// -*- 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 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<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); }

     ///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, 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