/* -*- C++ -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2003-2006
 * 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 flowalgs
/// \brief Implementation of the preflow algorithm.

namespace lemon {

  ///\ingroup flowalgs
  ///\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 Tolerance 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 Tolerance=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;

    Tolerance _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* exceptionName() const {
	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 tol Tolerance 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 Tolerance &_sr=Tolerance()) :
	_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
    Tolerance &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.  
    ///\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().
    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 ( _surely.positive(excess[w]) ) 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.
    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.less((*_flow)[e], (*_capacity)[e]) ) continue;
	  Node u=_g->source(e);
	  if ( level[u] >= _node_num ) {
	    bfs_queue.push(u);
	    level.set(u, l);
	    if ( _surely.positive(excess[u]) ) {
	      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 ( _surely.positive(excess[u]) ) {
	      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);
	  
	  //relabel
	  if ( _surely.positive(excess[w]) ) {
	    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.less((*_flow)[e] , (*_capacity)[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.less((*_flow)[e], (*_capacity)[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.less((*_flow)[e], (*_capacity)[e]) ) continue;
	Node v=_g->target(e);
	
	if( lev > level[v] ) { //Push is allowed now
	  
	  if ( !_surely.positive(excess[v]) && 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 ( _surely.positive(exc) ) {
	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 ( !_surely.positive(excess[v]) && 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.less((*_flow)[e],(*_capacity)[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 ( !_surely.positive(excess[w]) && 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];
	  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 ( !_surely.positive(excess[w]) && 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 ( !_surely.positive(excess[w]) && 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];
	  excess.set(w,exc);
	  
	  //putting the active nodes into the stack
	  int lev=level[w];
	    if ( _surely.positive(exc) && 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 flowalgs
  ///\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