Ticket #174: fa7562ef5f8e.patch

lemon/Makefile.am

@@ -27 +27 @@
         lemon/dfs.h \
         lemon/dijkstra.h \
         lemon/dim2.h \
+        lemon/elevator.h \
         lemon/error.h \
         lemon/full_graph.h \
         lemon/graph_to_eps.h \

new file lemon/elevator.h

@@ +1 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * 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_ELEVATOR_H
+#define LEMON_ELEVATOR_H
+
+///\ingroup auxdat
+///\file
+///\brief Elevator class
+///
+///Elevator class implements an efficient data structure
+///for labeling items in push-relabel type algorithms.
+///
+
+#include <test/test_tools.h>
+namespace lemon {
+
+  ///Class for handling "labels" in push-relabel type algorithms.
+
+  ///A class for handling "labels" in push-relabel type algorithms.
+  ///
+  ///\ingroup auxdat
+  ///Using this class you can assign "labels" (nonnegative integer numbers)
+  ///to the edges or nodes of a graph, manipulate and query them through
+  ///operations typically arising in "push-relabel" type algorithms.
+  ///
+  ///Each item is either \em active or not, and you can also choose a
+  ///highest level active item.
+  ///
+  ///\sa LinkedElevator
+  ///
+  ///\param Graph the underlying graph type
+  ///\param Item Type of the items the data is assigned to (Graph::Node,
+  ///Graph::Edge, Graph::UEdge)
+  template<class Graph, class Item>
+  class Elevator
+  {
+  public:
+
+    typedef Item Key;
+    typedef int Value;
+
+  private:
+
+    typedef typename std::vector<Item>::iterator Vit;
+    typedef typename ItemSetTraits<Graph,Item>::template Map<Vit>::Type VitMap;
+    typedef typename ItemSetTraits<Graph,Item>::template Map<int>::Type IntMap;
+
+    const Graph &_g;
+    int _max_level;
+    int _item_num;
+    VitMap _where;
+    IntMap _level;
+    std::vector<Item> _items;
+    std::vector<Vit> _first;
+    std::vector<Vit> _last_active;
+
+    int _highest_active;
+
+    void copy(Item i, Vit p)
+    {
+      _where[*p=i]=p;
+    }
+    void copy(Vit s, Vit p)
+    {
+      if(s!=p)
+        {
+          Item i=*s;
+          *p=i;
+          _where[i]=p;
+        }
+    }
+    void swap(Vit i, Vit j)
+    {
+      Item ti=*i;
+      Vit ct = _where[ti];
+      _where[ti]=_where[*i=*j];
+      _where[*j]=ct;
+      *j=ti;
+    }
+
+  public:
+
+    ///Constructor with given maximum level.
+
+    ///Constructor with given maximum level.
+    ///
+    ///\param g The underlying graph
+    ///\param max_level Set the range of the possible labels to
+    ///[0...\c max_level]
+    Elevator(const Graph &g,int max_level) :
+      _g(g),
+      _max_level(max_level),
+      _item_num(_max_level),
+      _where(g),
+      _level(g,0),
+      _items(_max_level),
+      _first(_max_level+2),
+      _last_active(_max_level+2),
+      _highest_active(-1) {}
+    ///Constructor.
+
+    ///Constructor.
+    ///
+    ///\param g The underlying graph
+    ///The range of the possible labels is [0...\c max_level],
+    ///where \c max_level is equal to the number of labeled items in the graph.
+    Elevator(const Graph &g) :
+      _g(g),
+      _max_level(countItems<Graph, Item>(g)),
+      _item_num(_max_level),
+      _where(g),
+      _level(g,0),
+      _items(_max_level),
+      _first(_max_level+2),
+      _last_active(_max_level+2),
+      _highest_active(-1)
+    {
+    }
+
+    ///Activate item \c i.
+
+    ///Activate item \c i.
+    ///\pre Item \c i shouldn't be active before.
+    void activate(Item i)
+    {
+      const int l=_level[i];
+      swap(_where[i],++_last_active[l]);
+      if(l>_highest_active) _highest_active=l;
+    }
+
+    ///Deactivate item \c i.
+
+    ///Deactivate item \c i.
+    ///\pre Item \c i must be active before.
+    void deactivate(Item i)
+    {
+      swap(_where[i],_last_active[_level[i]]--);
+      while(_highest_active>=0 &&
+            _last_active[_highest_active]<_first[_highest_active])
+        _highest_active--;
+    }
+
+    ///Query whether item \c i is active
+    bool active(Item i) const { return _where[i]<=_last_active[_level[i]]; }
+
+    ///Return the level of item \c i.
+    int operator[](Item i) const { return _level[i]; }
+
+    ///Return the number of items on level \c l.
+    int onLevel(int l) const
+    {
+      return _first[l+1]-_first[l];
+    }
+    ///Return true if the level is empty.
+    bool emptyLevel(int l) const
+    {
+      return _first[l+1]-_first[l]==0;
+    }
+    ///Return the number of items above level \c l.
+    int aboveLevel(int l) const
+    {
+      return _first[_max_level+1]-_first[l+1];
+    }
+    ///Return the number of active items on level \c l.
+    int activesOnLevel(int l) const
+    {
+      return _last_active[l]-_first[l]+1;
+    }
+    ///Return true if there is not active item on level \c l.
+    bool activeFree(int l) const
+    {
+      return _last_active[l]<_first[l];
+    }
+    ///Return the maximum allowed level.
+    int maxLevel() const
+    {
+      return _max_level;
+    }
+
+    ///\name Highest Active Item
+    ///Functions for working with the highest level
+    ///active item.
+
+    ///@{
+
+    ///Return a highest level active item.
+
+    ///Return a highest level active item.
+    ///
+    ///\return the highest level active item or INVALID if there is no active
+    ///item.
+    Item highestActive() const
+    {
+      return _highest_active>=0?*_last_active[_highest_active]:INVALID;
+    }
+
+    ///Return a highest active level.
+
+    ///Return a highest active level.
+    ///
+    ///\return the level of the highest active item or -1 if there is no active
+    ///item.
+    int highestActiveLevel() const
+    {
+      return _highest_active;
+    }
+
+    ///Lift the highest active item by one.
+
+    ///Lift the item returned by highestActive() by one.
+    ///
+    void liftHighestActive()
+    {
+      ++_level[*_last_active[_highest_active]];
+      swap(_last_active[_highest_active]--,_last_active[_highest_active+1]);
+      --_first[++_highest_active];
+    }
+
+    ///Lift the highest active item.
+
+    ///Lift the item returned by highestActive() to level \c new_level.
+    ///
+    ///\warning \c new_level must be strictly higher
+    ///than the current level.
+    ///
+    void liftHighestActive(int new_level)
+    {
+      const Item li = *_last_active[_highest_active];
+
+      copy(--_first[_highest_active+1],_last_active[_highest_active]--);
+      for(int l=_highest_active+1;l<new_level;l++)
+        {
+          copy(--_first[l+1],_first[l]);
+          --_last_active[l];
+        }
+      copy(li,_first[new_level]);
+      _level[li]=new_level;
+      _highest_active=new_level;
+    }
+
+    ///Lift the highest active item.
+
+    ///Lift the item returned by highestActive() to the top level and
+    ///deactivates it.
+    ///
+    ///\warning \c new_level must be strictly higher
+    ///than the current level.
+    ///
+    void liftHighestActiveToTop()
+    {
+      const Item li = *_last_active[_highest_active];
+
+      copy(--_first[_highest_active+1],_last_active[_highest_active]--);
+      for(int l=_highest_active+1;l<_max_level;l++)
+        {
+          copy(--_first[l+1],_first[l]);
+          --_last_active[l];
+        }
+      copy(li,_first[_max_level]);
+      --_last_active[_max_level];
+      _level[li]=_max_level;
+
+      while(_highest_active>=0 &&
+            _last_active[_highest_active]<_first[_highest_active])
+        _highest_active--;
+    }
+
+    ///@}
+
+    ///\name Active Item on Certain Level
+    ///Functions for working with the active items.
+
+    ///@{
+
+    ///Returns an active item on level \c l.
+
+    ///Returns an active item on level \c l.
+    ///
+    ///Returns an active item on level \c l or \ref INVALID if there is no such
+    ///an item. (\c l must be from the range [0...\c max_level].
+    Item activeOn(int l) const
+    {
+      return _last_active[l]>=_first[l]?*_last_active[l]:INVALID;
+    }
+
+    ///Lifts the active item returned by \c activeOn() member function.
+
+    ///Lifts the active item returned by \c activeOn() member function
+    ///by one.
+    Item liftActiveOn(int level)
+    {
+      ++_level[*_last_active[level]];
+      swap(_last_active[level]--, --_first[level+1]);
+      if (level+1>_highest_active) ++_highest_active;
+    }
+
+    ///Lifts the active item returned by \c activeOn() member function.
+
+    ///Lifts the active item returned by \c activeOn() member function
+    ///to the given level.
+    void liftActiveOn(int level, int new_level)
+    {
+      const Item ai = *_last_active[level];
+
+      copy(--_first[level+1], _last_active[level]--);
+      for(int l=level+1;l<new_level;l++)
+        {
+          copy(_last_active[l],_first[l]);
+          copy(--_first[l+1], _last_active[l]--);
+        }
+      copy(ai,_first[new_level]);
+      _level[ai]=new_level;
+      if (new_level>_highest_active) _highest_active=new_level;
+    }
+
+    ///Lifts the active item returned by \c activeOn() member function.
+
+    ///Lifts the active item returned by \c activeOn() member function
+    ///to the top level.
+    void liftActiveToTop(int level)
+    {
+      const Item ai = *_last_active[level];
+
+      copy(--_first[level+1],_last_active[level]--);
+      for(int l=level+1;l<_max_level;l++)
+        {
+          copy(_last_active[l],_first[l]);
+          copy(--_first[l+1], _last_active[l]--);
+        }
+      copy(ai,_first[_max_level]);
+      --_last_active[_max_level];
+      _level[ai]=_max_level;
+
+      if (_highest_active==level) {
+        while(_highest_active>=0 &&
+              _last_active[_highest_active]<_first[_highest_active])
+          _highest_active--;
+      }
+    }
+
+    ///@}
+
+    ///Lift an active item to a higher level.
+
+    ///Lift an active item to a higher level.
+    ///\param i The item to be lifted. It must be active.
+    ///\param new_level The new level of \c i. It must be strictly higher
+    ///than the current level.
+    ///
+    void lift(Item i, int new_level)
+    {
+      const int lo = _level[i];
+      const Vit w = _where[i];
+
+      copy(_last_active[lo],w);
+      copy(--_first[lo+1],_last_active[lo]--);
+      for(int l=lo+1;l<new_level;l++)
+        {
+          copy(_last_active[l],_first[l]);
+          copy(--_first[l+1],_last_active[l]--);
+        }
+      copy(i,_first[new_level]);
+      _level[i]=new_level;
+      if(new_level>_highest_active) _highest_active=new_level;
+    }
+
+    ///Mark the node as it did not reach the max level
+
+    ///Mark the node as it did not reach the max level. It sets the
+    ///level to the under the max level value. The node will be never
+    ///more activated because the push operation from the maximum
+    ///level is forbidden in the push-relabel algorithms. The node
+    ///should be lifted previously to the top level.
+    void markToBottom(Item i) {
+      _level[i] = _max_level - 1;
+    }
+
+    ///Lift all nodes on and above a level to the top (and deactivate them).
+
+    ///This function lifts all nodes on and above level \c l to \c
+    ///maxLevel(), and also deactivates them.
+    void liftToTop(int l)
+    {
+      const Vit f=_first[l];
+      const Vit tl=_first[_max_level];
+      for(Vit i=f;i!=tl;++i)
+        _level[*i]=_max_level;
+      for(int i=l;i<=_max_level;i++)
+        {
+          _first[i]=f;
+          _last_active[i]=f-1;
+        }
+      for(_highest_active=l-1;
+          _highest_active>=0 &&
+            _last_active[_highest_active]<_first[_highest_active];
+          _highest_active--) ;
+    }
+
+  private:
+    int _init_lev;
+    Vit _init_num;
+
+  public:
+
+    ///\name Initialization
+    ///Using this function you can initialize the levels of the item.
+    ///\n
+    ///This initializatios is started with calling \c initStart().
+    ///Then the
+    ///items should be listed levels by levels statring with the lowest one
+    ///(with level 0). This is done by using \c initAddItem()
+    ///and \c initNewLevel(). Finally \c initFinish() must be called.
+    ///The items not listed will be put on the highest level.
+    ///@{
+
+    ///Start the initialization process.
+
+    void initStart()
+    {
+      _init_lev=0;
+      _init_num=_items.begin();
+      _first[0]=_items.begin();
+      _last_active[0]=_items.begin()-1;
+      Vit n=_items.begin();
+      for(typename ItemSetTraits<Graph,Item>::ItemIt i(_g);i!=INVALID;++i)
+        {
+          *n=i;
+          _where[i]=n;
+          _level[i]=_max_level;
+          ++n;
+        }
+    }
+
+    ///Add an item to the current level.
+
+    void initAddItem(Item i)
+    {
+     swap(_where[i],_init_num);
+      _level[i]=_init_lev;
+      ++_init_num;
+    }
+
+    ///Start a new level.
+
+    ///Start a new level.
+    ///It shouldn't be used before the items on level 0 are listed.
+    void initNewLevel()
+    {
+      _init_lev++;
+      _first[_init_lev]=_init_num;
+      _last_active[_init_lev]=_init_num-1;
+    }
+
+    ///Finalize the initialization process.
+
+    void initFinish()
+    {
+      for(_init_lev++;_init_lev<=_max_level;_init_lev++)
+        {
+          _first[_init_lev]=_init_num;
+          _last_active[_init_lev]=_init_num-1;
+        }
+      _first[_max_level+1]=_items.begin()+_item_num;
+      _last_active[_max_level+1]=_items.begin()+_item_num-1;
+      _highest_active = -1;
+    }
+
+    ///@}
+
+  };
+
+  ///Class for handling "labels" in push-relabel type algorithms.
+
+  ///A class for handling "labels" in push-relabel type algorithms.
+  ///
+  ///\ingroup auxdat
+  ///Using this class you can assign "labels" (nonnegative integer numbers)
+  ///to the edges or nodes of a graph, manipulate and query them through
+  ///operations typically arising in "push-relabel" type algorithms.
+  ///
+  ///Each item is either \em active or not, and you can also choose a
+  ///highest level active item.
+  ///
+  ///\sa Elevator
+  ///
+  ///\param Graph the underlying graph type
+  ///\param Item Type of the items the data is assigned to (Graph::Node,
+  ///Graph::Edge, Graph::UEdge)
+  template <class Graph, class Item>
+  class LinkedElevator {
+  public:
+
+    typedef Item Key;
+    typedef int Value;
+
+  private:
+
+    typedef typename ItemSetTraits<Graph,Item>::
+    template Map<Item>::Type ItemMap;
+    typedef typename ItemSetTraits<Graph,Item>::
+    template Map<int>::Type IntMap;
+    typedef typename ItemSetTraits<Graph,Item>::
+    template Map<bool>::Type BoolMap;
+
+    const Graph &_graph;
+    int _max_level;
+    int _item_num;
+    std::vector<Item> _first, _last;
+    ItemMap _prev, _next;
+    int _highest_active;
+    IntMap _level;
+    BoolMap _active;
+
+  public:
+    ///Constructor with given maximum level.
+
+    ///Constructor with given maximum level.
+    ///
+    ///\param g The underlying graph
+    ///\param max_level Set the range of the possible labels to
+    ///[0...\c max_level]
+    LinkedElevator(const Graph& graph, int max_level)
+      : _graph(graph), _max_level(max_level), _item_num(_max_level),
+        _first(_max_level + 1), _last(_max_level + 1),
+        _prev(graph), _next(graph),
+        _highest_active(-1), _level(graph), _active(graph) {}
+
+    ///Constructor.
+
+    ///Constructor.
+    ///
+    ///\param g The underlying graph
+    ///The range of the possible labels is [0...\c max_level],
+    ///where \c max_level is equal to the number of labeled items in the graph.
+    LinkedElevator(const Graph& graph)
+      : _graph(graph), _max_level(countItems<Graph, Item>(graph)),
+        _item_num(_max_level),
+        _first(_max_level + 1), _last(_max_level + 1),
+        _prev(graph, INVALID), _next(graph, INVALID),
+        _highest_active(-1), _level(graph), _active(graph) {}
+
+
+    ///Activate item \c i.
+
+    ///Activate item \c i.
+    ///\pre Item \c i shouldn't be active before.
+    void activate(Item i) {
+      _active.set(i, true);
+
+      int level = _level[i];
+      if (level > _highest_active) {
+        _highest_active = level;
+      }
+
+      if (_prev[i] == INVALID || _active[_prev[i]]) return;
+      //unlace
+      _next.set(_prev[i], _next[i]);
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], _prev[i]);
+      } else {
+        _last[level] = _prev[i];
+      }
+      //lace
+      _next.set(i, _first[level]);
+      _prev.set(_first[level], i);
+      _prev.set(i, INVALID);
+      _first[level] = i;
+
+    }
+
+    ///Deactivate item \c i.
+
+    ///Deactivate item \c i.
+    ///\pre Item \c i must be active before.
+    void deactivate(Item i) {
+      _active.set(i, false);
+      int level = _level[i];
+
+      if (_next[i] == INVALID || !_active[_next[i]])
+        goto find_highest_level;
+
+      //unlace
+      _prev.set(_next[i], _prev[i]);
+      if (_prev[i] != INVALID) {
+        _next.set(_prev[i], _next[i]);
+      } else {
+        _first[_level[i]] = _next[i];
+      }
+      //lace
+      _prev.set(i, _last[level]);
+      _next.set(_last[level], i);
+      _next.set(i, INVALID);
+      _last[level] = i;
+
+    find_highest_level:
+      if (level == _highest_active) {
+        while (_highest_active >= 0 && activeFree(_highest_active))
+          --_highest_active;
+      }
+    }
+
+    ///Query whether item \c i is active
+    bool active(Item i) const { return _active[i]; }
+
+    ///Return the level of item \c i.
+    int operator[](Item i) const { return _level[i]; }
+
+    ///Return the number of items on level \c l.
+    int onLevel(int l) const {
+      int num = 0;
+      Item n = _first[l];
+      while (n != INVALID) {
+        ++num;
+        n = _next[n];
+      }
+      return num;
+    }
+
+    ///Return true if the level is empty.
+    bool emptyLevel(int l) const {
+      return _first[l] == INVALID;
+    }
+
+    ///Return the number of items above level \c l.
+    int aboveLevel(int l) const {
+      int num = 0;
+      for (int level = l + 1; level < _max_level; ++level)
+        num += onLevel(level);
+      return num;
+    }
+
+    ///Return the number of active items on level \c l.
+    int activesOnLevel(int l) const {
+      int num = 0;
+      Item n = _first[l];
+      while (n != INVALID && _active[n]) {
+        ++num;
+        n = _next[n];
+      }
+      return num;
+    }
+
+    ///Return true if there is not active item on level \c l.
+    bool activeFree(int l) const {
+      return _first[l] == INVALID || !_active[_first[l]];
+    }
+
+    ///Return the maximum allowed level.
+    int maxLevel() const {
+      return _max_level;
+    }
+
+    ///\name Highest Active Item
+    ///Functions for working with the highest level
+    ///active item.
+
+    ///@{
+
+    ///Return a highest level active item.
+
+    ///Return a highest level active item.
+    ///
+    ///\return the highest level active item or INVALID if there is no
+    ///active item.
+    Item highestActive() const {
+      return _highest_active >= 0 ? _first[_highest_active] : INVALID;
+    }
+
+    ///Return a highest active level.
+
+    ///Return a highest active level.
+    ///
+    ///\return the level of the highest active item or -1 if there is
+    ///no active item.
+    int highestActiveLevel() const {
+      return _highest_active;
+    }
+
+    ///Lift the highest active item by one.
+
+    ///Lift the item returned by highestActive() by one.
+    ///
+    void liftHighestActive() {
+      Item i = _first[_highest_active];
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], INVALID);
+        _first[_highest_active] = _next[i];
+      } else {
+        _first[_highest_active] = INVALID;
+        _last[_highest_active] = INVALID;
+      }
+      _level.set(i, ++_highest_active);
+      if (_first[_highest_active] == INVALID) {
+        _first[_highest_active] = i;
+        _last[_highest_active] = i;
+        _prev.set(i, INVALID);
+        _next.set(i, INVALID);
+      } else {
+        _prev.set(_first[_highest_active], i);
+        _next.set(i, _first[_highest_active]);
+        _first[_highest_active] = i;
+      }
+    }
+
+    ///Lift the highest active item.
+
+    ///Lift the item returned by highestActive() to level \c new_level.
+    ///
+    ///\warning \c new_level must be strictly higher
+    ///than the current level.
+    ///
+    void liftHighestActive(int new_level) {
+      Item i = _first[_highest_active];
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], INVALID);
+        _first[_highest_active] = _next[i];
+      } else {
+        _first[_highest_active] = INVALID;
+        _last[_highest_active] = INVALID;
+      }
+      _level.set(i, _highest_active = new_level);
+      if (_first[_highest_active] == INVALID) {
+        _first[_highest_active] = _last[_highest_active] = i;
+        _prev.set(i, INVALID);
+        _next.set(i, INVALID);
+      } else {
+        _prev.set(_first[_highest_active], i);
+        _next.set(i, _first[_highest_active]);
+        _first[_highest_active] = i;
+      }
+    }
+
+    ///Lift the highest active to top.
+
+    ///Lift the item returned by highestActive() to the top level and
+    ///deactivates the node.
+    ///
+    void liftHighestActiveToTop() {
+      Item i = _first[_highest_active];
+      _level.set(i, _max_level);
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], INVALID);
+        _first[_highest_active] = _next[i];
+      } else {
+        _first[_highest_active] = INVALID;
+        _last[_highest_active] = INVALID;
+      }
+      while (_highest_active >= 0 && activeFree(_highest_active))
+        --_highest_active;
+    }
+
+    ///@}
+
+    ///\name Active Item on Certain Level
+    ///Functions for working with the active items.
+
+    ///@{
+
+    ///Returns an active item on level \c l.
+
+    ///Returns an active item on level \c l.
+    ///
+    ///Returns an active item on level \c l or \ref INVALID if there is no such
+    ///an item. (\c l must be from the range [0...\c max_level].
+    Item activeOn(int l) const
+    {
+      return _active[_first[l]] ? _first[l] : INVALID;
+    }
+
+    ///Lifts the active item returned by \c activeOn() member function.
+
+    ///Lifts the active item returned by \c activeOn() member function
+    ///by one.
+    Item liftActiveOn(int l)
+    {
+      Item i = _first[l];
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], INVALID);
+        _first[l] = _next[i];
+      } else {
+        _first[l] = INVALID;
+        _last[l] = INVALID;
+      }
+      _level.set(i, ++l);
+      if (_first[l] == INVALID) {
+        _first[l] = _last[l] = i;
+        _prev.set(i, INVALID);
+        _next.set(i, INVALID);
+      } else {
+        _prev.set(_first[l], i);
+        _next.set(i, _first[l]);
+        _first[l] = i;
+      }
+      if (_highest_active < l) {
+        _highest_active = l;
+      }
+    }
+
+    /// \brief Lifts the active item returned by \c activeOn() member function.
+    ///
+    /// Lifts the active item returned by \c activeOn() member function
+    /// to the given level.
+    void liftActiveOn(int l, int new_level)
+    {
+      Item i = _first[l];
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], INVALID);
+        _first[l] = _next[i];
+      } else {
+        _first[l] = INVALID;
+        _last[l] = INVALID;
+      }
+      _level.set(i, l = new_level);
+      if (_first[l] == INVALID) {
+        _first[l] = _last[l] = i;
+        _prev.set(i, INVALID);
+        _next.set(i, INVALID);
+      } else {
+        _prev.set(_first[l], i);
+        _next.set(i, _first[l]);
+        _first[l] = i;
+      }
+      if (_highest_active < l) {
+        _highest_active = l;
+      }
+    }
+
+    ///Lifts the active item returned by \c activeOn() member function.
+
+    ///Lifts the active item returned by \c activeOn() member function
+    ///to the top level.
+    void liftActiveToTop(int l)
+    {
+      Item i = _first[l];
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], INVALID);
+        _first[l] = _next[i];
+      } else {
+        _first[l] = INVALID;
+        _last[l] = INVALID;
+      }
+      _level.set(i, _max_level);
+      if (l == _highest_active) {
+        while (_highest_active >= 0 && activeFree(_highest_active))
+          --_highest_active;
+      }
+    }
+
+    ///@}
+
+    /// \brief Lift an active item to a higher level.
+    ///
+    /// Lift an active item to a higher level.
+    /// \param i The item to be lifted. It must be active.
+    /// \param new_level The new level of \c i. It must be strictly higher
+    /// than the current level.
+    ///
+    void lift(Item i, int new_level) {
+      if (_next[i] != INVALID) {
+        _prev.set(_next[i], _prev[i]);
+      } else {
+        _last[new_level] = _prev[i];
+      }
+      if (_prev[i] != INVALID) {
+        _next.set(_prev[i], _next[i]);
+      } else {
+        _first[new_level] = _next[i];
+      }
+      _level.set(i, new_level);
+      if (_first[new_level] == INVALID) {
+        _first[new_level] = _last[new_level] = i;
+        _prev.set(i, INVALID);
+        _next.set(i, INVALID);
+      } else {
+        _prev.set(_first[new_level], i);
+        _next.set(i, _first[new_level]);
+        _first[new_level] = i;
+      }
+      if (_highest_active < new_level) {
+        _highest_active = new_level;
+      }
+    }
+
+    ///Mark the node as it did not reach the max level
+
+    ///Mark the node as it did not reach the max level. It sets the
+    ///level to the under the max level value. The node will be never
+    ///more activated because the push operation from the maximum
+    ///level is forbidden in the push-relabel algorithms. The node
+    ///should be lifted previously to the top level.
+    void markToBottom(Item i) {
+      _level.set(i, _max_level - 1);
+    }
+
+    ///Lift all nodes on and above a level to the top (and deactivate them).
+
+    ///This function lifts all nodes on and above level \c l to \c
+    ///maxLevel(), and also deactivates them.
+    void liftToTop(int l)  {
+      for (int i = l + 1; _first[i] != INVALID; ++i) {
+        Item n = _first[i];
+        while (n != INVALID) {
+          _level.set(n, _max_level);
+          n = _next[n];
+        }
+        _first[i] = INVALID;
+        _last[i] = INVALID;
+      }
+      if (_highest_active > l - 1) {
+        _highest_active = l - 1;
+        while (_highest_active >= 0 && activeFree(_highest_active))
+          --_highest_active;
+      }
+    }
+
+  private:
+
+    int _init_level;
+
+  public:
+
+    ///\name Initialization
+    ///Using this function you can initialize the levels of the item.
+    ///\n
+    ///This initializatios is started with calling \c initStart().
+    ///Then the
+    ///items should be listed levels by levels statring with the lowest one
+    ///(with level 0). This is done by using \c initAddItem()
+    ///and \c initNewLevel(). Finally \c initFinish() must be called.
+    ///The items not listed will be put on the highest level.
+    ///@{
+
+    ///Start the initialization process.
+
+    void initStart() {
+
+      for (int i = 0; i <= _max_level; ++i) {
+        _first[i] = _last[i] = INVALID;
+      }
+      _init_level = 0;
+      for(typename ItemSetTraits<Graph,Item>::ItemIt i(_graph);
+          i != INVALID; ++i) {
+        _level.set(i, _max_level);
+        _active.set(i, false);
+      }
+    }
+
+    ///Add an item to the current level.
+
+    void initAddItem(Item i) {
+      _level.set(i, _init_level);
+      if (_last[_init_level] == INVALID) {
+        _first[_init_level] = i;
+        _last[_init_level] = i;
+        _prev.set(i, INVALID);
+        _next.set(i, INVALID);
+      } else {
+        _prev.set(i, _last[_init_level]);
+        _next.set(i, INVALID);
+        _next.set(_last[_init_level], i);
+        _last[_init_level] = i;
+      }
+    }
+
+    ///Start a new level.
+
+    ///Start a new level.
+    ///It shouldn't be used before the items on level 0 are listed.
+    void initNewLevel() {
+      ++_init_level;
+    }
+
+    ///Finalize the initialization process.
+
+    void initFinish() {
+      _highest_active = -1;
+    }
+
+    ///@}
+
+  };
+
+
+} //END OF NAMESPACE LEMON
+
+#endif
+