z!=INVALID ) left.set(z,w);
-	  right.set(w,z);
-	  left.set(w,INVALID);
-	  level_list[newlevel]=w;
-	}
-      }
-    } //relabel
-
-    void printexcess() {////
-      std::cout << "Excesses:" <<std::endl;
-
-      for(NodeIt v(*g); v!=INVALID ; ++v) {
-	std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl; 
-      }
-    }
-
-    void printlevel() {////
-      std::cout << "Levels:" <<std::endl;
-
-      for(NodeIt v(*g); v!=INVALID ; ++v) {
-	std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
-      }
-    }
-
-    void printactive() {////
-      std::cout << "Levels:" <<std::endl;
-
-      for(NodeIt v(*g); v!=INVALID ; ++v) {
-	std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
-      }
-    }
-
-
-  };  //class MaxFlow
-} //namespace hugo
-
-#endif //HUGO_MAX_FLOW_H
-
-
-
-
diff -r eb9587f09b42 -r f8549e3f6c5a src/hugo/preflow.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/hugo/preflow.h	Mon Sep 13 13:57:13 2004 +0000
@@ -0,0 +1,796 @@
+// -*- C++ -*-
+#ifndef HUGO_PREFLOW_H
+#define HUGO_PREFLOW_H
+
+#include <vector>
+#include <queue>
+
+#include <hugo/invalid.h>
+#include <hugo/maps.h>
+
+/// \file
+/// \ingroup flowalgs
+
+namespace hugo {
+
+  /// \addtogroup flowalgs
+  /// @{                                                   
+
+  ///Preflow algorithms class.
+
+  ///This class provides an implementation of the \e preflow \e
+  ///algorithm producing a flow of maximum value in a directed
+  ///graph. The preflow algorithms are the fastest max flow algorithms
+  ///up-to-date. 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.
+  ///
+  ///After running \c phase1 or \c preflow, 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 Jacint Szabo 
+  template <typename Graph, typename Num,
+	    typename CapMap=typename Graph::template EdgeMap<Num>,
+            typename FlowMap=typename Graph::template EdgeMap<Num> >
+  class Preflow {
+  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 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
+    
+    typename Graph::template NodeMap<int> level;  
+    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 map.
+
+    ///Indicates the property of the starting flow map. 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{
+      NO_FLOW,
+      ZERO_FLOW,
+      GEN_FLOW,
+      PRE_FLOW
+    };
+
+    ///Indicates the state of the preflow algorithm.
+
+    ///Indicates the state of the preflow algorithm. The meanings are as follows:
+    ///- \c AFTER_NOTHING: before running the algorithm or at an unspecified state.
+    ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1
+    ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2()
+    ///
+    enum StatusEnum {
+      AFTER_NOTHING,
+      AFTER_PREFLOW_PHASE_1,      
+      AFTER_PREFLOW_PHASE_2
+    };
+    
+    protected: 
+      FlowEnum flow_prop;
+    StatusEnum status; // Do not needle this flag only if necessary.
+    
+  public: 
+    ///The constructor of the class.
+
+    ///The constructor of the class. 
+    ///\param _G The directed graph the algorithm runs on. 
+    ///\param _s The source node.
+    ///\param _t The target node.
+    ///\param _capacity The capacity of the edges. 
+    ///\param _flow The flow of the edges. 
+    ///Except the graph, all of these parameters can be reset by
+    ///calling \ref setSource, \ref setTarget, \ref setCap and \ref
+    ///setFlow, resp.
+      Preflow(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), 
+	flow_prop(NO_FLOW), status(AFTER_NOTHING) { }
+
+
+                                                                              
+    ///Runs the preflow algorithm.  
+
+    ///Runs the preflow algorithm. 
+    void run() {
+      phase1(flow_prop);
+      phase2();
+    }
+    
+    ///Runs the preflow algorithm.  
+    
+    ///Runs the preflow algorithm. 
+    ///\pre The starting flow map must be
+    /// - a constant zero flow if \c fp is \c ZERO_FLOW,
+    /// - an arbitrary flow if \c fp is \c GEN_FLOW,
+    /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
+    /// - any map if \c fp is NO_FLOW.
+    ///If the starting flow map is a flow or a preflow then 
+    ///the algorithm terminates faster.
+    void run(FlowEnum fp) {
+      flow_prop=fp;
+      run();
+    }
+      
+    ///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 minCut gives proper results.
+    ///\warning: \ref minMinCut and \ref maxMinCut do not
+    ///give minimum value cuts unless calling \ref phase2.
+    ///\pre The starting flow must be
+    /// - a constant zero flow if \c fp is \c ZERO_FLOW,
+    /// - an arbitary flow if \c fp is \c GEN_FLOW,
+    /// - an arbitary preflow if \c fp is \c PRE_FLOW,
+    /// - any map if \c fp is NO_FLOW.
+    void phase1(FlowEnum fp)
+    {
+      flow_prop=fp;
+      phase1();
+    }
+
+    
+    ///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 phase2.
+    void phase1()
+    {
+      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
+
+      VecNode first(n, INVALID);
+      NNMap next(*g, INVALID);
+
+      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(first, next, level_list, left, right);
+
+      //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 ( first[b]==INVALID ) --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, first, next, 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;
+	    }
+	  }
+	}
+      }
+      flow_prop=PRE_FLOW;
+      status=AFTER_PREFLOW_PHASE_1;
+    }
+    // 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 second phase of the preflow algorithm.
+
+    ///The preflow algorithm consists of two phases, this method runs
+    ///the second phase. After calling \ref phase1 and then
+    ///\ref phase2 the methods \ref flowValue, \ref minCut,
+    ///\ref minMinCut and \ref maxMinCut give proper results.
+    ///\pre \ref phase1 must be called before.
+    void phase2()
+    {
+
+      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
+
+    
+      VecNode first(n, INVALID);
+      NNMap next(*g, INVALID); 
+      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;
+
+	for(InEdgeIt e(*g,v); e!=INVALID; ++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;
+	    }
+	  }
+	}
+
+	for(OutEdgeIt e(*g,v); e!=INVALID; ++e) {
+	  if ( 0 >= (*flow)[e] ) continue;
+	  Node u=g->head(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;
+	    }
+	  }
+	}
+      }
+      b=n-2;
+
+      while ( true ) {
+
+	if ( b == 0 ) break;
+	if ( first[b]==INVALID ) --b;
+	else {
+	  Node w=first[b];
+	  first[b]=next[w];
+	  int newlevel=push(w,next, first);
+	  
+	  //relabel
+	  if ( excess[w] > 0 ) {
+	    level.set(w,++newlevel);
+	    next.set(w,first[newlevel]);
+	    first[newlevel]=w;
+	    b=newlevel;
+	  }
+	} 
+      } // while(true)
+      flow_prop=GEN_FLOW;
+      status=AFTER_PREFLOW_PHASE_2;
+    }
+
+    /// Returns the value of the maximum flow.
+
+    /// Returns the value of the maximum flow by returning the excess
+    /// of the target node \ref t. This value equals to the value of
+    /// the maximum flow already after running \ref phase1.
+    Num flowValue() const {
+      return excess[t];
+    }
+
+
+    ///Returns a minimum value cut.
+
+    ///Sets \c M to the characteristic vector of a minimum value
+    ///cut. This method can be called both after running \ref
+    ///phase1 and \ref phase2. It is much faster after
+    ///\ref phase1.  \pre M should be a node map of bools. \pre
+    ///If \ref mincut is called after \ref phase2 then M should
+    ///be initialized to false.
+    template<typename _CutMap>
+    void minCut(_CutMap& M) const {
+      switch ( status ) {
+	case AFTER_PREFLOW_PHASE_1:
+	for(NodeIt v(*g); v!=INVALID; ++v) {
+	  if (level[v] < n) {
+	    M.set(v, false);
+	  } else {
+	    M.set(v, true);
+	  }
+	}
+	break;
+	case AFTER_PREFLOW_PHASE_2:
+	minMinCut(M);
+	break;
+	case AFTER_NOTHING:
+	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 \ref
+    ///phase2 should already be run.
+    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();
+	
+	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
+	  Node v=g->head(e);
+	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
+	    queue.push(v);
+	    M.set(v, true);
+	  }
+	}
+	
+	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
+	  Node v=g->tail(e);
+	  if (!M[v] && (*flow)[e] > 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 \ref phase2() or preflow() should already be run.
+    template<typename _CutMap>
+    void maxMinCut(_CutMap& M) const {
+
+      for(NodeIt v(*g) ; v!=INVALID; ++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();
+
+	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
+	  Node v=g->tail(e);
+	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
+	    queue.push(v);
+	    M.set(v, false);
+	  }
+	}
+
+	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
+	  Node v=g->head(e);
+	  if (M[v] && (*flow)[e] > 0 ) {
+	    queue.push(v);
+	    M.set(v, false);
+	  }
+	}
+      }
+    }
+
+    ///Sets the source node to \c _s.
+
+    ///Sets the source node to \c _s.
+    /// 
+    void setSource(Node _s) { 
+      s=_s; 
+      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
+      status=AFTER_NOTHING; 
+    }
+
+    ///Sets the target node to \c _t.
+
+    ///Sets the target node to \c _t.
+    ///
+    void setTarget(Node _t) { 
+      t=_t; 
+      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
+      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; 
+      flow_prop=NO_FLOW;
+      status=AFTER_NOTHING; 
+    }
+
+
+  private:
+
+    int push(Node w, NNMap& next, VecNode& first) {
+
+      int lev=level[w];
+      Num exc=excess[w];
+      int newlevel=n;       //bound on the next level of w
+
+      for(OutEdgeIt e(*g,w) ; e!=INVALID; ++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 ) {
+	for(InEdgeIt e(*g,w) ; e!=INVALID; ++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(VecNode& first, NNMap& next, 
+			VecNode& level_list, NNMap& left, NNMap& right)
+    {
+      for(NodeIt v(*g); v!=INVALID; ++v) level.set(v,n);
+      std::queue<Node> bfs_queue;
+      
+      if ( flow_prop == GEN_FLOW || flow_prop == 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;
+	  
+	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++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 ( z!=INVALID ) left.set(z,w);
+	      right.set(w,z);
+	      level_list[l]=w;
+	      level.set(w, l);
+	    }
+	  }
+	  
+	  for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
+	    if ( 0 >= (*flow)[e] ) continue;
+	    Node w=g->head(e);
+	    if ( level[w] == n && w != s ) {
+	      bfs_queue.push(w);
+	      Node z=level_list[l];
+	      if ( z!=INVALID ) left.set(z,w);
+	      right.set(w,z);
+	      level_list[l]=w;
+	      level.set(w, l);
+	    }
+	  }
+	} //while
+      } //if
+
+
+      switch (flow_prop) {
+	case NO_FLOW:  
+	for(EdgeIt e(*g); e!=INVALID; ++e) flow->set(e,0);
+	case ZERO_FLOW:
+	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
+	
+	//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;
+	  
+	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
+	    Node w=g->tail(e);
+	    if ( level[w] == n && w != s ) {
+	      bfs_queue.push(w);
+	      Node z=level_list[l];
+	      if ( z!=INVALID ) left.set(z,w);
+	      right.set(w,z);
+	      level_list[l]=w;
+	      level.set(w, l);
+	    }
+	  }
+	}
+	
+	//the starting flow
+	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++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:
+	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
+	{
+	  Num exc=0;
+	  for(InEdgeIt e(*g,t) ; e!=INVALID; ++e) exc+=(*flow)[e];
+	  for(OutEdgeIt e(*g,t) ; e!=INVALID; ++e) exc-=(*flow)[e];
+	  excess.set(t,exc);
+	}
+
+	//the starting flow
+	for(OutEdgeIt e(*g,s); e!=INVALID; ++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);
+	  }
+	}
+	
+	for(InEdgeIt e(*g,s); e!=INVALID; ++e) {
+	  if ( (*flow)[e] <= 0 ) continue;
+	  Node w=g->tail(e);
+	  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)[e]);
+	    flow->set(e, 0);
+	  }
+	}
+	break;
+
+	case PRE_FLOW:	
+	//the starting flow
+	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++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]);
+	}
+	
+	for(InEdgeIt e(*g,s) ; e!=INVALID; ++e) {
+	  if ( (*flow)[e] <= 0 ) continue;
+	  Node w=g->tail(e);
+	  if ( level[w] < n ) flow->set(e, 0);
+	}
+	
+	//computing the excess
+	for(NodeIt w(*g); w!=INVALID; ++w) {
+	  Num exc=0;
+	  for(InEdgeIt e(*g,w); e!=INVALID; ++e) exc+=(*flow)[e];
+	  for(OutEdgeIt e(*g,w); e!=INVALID; ++e) exc-=(*flow)[e];
+	  excess.set(w,exc);
+	  
+	  //putting the active nodes into the stack
+	  int lev=level[w];
+	    if ( exc > 0 && lev < n && Node(w) != t ) {
+	      next.set(w,first[lev]);
+	      first[lev]=w;
+	    }
+	}
+	break;
+      } //switch
+    } //preflowPreproc
+
+
+    void relabel(Node w, int newlevel, VecNode& first, NNMap& next, 
+		 VecNode& level_list, NNMap& left,
+		 NNMap& right, int& b, int& k, bool what_heur )
+    {
+
+      int lev=level[w];
+
+      Node right_n=right[w];
+      Node left_n=left[w];
+
+      //unlacing starts
+      if ( right_n!=INVALID ) {
+	if ( left_n!=INVALID ) {
+	  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 ( left_n!=INVALID ) {
+	  right.set(left_n, INVALID);
+	} else {
+	  level_list[lev]=INVALID;
+	}
+      }
+      //unlacing ends
+
+      if ( level_list[lev]==INVALID ) {
+
+	//gapping starts
+	for (int i=lev; i!=k ; ) {
+	  Node v=level_list[++i];
+	  while ( v!=INVALID ) {
+	    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 ( z!=INVALID ) left.set(z,w);
+	  right.set(w,z);
+	  left.set(w,INVALID);
+	  level_list[newlevel]=w;
+	}
+      }
+    } //relabel
+
+  }; 
+} //namespace hugo
+
+#endif //HUGO_PREFLOW_H
+
+
+
+