/* -*- 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 <lemon/error.h>

#include <lemon/bits/invalid.h>

#include <lemon/tolerance.h>

#include <lemon/maps.h>

#include <lemon/graph_utils.h>

#include <lemon/elevator.h>

/// \file

/// \ingroup max_flow

/// \brief Implementation of the preflow algorithm.

namespace lemon { 

  /// \brief Default traits class of Preflow class.

  ///

  /// Default traits class of Preflow class.

  /// \param _Graph Graph type.

  /// \param _CapacityMap Type of capacity map.

  template <typename _Graph, typename _CapacityMap>

  struct PreflowDefaultTraits {

    /// \brief The graph type the algorithm runs on. 

    typedef _Graph Graph;

    /// \brief The type of the map that stores the edge capacities.

    ///

    /// The type of the map that stores the edge capacities.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef _CapacityMap CapacityMap;

    /// \brief The type of the length of the edges.

    typedef typename CapacityMap::Value Value;

    /// \brief The map type that stores the flow values.

    ///

    /// The map type that stores the flow values. 

    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Graph::template EdgeMap<Value> FlowMap;

    /// \brief Instantiates a FlowMap.

    ///

    /// This function instantiates a \ref FlowMap. 

    /// \param graph The graph, to which we would like to define the flow map.

    static FlowMap* createFlowMap(const Graph& graph) {

      return new FlowMap(graph);

    }

    /// \brief The eleavator type used by Preflow algorithm.

    /// 

    /// The elevator type used by Preflow algorithm.

    ///

    /// \sa Elevator

    /// \sa LinkedElevator

    typedef LinkedElevator<Graph, typename Graph::Node> Elevator;

    /// \brief Instantiates an Elevator.

    ///

    /// This function instantiates a \ref Elevator. 

    /// \param graph The graph, to which we would like to define the elevator.

    /// \param max_level The maximum level of the elevator.

    static Elevator* createElevator(const Graph& graph, int max_level) {

      return new Elevator(graph, max_level);

    }

    /// \brief The tolerance used by the algorithm

    ///

    /// The tolerance used by the algorithm to handle inexact computation.

    typedef Tolerance<Value> Tolerance;

  };

  /// \ingroup max_flow

  ///

  /// \brief %Preflow algorithms class.

  ///

  /// This class provides an implementation of the Goldberg's \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 current implementation use a mixture of the

  /// \e "highest label" and the \e "bound decrease" heuristics.

  /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$.

  ///

  /// The algorithm consists from two phases. After the first phase

  /// the maximal flow value and the minimum cut can be obtained. The

  /// second phase constructs the feasible maximum flow on each edge.

  ///

  /// \param _Graph The directed graph type the algorithm runs on.

  /// \param _CapacityMap The flow map type.

  /// \param _Traits Traits class to set various data types used by

  /// the algorithm.  The default traits class is \ref

  /// PreflowDefaultTraits.  See \ref PreflowDefaultTraits for the

  /// documentation of a %Preflow traits class. 

  ///

  ///\author Jacint Szabo and Balazs Dezso

#ifdef DOXYGEN

  template <typename _Graph, typename _CapacityMap, typename _Traits>

#else

  template <typename _Graph, 

	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,

	    typename _Traits = PreflowDefaultTraits<_Graph, _CapacityMap> >

#endif

  class Preflow {

  public:

    typedef _Traits Traits;

    typedef typename Traits::Graph Graph;

    typedef typename Traits::CapacityMap CapacityMap;

    typedef typename Traits::Value Value; 

    typedef typename Traits::FlowMap FlowMap;

    typedef typename Traits::Elevator Elevator;

    typedef typename Traits::Tolerance Tolerance;

    /// \brief \ref Exception for uninitialized parameters.

    ///

    /// This error represents problems in the initialization

    /// of the parameters of the algorithms.

    class UninitializedParameter : public lemon::UninitializedParameter {

    public:

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

	return "lemon::Preflow::UninitializedParameter";

      }

    };

  private:

    GRAPH_TYPEDEFS(typename Graph);

    const Graph& _graph;

    const CapacityMap* _capacity;

    int _node_num;

    Node _source, _target;

    FlowMap* _flow;

    bool _local_flow;

    Elevator* _level;

    bool _local_level;

    typedef typename Graph::template NodeMap<Value> ExcessMap;

    ExcessMap* _excess;

    Tolerance _tolerance;

    bool _phase;

    void createStructures() {

      _node_num = countNodes(_graph);

      if (!_flow) {

	_flow = Traits::createFlowMap(_graph);

	_local_flow = true;

      }

      if (!_level) {

	_level = Traits::createElevator(_graph, _node_num);

	_local_level = true;

      }

      if (!_excess) {

	_excess = new ExcessMap(_graph);

      }

    }

    void destroyStructures() {

      if (_local_flow) {

	delete _flow;

      }

      if (_local_level) {

	delete _level;

      }

      if (_excess) {

	delete _excess;

      }

    }

  public:

    typedef Preflow Create;

    ///\name Named template parameters

    ///@{

    template <typename _FlowMap>

    struct DefFlowMapTraits : public Traits {

      typedef _FlowMap FlowMap;

      static FlowMap *createFlowMap(const Graph&) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// FlowMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting FlowMap

    /// type

    template <typename _FlowMap>

    struct DefFlowMap 

      : public Preflow<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > {

      typedef Preflow<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > Create;

    };

    template <typename _Elevator>

    struct DefElevatorTraits : public Traits {

      typedef _Elevator Elevator;

      static Elevator *createElevator(const Graph&, int) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// Elevator type

    ///

    /// \ref named-templ-param "Named parameter" for setting Elevator

    /// type

    template <typename _Elevator>

    struct DefElevator 

      : public Preflow<Graph, CapacityMap, DefElevatorTraits<_Elevator> > {

      typedef Preflow<Graph, CapacityMap, DefElevatorTraits<_Elevator> > Create;

    };

    template <typename _Elevator>

    struct DefStandardElevatorTraits : public Traits {

      typedef _Elevator Elevator;

      static Elevator *createElevator(const Graph& graph, int max_level) {

	return new Elevator(graph, max_level);

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// Elevator type

    ///

    /// \ref named-templ-param "Named parameter" for setting Elevator

    /// type. The Elevator should be standard constructor interface, ie.

    /// the graph and the maximum level should be passed to it.

    template <typename _Elevator>

    struct DefStandardElevator 

      : public Preflow<Graph, CapacityMap, 

		       DefStandardElevatorTraits<_Elevator> > {

      typedef Preflow<Graph, CapacityMap, 

		      DefStandardElevatorTraits<_Elevator> > Create;

    };    

    /// @}

  protected:

    Preflow() {}

  public:

    /// \brief The constructor of the class.

    ///

    /// The constructor of the class. 

    /// \param graph The directed graph the algorithm runs on. 

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

    /// \param source The source node.

    /// \param target The target node.

    Preflow(const Graph& graph, const CapacityMap& capacity, 

	       Node source, Node target) 

      : _graph(graph), _capacity(&capacity), 

	_node_num(0), _source(source), _target(target), 

	_flow(0), _local_flow(false),

	_level(0), _local_level(false),

	_excess(0), _tolerance(), _phase() {}

    /// \brief Destrcutor.

    ///

    /// Destructor.

    ~Preflow() {

      destroyStructures();

    }

    /// \brief Sets the capacity map.

    ///

    /// Sets the capacity map.

    /// \return \c (*this)

    Preflow& capacityMap(const CapacityMap& map) {

      _capacity = ↦

      return *this;

    }

    /// \brief Sets the flow map.

    ///

    /// Sets the flow map.

    /// \return \c (*this)

    Preflow& flowMap(FlowMap& map) {

      if (_local_flow) {

	delete _flow;

	_local_flow = false;

      }

      _flow = ↦

      return *this;

    }

    /// \brief Returns the flow map.

    ///

    /// \return The flow map.

    const FlowMap& flowMap() {

      return *_flow;

    }

    /// \brief Sets the elevator.

    ///

    /// Sets the elevator.

    /// \return \c (*this)

    Preflow& elevator(Elevator& elevator) {

      if (_local_level) {

	delete _level;

	_local_level = false;

      }

      _level = &elevator;

      return *this;

    }

    /// \brief Returns the elevator.

    ///

    /// \return The elevator.

    const Elevator& elevator() {

      return *_level;

    }

    /// \brief Sets the source node.

    ///

    /// Sets the source node.

    /// \return \c (*this)

    Preflow& source(const Node& node) {

      _source = node;

      return *this;

    }

    /// \brief Sets the target node.

    ///

    /// Sets the target node.

    /// \return \c (*this)

    Preflow& target(const Node& node) {

      _target = node;

      return *this;

    }

    /// \brief Sets the tolerance used by algorithm.

    ///

    /// Sets the tolerance used by algorithm.

    Preflow& tolerance(const Tolerance& tolerance) const {

      _tolerance = tolerance;

      return *this;

    } 

    /// \brief Returns the tolerance used by algorithm.

    ///

    /// Returns the tolerance used by algorithm.

    const Tolerance& tolerance() const {

      return tolerance;

    } 

    /// \name Execution control The simplest way to execute the

    /// algorithm is to use one of the member functions called \c

    /// run().  

    /// \n

    /// If you need more control on initial solution or

    /// execution then you have to call one \ref init() function and then

    /// the startFirstPhase() and if you need the startSecondPhase().  

    ///@{

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures.

    ///

    void init() {

      createStructures();

      _phase = true;

      for (NodeIt n(_graph); n != INVALID; ++n) {

	_excess->set(n, 0);

      }

      for (EdgeIt e(_graph); e != INVALID; ++e) {

	_flow->set(e, 0);

      }

      typename Graph::template NodeMap<bool> reached(_graph, false);

      _level->initStart();

      _level->initAddItem(_target);

      std::vector<Node> queue;

      reached.set(_source, true);

      queue.push_back(_target);

      reached.set(_target, true);

      while (!queue.empty()) {

	_level->initNewLevel();

	std::vector<Node> nqueue;

	for (int i = 0; i < int(queue.size()); ++i) {

	  Node n = queue[i];

	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Node u = _graph.source(e);

	    if (!reached[u] && _tolerance.positive((*_capacity)[e])) {

	      reached.set(u, true);

	      _level->initAddItem(u);

	      nqueue.push_back(u);

	    }

	  }

	}

	queue.swap(nqueue);

      }

      _level->initFinish();

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

	if (_tolerance.positive((*_capacity)[e])) {

	  Node u = _graph.target(e);

	  if ((*_level)[u] == _level->maxLevel()) continue;

	  _flow->set(e, (*_capacity)[e]);

	  _excess->set(u, (*_excess)[u] + (*_capacity)[e]);

	  if (u != _target && !_level->active(u)) {

	    _level->activate(u);

	  }

	}

      }

    }

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures and sets the initial

    /// flow to the given \c flowMap. The \c flowMap should contain a

    /// flow or at least a preflow, ie. in each node excluding the

    /// target the incoming flow should greater or equal to the

    /// outgoing flow.

    /// \return %False when the given \c flowMap is not a preflow. 

    template <typename FlowMap>

    bool flowInit(const FlowMap& flowMap) {

      createStructures();

      for (EdgeIt e(_graph); e != INVALID; ++e) {

	_flow->set(e, flowMap[e]);

      }

      for (NodeIt n(_graph); n != INVALID; ++n) {

	Value excess = 0;

	for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	  excess += (*_flow)[e];

	}

	for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

	  excess -= (*_flow)[e];

	}

	if (excess < 0 && n != _source) return false;

	_excess->set(n, excess);

      }

      typename Graph::template NodeMap<bool> reached(_graph, false);

      _level->initStart();

      _level->initAddItem(_target);

      std::vector<Node> queue;

      reached.set(_source, true);

      queue.push_back(_target);

      reached.set(_target, true);

      while (!queue.empty()) {

	_level->initNewLevel();

	std::vector<Node> nqueue;

	for (int i = 0; i < int(queue.size()); ++i) {

	  Node n = queue[i];

	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Node u = _graph.source(e);

	    if (!reached[u] && 

		_tolerance.positive((*_capacity)[e] - (*_flow)[e])) {

	      reached.set(u, true);

	      _level->initAddItem(u);

	      nqueue.push_back(u);

	    }

	  }

	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Node v = _graph.target(e);

	    if (!reached[v] && _tolerance.positive((*_flow)[e])) {

	      reached.set(v, true);

	      _level->initAddItem(v);

	      nqueue.push_back(v);

	    }

	  }

	}

	queue.swap(nqueue);

      }

      _level->initFinish();

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

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

	if (_tolerance.positive(rem)) {

	  Node u = _graph.target(e);

	  if ((*_level)[u] == _level->maxLevel()) continue;

	  _flow->set(e, (*_capacity)[e]);

	  _excess->set(u, (*_excess)[u] + rem);

	  if (u != _target && !_level->active(u)) {

	    _level->activate(u);

	  }

	}

      }

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

	Value rem = (*_flow)[e]; 

	if (_tolerance.positive(rem)) {

	  Node v = _graph.source(e);

	  if ((*_level)[v] == _level->maxLevel()) continue;

	  _flow->set(e, 0);

	  _excess->set(v, (*_excess)[v] + rem);

	  if (v != _target && !_level->active(v)) {

	    _level->activate(v);

	  }

	}

      }

      return true;

    }

    /// \brief Starts 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.     

    /// \pre One of the \ref init() functions should be called. 

    void startFirstPhase() {

      _phase = true;

      Node n = _level->highestActive();

      int level = _level->highestActiveLevel();

      while (n != INVALID) {

	int num = _node_num;

	while (num > 0 && n != INVALID) {

	  Value excess = (*_excess)[n];

	  int new_level = _level->maxLevel();

	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

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

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

	    Node v = _graph.target(e);

	    if ((*_level)[v] < level) {

	      if (!_level->active(v) && v != _target) {

		_level->activate(v);

	      }

	      if (!_tolerance.less(rem, excess)) {

		_flow->set(e, (*_flow)[e] + excess);

		_excess->set(v, (*_excess)[v] + excess);

		excess = 0;

		goto no_more_push_1;

	      } else {

		excess -= rem;

		_excess->set(v, (*_excess)[v] + rem);

		_flow->set(e, (*_capacity)[e]);

	      }

	    } else if (new_level > (*_level)[v]) {

	      new_level = (*_level)[v];

	    }

	  }

	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Value rem = (*_flow)[e];

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

	    Node v = _graph.source(e);

	    if ((*_level)[v] < level) {

	      if (!_level->active(v) && v != _target) {

		_level->activate(v);

	      }

	      if (!_tolerance.less(rem, excess)) {

		_flow->set(e, (*_flow)[e] - excess);

		_excess->set(v, (*_excess)[v] + excess);

		excess = 0;

		goto no_more_push_1;

	      } else {

		excess -= rem;

		_excess->set(v, (*_excess)[v] + rem);

		_flow->set(e, 0);

	      }

	    } else if (new_level > (*_level)[v]) {

	      new_level = (*_level)[v];

	    }

	  }

	no_more_push_1:

	  _excess->set(n, excess);

	  if (excess != 0) {

	    if (new_level + 1 < _level->maxLevel()) {

	      _level->liftHighestActive(new_level + 1);

	    } else {

	      _level->liftHighestActiveToTop();

	    }

	    if (_level->emptyLevel(level)) {

	      _level->liftToTop(level);

	    }

	  } else {

	    _level->deactivate(n);

	  }

	  n = _level->highestActive();

	  level = _level->highestActiveLevel();

	  --num;

	}

	num = _node_num * 20;

	while (num > 0 && n != INVALID) {

	  Value excess = (*_excess)[n];

	  int new_level = _level->maxLevel();

	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

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

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

	    Node v = _graph.target(e);

	    if ((*_level)[v] < level) {

	      if (!_level->active(v) && v != _target) {

		_level->activate(v);

	      }

	      if (!_tolerance.less(rem, excess)) {

		_flow->set(e, (*_flow)[e] + excess);

		_excess->set(v, (*_excess)[v] + excess);

		excess = 0;

		goto no_more_push_2;

	      } else {

		excess -= rem;

		_excess->set(v, (*_excess)[v] + rem);

		_flow->set(e, (*_capacity)[e]);

	      }

	    } else if (new_level > (*_level)[v]) {

	      new_level = (*_level)[v];

	    }

	  }

	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Value rem = (*_flow)[e];

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

	    Node v = _graph.source(e);

	    if ((*_level)[v] < level) {

	      if (!_level->active(v) && v != _target) {

		_level->activate(v);

	      }

	      if (!_tolerance.less(rem, excess)) {

		_flow->set(e, (*_flow)[e] - excess);

		_excess->set(v, (*_excess)[v] + excess);

		excess = 0;

		goto no_more_push_2;

	      } else {

		excess -= rem;

		_excess->set(v, (*_excess)[v] + rem);

		_flow->set(e, 0);

	      }

	    } else if (new_level > (*_level)[v]) {

	      new_level = (*_level)[v];

	    }

	  }

	no_more_push_2:

	  _excess->set(n, excess);

	  if (excess != 0) {

	    if (new_level + 1 < _level->maxLevel()) {

	      _level->liftActiveOn(level, new_level + 1);

	    } else {

	      _level->liftActiveToTop(level);

	    }

	    if (_level->emptyLevel(level)) {

	      _level->liftToTop(level);

	    }

	  } else {

	    _level->deactivate(n);

	  }

	  while (level >= 0 && _level->activeFree(level)) {

	    --level;

	  }

	  if (level == -1) {

	    n = _level->highestActive();

	    level = _level->highestActiveLevel();

	  } else {

	    n = _level->activeOn(level);

	  }

	  --num;

	}

      }

    }

    /// \brief Starts the second phase of the preflow algorithm.

    ///

    /// The preflow algorithm consists of two phases, this method runs

    /// the second phase. After calling \ref init() and \ref

    /// startFirstPhase() and then \ref startSecondPhase(), \ref

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

    /// value of a maximum flow, \ref minCut() returns a minimum cut

    /// \pre The \ref init() and startFirstPhase() functions should be

    /// called before.

    void startSecondPhase() {

      _phase = false;

      typename Graph::template NodeMap<bool> reached(_graph);

      for (NodeIt n(_graph); n != INVALID; ++n) {

	reached.set(n, (*_level)[n] < _level->maxLevel());

      }

      _level->initStart();

      _level->initAddItem(_source);

      std::vector<Node> queue;

      queue.push_back(_source);

      reached.set(_source, true);

      while (!queue.empty()) {

	_level->initNewLevel();

	std::vector<Node> nqueue;

	for (int i = 0; i < int(queue.size()); ++i) {

	  Node n = queue[i];

	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Node v = _graph.target(e);

	    if (!reached[v] && _tolerance.positive((*_flow)[e])) {

	      reached.set(v, true);

	      _level->initAddItem(v);

	      nqueue.push_back(v);

	    }

	  }

	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	    Node u = _graph.source(e);

	    if (!reached[u] && 

		_tolerance.positive((*_capacity)[e] - (*_flow)[e])) {

	      reached.set(u, true);

	      _level->initAddItem(u);

	      nqueue.push_back(u);

	    }

	  }

	}

	queue.swap(nqueue);

      }

      _level->initFinish();

      for (NodeIt n(_graph); n != INVALID; ++n) {

	if (!reached[n]) {

	  _level->markToBottom(n);

	} else if ((*_excess)[n] > 0 && _target != n) {

	  _level->activate(n);

	}

      }

      Node n;

      while ((n = _level->highestActive()) != INVALID) {

	Value excess = (*_excess)[n];

	int level = _level->highestActiveLevel();

	int new_level = _level->maxLevel();

	for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

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

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

	  Node v = _graph.target(e);

	  if ((*_level)[v] < level) {

	    if (!_level->active(v) && v != _source) {

	      _level->activate(v);

	    }

	    if (!_tolerance.less(rem, excess)) {

	      _flow->set(e, (*_flow)[e] + excess);

	      _excess->set(v, (*_excess)[v] + excess);

	      excess = 0;

	      goto no_more_push;

	    } else {

	      excess -= rem;

	      _excess->set(v, (*_excess)[v] + rem);

	      _flow->set(e, (*_capacity)[e]);

	    }

	  } else if (new_level > (*_level)[v]) {

	    new_level = (*_level)[v];

	  }

	}

	for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

	  Value rem = (*_flow)[e];

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

	  Node v = _graph.source(e);

	  if ((*_level)[v] < level) {

	    if (!_level->active(v) && v != _source) {

	      _level->activate(v);

	    }

	    if (!_tolerance.less(rem, excess)) {

	      _flow->set(e, (*_flow)[e] - excess);

	      _excess->set(v, (*_excess)[v] + excess);

	      excess = 0;

	      goto no_more_push;

	    } else {

	      excess -= rem;

	      _excess->set(v, (*_excess)[v] + rem);

	      _flow->set(e, 0);

	    }

	  } else if (new_level > (*_level)[v]) {

	    new_level = (*_level)[v];

	  }

	}

      no_more_push:

	_excess->set(n, excess);

	if (excess != 0) {

	  if (new_level + 1 < _level->maxLevel()) {

	    _level->liftHighestActive(new_level + 1);

	  } else {

	    // Calculation error 

	    _level->liftHighestActiveToTop();

	  }

	  if (_level->emptyLevel(level)) {

	    // Calculation error 

	    _level->liftToTop(level);

	  }

	} else {

	  _level->deactivate(n);

	}

      }

    }

    /// \brief Runs the preflow algorithm.  

    ///

    /// Runs the preflow algorithm.

    /// \note pf.run() is just a shortcut of the following code.

    /// \code

    ///   pf.init();

    ///   pf.startFirstPhase();

    ///   pf.startSecondPhase();

    /// \endcode

    void run() {

      init();

      startFirstPhase();

      startSecondPhase();

    }

    /// \brief Runs the preflow algorithm to compute the minimum cut.  

    ///

    /// Runs the preflow algorithm to compute the minimum cut.

    /// \note pf.runMinCut() is just a shortcut of the following code.

    /// \code

    ///   pf.init();

    ///   pf.startFirstPhase();

    /// \endcode

    void runMinCut() {

      init();

      startFirstPhase();

    }

    /// @}

    /// \name Query Functions

    /// The result of the %Preflow algorithm can be obtained using these

    /// functions.\n

    /// Before the use of these functions,

    /// either run() or start() must be called.

    ///@{

    /// \brief 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 the first phase.

    Value flowValue() const {

      return (*_excess)[_target];

    }

    /// \brief Returns true when the node is on the source side of minimum cut.

    ///

    /// Returns true when the node is on the source side of minimum

    /// cut. This method can be called both after running \ref

    /// startFirstPhase() and \ref startSecondPhase().

    bool minCut(const Node& node) const {

      return ((*_level)[node] == _level->maxLevel()) == _phase;

    }

    /// \brief Returns a minimum value cut.

    ///

    /// Sets the \c cutMap to the characteristic vector of a minimum value

    /// cut. This method can be called both after running \ref

    /// startFirstPhase() and \ref startSecondPhase(). The result after second

    /// phase could be changed slightly if inexact computation is used.

    /// \pre The \c cutMap should be a bool-valued node-map.

    template <typename CutMap>

    void minCutMap(CutMap& cutMap) const {

      for (NodeIt n(_graph); n != INVALID; ++n) {

	cutMap.set(n, minCut(n));

      }

    }

    /// \brief Returns the flow on the edge.

    ///

    /// Sets the \c flowMap to the flow on the edges. This method can

    /// be called after the second phase of algorithm.

    Value flow(const Edge& edge) const {

      return (*_flow)[edge];

    }

    /// @}    

  };

}

#endif