/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2007

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_PREFLOW_H

#define LEMON_PREFLOW_H

#include <vector>

#include <queue>

#include <lemon/error.h>

#include <lemon/bits/invalid.h>

#include <lemon/tolerance.h>

#include <lemon/maps.h>

#include <lemon/graph_utils.h>

/// \file

/// \ingroup max_flow

/// \brief Implementation of the preflow algorithm.

namespace lemon {

  ///\ingroup max_flow

  ///\brief %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 known max flow algorithms. 

  ///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 source, \ref target, \ref capacityMap and \ref

  ///flowMap.

  ///

  ///After running \ref lemon::Preflow::phase1() "phase1()"

  ///or \ref lemon::Preflow::run() "run()", the maximal flow

  ///value can be obtained by calling \ref flowValue(). The minimum

  ///value cut can be written into a <tt>bool</tt> node map 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 CapacityMap The capacity map type.

  ///\param FlowMap The flow map type.

  ///\param Tol The tolerance type. 

  ///

  ///\author Jacint Szabo 

  ///\todo Second template parameter is superfluous

  template <typename Graph, typename Num,

	    typename CapacityMap=typename Graph::template EdgeMap<Num>,

            typename FlowMap=typename Graph::template EdgeMap<Num>,

	    typename Tol=Tolerance<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 _source;

    Node _target;

    const CapacityMap* _capacity;

    FlowMap* _flow;

    Tol _surely;

    int _node_num;      //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:

    ///\ref Exception for the case when s=t.

    ///\ref Exception for the case when the source equals the target.

    class InvalidArgument : public lemon::LogicError {

    public:

      virtual const char* what() const throw() {

	return "lemon::Preflow::InvalidArgument";

      }

    };

    ///Indicates the property of the starting flow map.

    ///Indicates the property of the starting flow map.

    ///

    enum FlowEnum{

      ///indicates an unspecified edge map. \c flow will be 

      ///set to the constant zero flow in the beginning of

      ///the algorithm in this case.

      NO_FLOW,

      ///constant zero flow

      ZERO_FLOW,

      ///any flow, i.e. the sum of the in-flows equals to

      ///the sum of the out-flows in every node except the \c source and

      ///the \c target.

      GEN_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 \c source.

      PRE_FLOW

    };

    ///Indicates the state of the preflow algorithm.

    ///Indicates the state of the preflow algorithm.

    ///

    enum StatusEnum {

      ///before running the algorithm or

      ///at an unspecified state.

      AFTER_NOTHING,

      ///right after running \ref phase1()

      AFTER_PREFLOW_PHASE_1,      

      ///after running \ref phase2()

      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 _gr The directed graph the algorithm runs on. 

    ///\param _s The source node.

    ///\param _t The target node.

    ///\param _cap The capacity of the edges. 

    ///\param _f The flow of the edges. 

    ///\param _sr Tol class.

    ///Except the graph, all of these parameters can be reset by

    ///calling \ref source, \ref target, \ref capacityMap and \ref

    ///flowMap, resp.

    Preflow(const Graph& _gr, Node _s, Node _t, 

            const CapacityMap& _cap, FlowMap& _f,

            const Tol &_sr=Tol()) :

	_g(&_gr), _source(_s), _target(_t), _capacity(&_cap),

	_flow(&_f), _surely(_sr),

	_node_num(countNodes(_gr)), level(_gr), excess(_gr,0), 

	flow_prop(NO_FLOW), status(AFTER_NOTHING) { 

	if ( _source==_target )

	  throw InvalidArgument();

    }

    ///Give a reference to the tolerance handler class

    ///Give a reference to the tolerance handler class

    ///\sa Tolerance

    Tol &tolerance() { return _surely; }

    ///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, although a

    ///maximum flow is not yet obtained. So after calling this method

    ///\ref flowValue returns the value of a maximum flow and \ref

    ///minCut returns a minimum cut.     

    ///\warning \ref minMinCut and \ref maxMinCut do not give minimum

    ///value cuts unless calling \ref phase2.  

    ///\warning A real flow map (i.e. not \ref lemon::NullMap "NullMap")

    ///is needed for this phase.

    ///\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, although a

    ///maximum flow is not yet obtained. So after calling this method

    ///\ref flowValue returns the value of a maximum flow and \ref

    ///minCut returns a minimum cut.

    ///\warning \ref minMinCut() and \ref maxMinCut() do not

    ///give minimum value cuts unless calling \ref phase2().

    ///\warning A real flow map (i.e. not \ref lemon::NullMap "NullMap")

    ///is needed for this phase.

    void phase1()

    {

      int heur0=int(H0*_node_num);  //time while running 'bound decrease'

      int heur1=int(H1*_node_num);  //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=_node_num-2;  //bound on the highest level under n containing a node

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

      VecNode first(_node_num, INVALID);

      NNMap next(*_g, INVALID);

      NNMap left(*_g, INVALID);

      NNMap right(*_g, INVALID);

      VecNode level_list(_node_num,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(),

    /// \ref flowMap() return a maximum flow, \ref flowValue

    ///returns the value of a maximum flow, \ref minCut returns a

    ///minimum cut, while the methods \ref minMinCut and \ref

    ///maxMinCut return the inclusionwise minimum and maximum cuts of

    ///minimum value, resp.  \pre \ref phase1 must be called before.

    ///

    /// \todo The inexact computation can cause positive excess on a set of 

    /// unpushable nodes. We may have to watch the empty level in this case 

    /// due to avoid the terrible long running time.

    void phase2()

    {

      int k=_node_num-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(_node_num, INVALID);

      NNMap next(*_g, INVALID); 

      level.set(_source,0);

      std::queue<Node> bfs_queue;

      bfs_queue.push(_source);

      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 ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue;

	  Node u=_g->source(e);

	  if ( level[u] >= _node_num ) {

	    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 ( !_surely.positive((*_flow)[e]) ) continue;

	  Node u=_g->target(e);

	  if ( level[u] >= _node_num ) {

	    bfs_queue.push(u);

	    level.set(u, l);

	    if ( excess[u] != 0 ) {

	      next.set(u,first[l]);

	      first[l]=u;

	    }

	  }

	}

      }

      b=_node_num-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);

          if ( newlevel == _node_num) {

            excess.set(w, 0);

	    level.set(w,_node_num);

          }

	  //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 \c t. This value equals to the value of

    /// the maximum flow already after running \ref phase1.

    Num flowValue() const {

      return excess[_target];

    }

    ///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 bool-valued node-map. \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] < _node_num) {

	    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(_source,true);

      queue.push(_source);

      while (!queue.empty()) {

	Node w=queue.front();

	queue.pop();

	for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {

	  Node v=_g->target(e);

	  if (!M[v] && _surely.positive((*_capacity)[e] -(*_flow)[e]) ) {

	    queue.push(v);

	    M.set(v, true);

	  }

	}

	for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {

	  Node v=_g->source(e);

	  if (!M[v] && _surely.positive((*_flow)[e]) ) {

	    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 run() 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(_target,false);

      queue.push(_target);

      while (!queue.empty()) {

        Node w=queue.front();

	queue.pop();

	for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {

	  Node v=_g->source(e);

	  if (M[v] && _surely.positive((*_capacity)[e] - (*_flow)[e]) ) {

	    queue.push(v);

	    M.set(v, false);

	  }

	}

	for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {

	  Node v=_g->target(e);

	  if (M[v] && _surely.positive((*_flow)[e]) ) {

	    queue.push(v);

	    M.set(v, false);

	  }

	}

      }

    }

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

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

    /// 

    void source(Node _s) { 

      _source=_s; 

      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;

      status=AFTER_NOTHING; 

    }

    ///Returns the source node.

    ///Returns the source node.

    /// 

    Node source() const { 

      return _source;

    }

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

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

    ///

    void target(Node _t) { 

      _target=_t; 

      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;

      status=AFTER_NOTHING; 

    }

    ///Returns the target node.

    ///Returns the target node.

    /// 

    Node target() const { 

      return _target;

    }

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

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

    /// 

    void capacityMap(const CapacityMap& _cap) { 

      _capacity=&_cap; 

      status=AFTER_NOTHING; 

    }

    /// Returns a reference to capacity map.

    /// Returns a reference to capacity map.

    /// 

    const CapacityMap &capacityMap() const { 

      return *_capacity;

    }

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

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

    /// 

    void flowMap(FlowMap& _f) { 

      _flow=&_f; 

      flow_prop=NO_FLOW;

      status=AFTER_NOTHING; 

    }

    /// Returns a reference to flow map.

    /// Returns a reference to flow map.

    /// 

    const FlowMap &flowMap() const { 

      return *_flow;

    }

  private:

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

      int lev=level[w];

      Num exc=excess[w];

      int newlevel=_node_num;       //bound on the next level of w

      for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {

	if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue;

	Node v=_g->target(e);

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

	  if ( excess[v] == 0 && v!=_target && v!=_source ) {

	    next.set(v,first[level[v]]);

	    first[level[v]]=v;

	  }

	  Num cap=(*_capacity)[e];

	  Num flo=(*_flow)[e];

	  Num remcap=cap-flo;

	  if ( ! _surely.less(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 ( !_surely.positive((*_flow)[e]) ) continue;

	  Node v=_g->source(e);

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

	    if ( excess[v] == 0 && v!=_target && v!=_source ) {

	      next.set(v,first[level[v]]);

	      first[level[v]]=v;

	    }

	    Num flo=(*_flow)[e];

	    if ( !_surely.less(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,_node_num);

      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(_target,0);

	bfs_queue.push(_target);

	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 ( !_surely.positive((*_capacity)[e] - (*_flow)[e] )) continue;

	    Node w=_g->source(e);

	    if ( level[w] == _node_num && w != _source ) {

	      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 ( !_surely.positive((*_flow)[e]) ) continue;

	    Node w=_g->target(e);

	    if ( level[w] == _node_num && w != _source ) {

	      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(_target,0);

	bfs_queue.push(_target);

	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->source(e);

	    if ( level[w] == _node_num && w != _source ) {

	      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,_source) ; e!=INVALID; ++e) {

	  Num c=(*_capacity)[e];

	  if ( !_surely.positive(c) ) continue;

	  Node w=_g->target(e);

	  if ( level[w] < _node_num ) {

	    if ( excess[w] == 0 && w!=_target ) { //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,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];

	  for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];

          if (!_surely.positive(exc)) {

            exc = 0;

          }

          excess.set(_target,exc);

	}

	//the starting flow

	for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e)	{

	  Num rem=(*_capacity)[e]-(*_flow)[e];

	  if ( !_surely.positive(rem) ) continue;

	  Node w=_g->target(e);

	  if ( level[w] < _node_num ) {

	    if ( excess[w] == 0 && w!=_target ) { //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,_source); e!=INVALID; ++e) {

	  if ( !_surely.positive((*_flow)[e]) ) continue;

	  Node w=_g->source(e);

	  if ( level[w] < _node_num ) {

	    if ( excess[w] == 0 && w!=_target ) {

	      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,_source) ; e!=INVALID; ++e) {

	  Num rem=(*_capacity)[e]-(*_flow)[e];

	  if ( !_surely.positive(rem) ) continue;

	  Node w=_g->target(e);

	  if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);

	}

	for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {

	  if ( !_surely.positive((*_flow)[e]) ) continue;

	  Node w=_g->source(e);

	  if ( level[w] < _node_num ) _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];

          if (!_surely.positive(exc)) {

            exc = 0;

          }

	  excess.set(w,exc);

	  //putting the active nodes into the stack

	  int lev=level[w];

	    if ( exc != 0 && lev < _node_num && Node(w) != _target ) {

	      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,_node_num);

	    v=right[v];

	  }

	  level_list[i]=INVALID;

	  if ( !what_heur ) first[i]=INVALID;

	}

	level.set(w,_node_num);

	b=lev-1;

	k=b;

	//gapping ends

      } else {

	if ( newlevel == _node_num ) level.set(w,_node_num);

	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

  }; 

  ///\ingroup max_flow

  ///\brief Function type interface for Preflow algorithm.

  ///

  ///Function type interface for Preflow algorithm.

  ///\sa Preflow

  template<class GR, class CM, class FM>

  Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,

			    typename GR::Node source,

			    typename GR::Node target,

			    const CM &cap,

			    FM &flow

			    )

  {

    return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);

  }

} //namespace lemon

#endif //LEMON_PREFLOW_H