/* -*- 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_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[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);

       }

     }

     ///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