// -*- 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