diff -r e9c203fb003d -r 994c7df296c9 lemon/preflow.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/preflow.h	Thu Dec 10 17:05:35 2009 +0100
@@ -0,0 +1,965 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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/tolerance.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.
+  /// \tparam GR Digraph type.
+  /// \tparam CAP Capacity map type.
+  template <typename GR, typename CAP>
+  struct PreflowDefaultTraits {
+
+    /// \brief The type of the digraph the algorithm runs on.
+    typedef GR Digraph;
+
+    /// \brief The type of the map that stores the arc capacities.
+    ///
+    /// The type of the map that stores the arc capacities.
+    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef CAP CapacityMap;
+
+    /// \brief The type of the flow values.
+    typedef typename CapacityMap::Value Value;
+
+    /// \brief The type of the map that stores the flow values.
+    ///
+    /// The type of the map that stores the flow values.
+    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
+    typedef typename Digraph::template ArcMap<Value> FlowMap;
+
+    /// \brief Instantiates a FlowMap.
+    ///
+    /// This function instantiates a \ref FlowMap.
+    /// \param digraph The digraph for which we would like to define
+    /// the flow map.
+    static FlowMap* createFlowMap(const Digraph& digraph) {
+      return new FlowMap(digraph);
+    }
+
+    /// \brief The elevator type used by Preflow algorithm.
+    ///
+    /// The elevator type used by Preflow algorithm.
+    ///
+    /// \sa Elevator
+    /// \sa LinkedElevator
+    typedef LinkedElevator<Digraph, typename Digraph::Node> Elevator;
+
+    /// \brief Instantiates an Elevator.
+    ///
+    /// This function instantiates an \ref Elevator.
+    /// \param digraph The digraph for which we would like to define
+    /// the elevator.
+    /// \param max_level The maximum level of the elevator.
+    static Elevator* createElevator(const Digraph& digraph, int max_level) {
+      return new Elevator(digraph, max_level);
+    }
+
+    /// \brief The tolerance used by the algorithm
+    ///
+    /// The tolerance used by the algorithm to handle inexact computation.
+    typedef lemon::Tolerance<Value> Tolerance;
+
+  };
+
+
+  /// \ingroup max_flow
+  ///
+  /// \brief %Preflow algorithm class.
+  ///
+  /// This class provides an implementation of Goldberg-Tarjan's \e preflow
+  /// \e push-relabel algorithm producing a \ref max_flow
+  /// "flow of maximum value" in a digraph.
+  /// The preflow algorithms are the fastest known maximum
+  /// 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 of two phases. After the first phase
+  /// the maximum flow value and the minimum cut is obtained. The
+  /// second phase constructs a feasible maximum flow on each arc.
+  ///
+  /// \tparam GR The type of the digraph the algorithm runs on.
+  /// \tparam CAP The type of the capacity map. The default map
+  /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
+#ifdef DOXYGEN
+  template <typename GR, typename CAP, typename TR>
+#else
+  template <typename GR,
+            typename CAP = typename GR::template ArcMap<int>,
+            typename TR = PreflowDefaultTraits<GR, CAP> >
+#endif
+  class Preflow {
+  public:
+
+    ///The \ref PreflowDefaultTraits "traits class" of the algorithm.
+    typedef TR Traits;
+    ///The type of the digraph the algorithm runs on.
+    typedef typename Traits::Digraph Digraph;
+    ///The type of the capacity map.
+    typedef typename Traits::CapacityMap CapacityMap;
+    ///The type of the flow values.
+    typedef typename Traits::Value Value;
+
+    ///The type of the flow map.
+    typedef typename Traits::FlowMap FlowMap;
+    ///The type of the elevator.
+    typedef typename Traits::Elevator Elevator;
+    ///The type of the tolerance.
+    typedef typename Traits::Tolerance Tolerance;
+
+  private:
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+    const Digraph& _graph;
+    const CapacityMap* _capacity;
+
+    int _node_num;
+
+    Node _source, _target;
+
+    FlowMap* _flow;
+    bool _local_flow;
+
+    Elevator* _level;
+    bool _local_level;
+
+    typedef typename Digraph::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 T>
+    struct SetFlowMapTraits : public Traits {
+      typedef T FlowMap;
+      static FlowMap *createFlowMap(const Digraph&) {
+        LEMON_ASSERT(false, "FlowMap is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// FlowMap type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting FlowMap
+    /// type.
+    template <typename T>
+    struct SetFlowMap
+      : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<T> > {
+      typedef Preflow<Digraph, CapacityMap,
+                      SetFlowMapTraits<T> > Create;
+    };
+
+    template <typename T>
+    struct SetElevatorTraits : public Traits {
+      typedef T Elevator;
+      static Elevator *createElevator(const Digraph&, int) {
+        LEMON_ASSERT(false, "Elevator is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// Elevator type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting Elevator
+    /// type. If this named parameter is used, then an external
+    /// elevator object must be passed to the algorithm using the
+    /// \ref elevator(Elevator&) "elevator()" function before calling
+    /// \ref run() or \ref init().
+    /// \sa SetStandardElevator
+    template <typename T>
+    struct SetElevator
+      : public Preflow<Digraph, CapacityMap, SetElevatorTraits<T> > {
+      typedef Preflow<Digraph, CapacityMap,
+                      SetElevatorTraits<T> > Create;
+    };
+
+    template <typename T>
+    struct SetStandardElevatorTraits : public Traits {
+      typedef T Elevator;
+      static Elevator *createElevator(const Digraph& digraph, int max_level) {
+        return new Elevator(digraph, max_level);
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// Elevator type with automatic allocation
+    ///
+    /// \ref named-templ-param "Named parameter" for setting Elevator
+    /// type with automatic allocation.
+    /// The Elevator should have standard constructor interface to be
+    /// able to automatically created by the algorithm (i.e. the
+    /// digraph and the maximum level should be passed to it).
+    /// However an external elevator object could also be passed to the
+    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
+    /// before calling \ref run() or \ref init().
+    /// \sa SetElevator
+    template <typename T>
+    struct SetStandardElevator
+      : public Preflow<Digraph, CapacityMap,
+                       SetStandardElevatorTraits<T> > {
+      typedef Preflow<Digraph, CapacityMap,
+                      SetStandardElevatorTraits<T> > Create;
+    };
+
+    /// @}
+
+  protected:
+
+    Preflow() {}
+
+  public:
+
+
+    /// \brief The constructor of the class.
+    ///
+    /// The constructor of the class.
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param capacity The capacity of the arcs.
+    /// \param source The source node.
+    /// \param target The target node.
+    Preflow(const Digraph& digraph, const CapacityMap& capacity,
+            Node source, Node target)
+      : _graph(digraph), _capacity(&capacity),
+        _node_num(0), _source(source), _target(target),
+        _flow(0), _local_flow(false),
+        _level(0), _local_level(false),
+        _excess(0), _tolerance(), _phase() {}
+
+    /// \brief Destructor.
+    ///
+    /// Destructor.
+    ~Preflow() {
+      destroyStructures();
+    }
+
+    /// \brief Sets the capacity map.
+    ///
+    /// Sets the capacity map.
+    /// \return <tt>(*this)</tt>
+    Preflow& capacityMap(const CapacityMap& map) {
+      _capacity = &map;
+      return *this;
+    }
+
+    /// \brief Sets the flow map.
+    ///
+    /// Sets the flow map.
+    /// If you don't use this function before calling \ref run() or
+    /// \ref init(), an instance will be allocated automatically.
+    /// The destructor deallocates this automatically allocated map,
+    /// of course.
+    /// \return <tt>(*this)</tt>
+    Preflow& flowMap(FlowMap& map) {
+      if (_local_flow) {
+        delete _flow;
+        _local_flow = false;
+      }
+      _flow = &map;
+      return *this;
+    }
+
+    /// \brief Sets the source node.
+    ///
+    /// Sets the source node.
+    /// \return <tt>(*this)</tt>
+    Preflow& source(const Node& node) {
+      _source = node;
+      return *this;
+    }
+
+    /// \brief Sets the target node.
+    ///
+    /// Sets the target node.
+    /// \return <tt>(*this)</tt>
+    Preflow& target(const Node& node) {
+      _target = node;
+      return *this;
+    }
+
+    /// \brief Sets the elevator used by algorithm.
+    ///
+    /// Sets the elevator used by algorithm.
+    /// If you don't use this function before calling \ref run() or
+    /// \ref init(), an instance will be allocated automatically.
+    /// The destructor deallocates this automatically allocated elevator,
+    /// of course.
+    /// \return <tt>(*this)</tt>
+    Preflow& elevator(Elevator& elevator) {
+      if (_local_level) {
+        delete _level;
+        _local_level = false;
+      }
+      _level = &elevator;
+      return *this;
+    }
+
+    /// \brief Returns a const reference to the elevator.
+    ///
+    /// Returns a const reference to the elevator.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    const Elevator& elevator() const {
+      return *_level;
+    }
+
+    /// \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 a const reference to the tolerance.
+    ///
+    /// Returns a const reference to the tolerance.
+    const Tolerance& tolerance() const {
+      return tolerance;
+    }
+
+    /// \name Execution Control
+    /// The simplest way to execute the preflow algorithm is to use
+    /// \ref run() or \ref runMinCut().\n
+    /// If you need more control on the initial solution or the execution,
+    /// first you have to call one of the \ref init() functions, then
+    /// \ref startFirstPhase() and if you need it \ref startSecondPhase().
+
+    ///@{
+
+    /// \brief Initializes the internal data structures.
+    ///
+    /// Initializes the internal data structures and sets the initial
+    /// flow to zero on each arc.
+    void init() {
+      createStructures();
+
+      _phase = true;
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        (*_excess)[n] = 0;
+      }
+
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        _flow->set(e, 0);
+      }
+
+      typename Digraph::template NodeMap<bool> reached(_graph, false);
+
+      _level->initStart();
+      _level->initAddItem(_target);
+
+      std::vector<Node> queue;
+      reached[_source] = true;
+
+      queue.push_back(_target);
+      reached[_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 (InArcIt e(_graph, n); e != INVALID; ++e) {
+            Node u = _graph.source(e);
+            if (!reached[u] && _tolerance.positive((*_capacity)[e])) {
+              reached[u] = true;
+              _level->initAddItem(u);
+              nqueue.push_back(u);
+            }
+          }
+        }
+        queue.swap(nqueue);
+      }
+      _level->initFinish();
+
+      for (OutArcIt 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)[u] += (*_capacity)[e];
+          if (u != _target && !_level->active(u)) {
+            _level->activate(u);
+          }
+        }
+      }
+    }
+
+    /// \brief Initializes the internal data structures using the
+    /// given flow map.
+    ///
+    /// 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, i.e. at each node excluding the
+    /// source node the incoming flow should greater or equal to the
+    /// outgoing flow.
+    /// \return \c false if the given \c flowMap is not a preflow.
+    template <typename FlowMap>
+    bool init(const FlowMap& flowMap) {
+      createStructures();
+
+      for (ArcIt e(_graph); e != INVALID; ++e) {
+        _flow->set(e, flowMap[e]);
+      }
+
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        Value excess = 0;
+        for (InArcIt e(_graph, n); e != INVALID; ++e) {
+          excess += (*_flow)[e];
+        }
+        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+          excess -= (*_flow)[e];
+        }
+        if (excess < 0 && n != _source) return false;
+        (*_excess)[n] = excess;
+      }
+
+      typename Digraph::template NodeMap<bool> reached(_graph, false);
+
+      _level->initStart();
+      _level->initAddItem(_target);
+
+      std::vector<Node> queue;
+      reached[_source] = true;
+
+      queue.push_back(_target);
+      reached[_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 (InArcIt e(_graph, n); e != INVALID; ++e) {
+            Node u = _graph.source(e);
+            if (!reached[u] &&
+                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
+              reached[u] = true;
+              _level->initAddItem(u);
+              nqueue.push_back(u);
+            }
+          }
+          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
+            Node v = _graph.target(e);
+            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
+              reached[v] = true;
+              _level->initAddItem(v);
+              nqueue.push_back(v);
+            }
+          }
+        }
+        queue.swap(nqueue);
+      }
+      _level->initFinish();
+
+      for (OutArcIt 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)[u] += rem;
+          if (u != _target && !_level->active(u)) {
+            _level->activate(u);
+          }
+        }
+      }
+      for (InArcIt 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)[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 must be called before
+    /// using this function.
+    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 (OutArcIt 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)[v] += excess;
+                excess = 0;
+                goto no_more_push_1;
+              } else {
+                excess -= rem;
+                (*_excess)[v] += rem;
+                _flow->set(e, (*_capacity)[e]);
+              }
+            } else if (new_level > (*_level)[v]) {
+              new_level = (*_level)[v];
+            }
+          }
+
+          for (InArcIt 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)[v] += excess;
+                excess = 0;
+                goto no_more_push_1;
+              } else {
+                excess -= rem;
+                (*_excess)[v] += rem;
+                _flow->set(e, 0);
+              }
+            } else if (new_level > (*_level)[v]) {
+              new_level = (*_level)[v];
+            }
+          }
+
+        no_more_push_1:
+
+          (*_excess)[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 (OutArcIt 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)[v] += excess;
+                excess = 0;
+                goto no_more_push_2;
+              } else {
+                excess -= rem;
+                (*_excess)[v] += rem;
+                _flow->set(e, (*_capacity)[e]);
+              }
+            } else if (new_level > (*_level)[v]) {
+              new_level = (*_level)[v];
+            }
+          }
+
+          for (InArcIt 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)[v] += excess;
+                excess = 0;
+                goto no_more_push_2;
+              } else {
+                excess -= rem;
+                (*_excess)[v] += rem;
+                _flow->set(e, 0);
+              }
+            } else if (new_level > (*_level)[v]) {
+              new_level = (*_level)[v];
+            }
+          }
+
+        no_more_push_2:
+
+          (*_excess)[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 one of the \ref init() functions
+    /// and \ref startFirstPhase() and then \ref startSecondPhase(),
+    /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the
+    /// value of a maximum flow, \ref minCut() returns a minimum cut
+    /// \pre One of the \ref init() functions and \ref startFirstPhase()
+    /// must be called before using this function.
+    void startSecondPhase() {
+      _phase = false;
+
+      typename Digraph::template NodeMap<bool> reached(_graph);
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        reached[n] = (*_level)[n] < _level->maxLevel();
+      }
+
+      _level->initStart();
+      _level->initAddItem(_source);
+
+      std::vector<Node> queue;
+      queue.push_back(_source);
+      reached[_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 (OutArcIt e(_graph, n); e != INVALID; ++e) {
+            Node v = _graph.target(e);
+            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
+              reached[v] = true;
+              _level->initAddItem(v);
+              nqueue.push_back(v);
+            }
+          }
+          for (InArcIt e(_graph, n); e != INVALID; ++e) {
+            Node u = _graph.source(e);
+            if (!reached[u] &&
+                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
+              reached[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->dirtyTopButOne(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 (OutArcIt 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)[v] += excess;
+              excess = 0;
+              goto no_more_push;
+            } else {
+              excess -= rem;
+              (*_excess)[v] += rem;
+              _flow->set(e, (*_capacity)[e]);
+            }
+          } else if (new_level > (*_level)[v]) {
+            new_level = (*_level)[v];
+          }
+        }
+
+        for (InArcIt 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)[v] += excess;
+              excess = 0;
+              goto no_more_push;
+            } else {
+              excess -= rem;
+              (*_excess)[v] += rem;
+              _flow->set(e, 0);
+            }
+          } else if (new_level > (*_level)[v]) {
+            new_level = (*_level)[v];
+          }
+        }
+
+      no_more_push:
+
+        (*_excess)[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 results of the preflow algorithm can be obtained using these
+    /// functions.\n
+    /// Either one of the \ref run() "run*()" functions or one of the
+    /// \ref startFirstPhase() "start*()" functions should be called
+    /// before using them.
+
+    ///@{
+
+    /// \brief Returns the value of the maximum flow.
+    ///
+    /// Returns the value of the maximum flow by returning the excess
+    /// of the target node. This value equals to the value of
+    /// the maximum flow already after the first phase of the algorithm.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    Value flowValue() const {
+      return (*_excess)[_target];
+    }
+
+    /// \brief Returns the flow value on the given arc.
+    ///
+    /// Returns the flow value on the given arc. This method can
+    /// be called after the second phase of the algorithm.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    Value flow(const Arc& arc) const {
+      return (*_flow)[arc];
+    }
+
+    /// \brief Returns a const reference to the flow map.
+    ///
+    /// Returns a const reference to the arc map storing the found flow.
+    /// This method can be called after the second phase of the algorithm.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    const FlowMap& flowMap() const {
+      return *_flow;
+    }
+
+    /// \brief Returns \c true when the node is on the source side of the
+    /// minimum cut.
+    ///
+    /// Returns true when the node is on the source side of the found
+    /// minimum cut. This method can be called both after running \ref
+    /// startFirstPhase() and \ref startSecondPhase().
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    bool minCut(const Node& node) const {
+      return ((*_level)[node] == _level->maxLevel()) == _phase;
+    }
+
+    /// \brief Gives back a minimum value cut.
+    ///
+    /// Sets \c cutMap to the characteristic vector of a minimum value
+    /// cut. \c cutMap should be a \ref concepts::WriteMap "writable"
+    /// node map with \c bool (or convertible) value type.
+    ///
+    /// This method can be called both after running \ref startFirstPhase()
+    /// and \ref startSecondPhase(). The result after the second phase
+    /// could be slightly different if inexact computation is used.
+    ///
+    /// \note This function calls \ref minCut() for each node, so it runs in
+    /// O(n) time.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    template <typename CutMap>
+    void minCutMap(CutMap& cutMap) const {
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        cutMap.set(n, minCut(n));
+      }
+    }
+
+    /// @}
+  };
+}
+
+#endif