/* -*- C++ -*-

 *

 * 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;

    }