RhodeCode

EXTRA_DIST += \

	lemon/lemon.pc.in \

	lemon/CMakeLists.txt \

	lemon/config.h.cmake

pkgconfig_DATA += lemon/lemon.pc

lib_LTLIBRARIES += lemon/libemon.la

lemon_libemon_la_SOURCES = \

	lemon/arg_parser.cc \

	lemon/base.cc \

	lemon/color.cc \

	lemon/lp_base.cc \

	lemon/lp_skeleton.cc \

	lemon/random.cc \

	lemon/bits/windows.cc

nodist_lemon_HEADERS = lemon/config.h	

lemon_libemon_la_CXXFLAGS = \

	$(AM_CXXFLAGS) \

	$(GLPK_CFLAGS) \

	$(CPLEX_CFLAGS) \

	$(SOPLEX_CXXFLAGS) \

	$(CLP_CXXFLAGS) \

	$(CBC_CXXFLAGS)

lemon_libemon_la_LDFLAGS = \

	$(GLPK_LIBS) \

	$(CPLEX_LIBS) \

	$(SOPLEX_LIBS) \

	$(CLP_LIBS) \

	$(CBC_LIBS)

if HAVE_GLPK

lemon_libemon_la_SOURCES += lemon/glpk.cc

endif

if HAVE_CPLEX

lemon_libemon_la_SOURCES += lemon/cplex.cc

endif

if HAVE_SOPLEX

lemon_libemon_la_SOURCES += lemon/soplex.cc

endif

if HAVE_CLP

lemon_libemon_la_SOURCES += lemon/clp.cc

endif

if HAVE_CBC

lemon_libemon_la_SOURCES += lemon/cbc.cc

endif

lemon_HEADERS += \

	lemon/adaptors.h \

	lemon/arg_parser.h \

	lemon/assert.h \

	lemon/bellman_ford.h \

	lemon/bfs.h \

	lemon/bin_heap.h \

	lemon/bucket_heap.h \

	lemon/cbc.h \

	lemon/circulation.h \

	lemon/clp.h \

	lemon/color.h \

	lemon/concept_check.h \

	lemon/connectivity.h \

	lemon/counter.h \

	lemon/core.h \

	lemon/cplex.h \

	lemon/dfs.h \

	lemon/dijkstra.h \

	lemon/dim2.h \

	lemon/dimacs.h \

	lemon/edge_set.h \

	lemon/elevator.h \

	lemon/error.h \

	lemon/euler.h \

	lemon/fib_heap.h \

	lemon/full_graph.h \

	lemon/glpk.h \

	lemon/gomory_hu.h \

	lemon/graph_to_eps.h \

	lemon/grid_graph.h \

	lemon/hypercube_graph.h \

	lemon/kruskal.h \

	lemon/hao_orlin.h \

	lemon/lgf_reader.h \

	lemon/lgf_writer.h \

	lemon/list_graph.h \

	lemon/lp.h \

	lemon/lp_base.h \

	lemon/lp_skeleton.h \

	lemon/maps.h \

	lemon/matching.h \

	lemon/math.h \

	lemon/min_cost_arborescence.h \

	lemon/nauty_reader.h \

	lemon/network_simplex.h \

	lemon/pairing_heap.h \

	lemon/path.h \

	lemon/preflow.h \

	lemon/radix_heap.h \

	lemon/radix_sort.h \

	lemon/random.h \

	lemon/smart_graph.h \

	lemon/soplex.h \

	lemon/suurballe.h \

	lemon/time_measure.h \

	lemon/tolerance.h \

	lemon/unionfind.h \

	lemon/bits/windows.h

bits_HEADERS += \

	lemon/bits/alteration_notifier.h \

	lemon/bits/array_map.h \

	lemon/bits/bezier.h \

	lemon/bits/default_map.h \

	lemon/bits/edge_set_extender.h \

	lemon/bits/enable_if.h \

	lemon/bits/graph_adaptor_extender.h \

	lemon/bits/graph_extender.h \

	lemon/bits/map_extender.h \

	lemon/bits/path_dump.h \

	lemon/bits/solver_bits.h \

	lemon/bits/traits.h \

	lemon/bits/variant.h \

	lemon/bits/vector_map.h

concept_HEADERS += \

	lemon/concepts/digraph.h \

	lemon/concepts/graph.h \

	lemon/concepts/graph_components.h \

	lemon/concepts/heap.h \

	lemon/concepts/maps.h \

	lemon/concepts/path.h

/* -*- 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.

 *

 */

///\file

///\ingroup heaps

///\brief Binomial Heap implementation.

#include <vector>

#include <utility>

#include <functional>

#include <lemon/math.h>

#include <lemon/counter.h>

namespace lemon {

  /// \ingroup heaps

  ///

  ///\brief Binomial heap data structure.

  ///

  /// This class implements the \e binomial \e heap data structure.

  /// It fully conforms to the \ref concepts::Heap "heap concept".

  ///

  /// The methods \ref increase() and \ref erase() are not efficient

  /// in a binomial heap. In case of many calls of these operations,

  /// it is better to use other heap structure, e.g. \ref BinHeap

  /// "binary heap".

  ///

  /// \tparam PR Type of the priorities of the items.

  /// \tparam IM A read-writable item map with \c int values, used

  /// internally to handle the cross references.

  /// \tparam CMP A functor class for comparing the priorities.

  /// The default is \c std::less<PR>.

#ifdef DOXYGEN

  template <typename PR, typename IM, typename CMP>

#else

  template <typename PR, typename IM, typename CMP = std::less<PR> >

#endif

  public:

    /// Type of the item-int map.

    typedef IM ItemIntMap;

    /// Type of the priorities.

    typedef PR Prio;

    /// Type of the items stored in the heap.

    typedef typename ItemIntMap::Key Item;

    /// Functor type for comparing the priorities.

    typedef CMP Compare;

    /// \brief Type to represent the states of the items.

    ///

    /// Each item has a state associated to it. It can be "in heap",

    /// "pre-heap" or "post-heap". The latter two are indifferent from the

    /// heap's point of view, but may be useful to the user.

    ///

    /// The item-int map must be initialized in such way that it assigns

    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.

    enum State {

      IN_HEAP = 0,    ///< = 0.

      PRE_HEAP = -1,  ///< = -1.

      POST_HEAP = -2  ///< = -2.

    };

  private:

    class Store;

    std::vector<Store> _data;

    int _min, _head;

    ItemIntMap &_iim;

    Compare _comp;

    int _num_items;

  public:

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

      : _min(0), _head(-1), _iim(map), _num_items(0) {}

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    /// \param comp The function object used for comparing the priorities.

      : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {}

    /// \brief The number of items stored in the heap.

    ///

    /// This function returns the number of items stored in the heap.

    int size() const { return _num_items; }

    /// \brief Check if the heap is empty.

    ///

    /// This function returns \c true if the heap is empty.

    bool empty() const { return _num_items==0; }

    /// \brief Make the heap empty.

    ///

    /// This functon makes the heap empty.

    /// It does not change the cross reference map. If you want to reuse

    /// a heap that is not surely empty, you should first clear it and

    /// then you should set the cross reference map to \c PRE_HEAP

    /// for each item.

    void clear() {

      _data.clear(); _min=0; _num_items=0; _head=-1;

    }

    /// \brief Set the priority of an item or insert it, if it is

    /// not stored in the heap.

    ///

    /// This method sets the priority of the given item if it is

    /// already stored in the heap. Otherwise it inserts the given

    /// item into the heap with the given priority.

    /// \param item The item.

    /// \param value The priority.

    void set (const Item& item, const Prio& value) {

      int i=_iim[item];

      if ( i >= 0 && _data[i].in ) {

        if ( _comp(value, _data[i].prio) ) decrease(item, value);

        if ( _comp(_data[i].prio, value) ) increase(item, value);

      } else push(item, value);

    }

    /// \brief Insert an item into the heap with the given priority.

    ///

    /// This function inserts the given item into the heap with the

    /// given priority.

    /// \param item The item to insert.

    /// \param value The priority of the item.

    /// \pre \e item must not be stored in the heap.

    void push (const Item& item, const Prio& value) {

      int i=_iim[item];

      if ( i<0 ) {

        int s=_data.size();

        _iim.set( item,s );

        Store st;

        st.name=item;

        st.prio=value;

        _data.push_back(st);

        i=s;

      }

      else {

        _data[i].parent=_data[i].right_neighbor=_data[i].child=-1;

        _data[i].degree=0;

        _data[i].in=true;

        _data[i].prio=value;

      }

      if( 0==_num_items ) {

        _head=i;

        _min=i;

      } else {

        merge(i);

        if( _comp(_data[i].prio, _data[_min].prio) ) _min=i;

      }

      ++_num_items;

    }

    /// \brief Return the item having minimum priority.

    ///

    /// This function returns the item having minimum priority.

    /// \pre The heap must be non-empty.

    Item top() const { return _data[_min].name; }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

    /// \pre The heap must be non-empty.

    Prio prio() const { return _data[_min].prio; }

    /// \brief The priority of the given item.

    ///

    /// This function returns the priority of the given item.

    /// \param item The item.

    /// \pre \e item must be in the heap.

    const Prio& operator[](const Item& item) const {

      return _data[_iim[item]].prio;

    }

    /// \brief Remove the item having minimum priority.

             x=_data[x].right_neighbor ) {

          if( _comp( _data[x].prio,min_val ) ) {

            min_val=_data[x].prio;

            min_loc=x;

          }

        }

        return min_loc;

      }

      else return -1;

    }

    // Merge the heap with another heap starting at the given position

    void merge(int a) {

      if( _head==-1 || a==-1 ) return;

      if( _data[a].right_neighbor==-1 &&

          _data[a].degree<=_data[_head].degree ) {

        _data[a].right_neighbor=_head;

        _head=a;

      } else {

        interleave(a);

      }

      if( _data[_head].right_neighbor==-1 ) return;

      int x=_head;

      int x_prev=-1, x_next=_data[x].right_neighbor;

      while( x_next!=-1 ) {

        if( _data[x].degree!=_data[x_next].degree ||

            ( _data[x_next].right_neighbor!=-1 &&

              _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {

          x_prev=x;

          x=x_next;

        }

        else {

          if( _comp(_data[x_next].prio,_data[x].prio) ) {

            if( x_prev==-1 ) {

              _head=x_next;

            } else {

              _data[x_prev].right_neighbor=x_next;

            }

            fuse(x,x_next);

            x=x_next;

          }

          else {

            _data[x].right_neighbor=_data[x_next].right_neighbor;

            fuse(x_next,x);

          }

        }

        x_next=_data[x].right_neighbor;

      }

    }

    // Interleave the elements of the given list into the list of the roots

    void interleave(int a) {

      int p=_head, q=a;

      int curr=_data.size();

      _data.push_back(Store());

      while( p!=-1 || q!=-1 ) {

        if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) {

          _data[curr].right_neighbor=p;

          curr=p;

          p=_data[p].right_neighbor;

        }

        else {

          _data[curr].right_neighbor=q;

          curr=q;

          q=_data[q].right_neighbor;

        }

      }

      _head=_data.back().right_neighbor;

      _data.pop_back();

    }

    // Lace node a under node b

    void fuse(int a, int b) {

      _data[a].parent=b;

      _data[a].right_neighbor=_data[b].child;

      _data[b].child=a;

      ++_data[b].degree;

    }

    // Unlace node a (if it has siblings)

    void unlace(int a) {

      int neighb=_data[a].right_neighbor;

      int other=_head;

      while( _data[other].right_neighbor!=a )

        other=_data[other].right_neighbor;

      _data[other].right_neighbor=neighb;

    }

  private:

    class Store {

      Item name;

      int parent;

      int right_neighbor;

      int child;

      int degree;

      bool in;

      Prio prio;

      Store() : parent(-1), right_neighbor(-1), child(-1), degree(0),

        in(true) {}

    };

  };

} //namespace lemon

/* -*- 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.

 *

 */

///\ingroup heaps

///\file

#include <vector>

#include <utility>

#include <functional>

namespace lemon {

  /// \ingroup heaps

  ///

  ///

  /// It fully conforms to the \ref concepts::Heap "heap concept".

  ///

  /// \ref BinHeap "binary heap" structure, its nodes have at most

  ///

  /// \tparam PR Type of the priorities of the items.

  /// \tparam IM A read-writable item map with \c int values, used

  /// internally to handle the cross references.

  /// children. The default is 16. Powers of two are suggested to use

  /// so that the multiplications and divisions needed to traverse the

  /// nodes of the heap could be performed faster.

  /// \tparam CMP A functor class for comparing the priorities.

  /// The default is \c std::less<PR>.

  ///

  ///\sa BinHeap

  ///\sa FouraryHeap

#ifdef DOXYGEN

#else

            typename CMP = std::less<PR> >

#endif

  public:

    /// Type of the item-int map.

    typedef IM ItemIntMap;

    /// Type of the priorities.

    typedef PR Prio;

    /// Type of the items stored in the heap.

    typedef typename ItemIntMap::Key Item;

    /// Type of the item-priority pairs.

    typedef std::pair<Item,Prio> Pair;

    /// Functor type for comparing the priorities.

    typedef CMP Compare;

    /// \brief Type to represent the states of the items.

    ///

    /// Each item has a state associated to it. It can be "in heap",

    /// "pre-heap" or "post-heap". The latter two are indifferent from the

    /// heap's point of view, but may be useful to the user.

    ///

    /// The item-int map must be initialized in such way that it assigns

    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.

    enum State {

      IN_HEAP = 0,    ///< = 0.

      PRE_HEAP = -1,  ///< = -1.

      POST_HEAP = -2  ///< = -2.

    };

  private:

    std::vector<Pair> _data;

    Compare _comp;

    ItemIntMap &_iim;

  public:

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    /// \param comp The function object used for comparing the priorities.

      : _iim(map), _comp(comp) {}

    /// \brief The number of items stored in the heap.

    ///

    /// This function returns the number of items stored in the heap.

    int size() const { return _data.size(); }

    /// \brief Check if the heap is empty.

    ///

    /// This function returns \c true if the heap is empty.

    bool empty() const { return _data.empty(); }

    /// \brief Make the heap empty.

    ///

    /// This functon makes the heap empty.

    /// It does not change the cross reference map. If you want to reuse

    /// a heap that is not surely empty, you should first clear it and

    /// then you should set the cross reference map to \c PRE_HEAP

    /// for each item.

    void clear() { _data.clear(); }

  private:

    bool less(const Pair &p1, const Pair &p2) const {

      return _comp(p1.second, p2.second);

    }

    void bubbleUp(int hole, Pair p) {

      int par = parent(hole);

      while( hole>0 && less(p,_data[par]) ) {

        move(_data[par],hole);

        hole = par;

        par = parent(hole);

      }

      move(p, hole);

    }

    void bubbleDown(int hole, Pair p, int length) {

      if( length>1 ) {

        int child = firstChild(hole);

          int min=child;

            if( less(_data[child+i], _data[min]) )

              min=child+i;

          }

          if( !less(_data[min], p) )

            goto ok;

          move(_data[min], hole);

          hole = min;

          child = firstChild(hole);

        }

        if ( child<length ) {

          int min = child;

          while (++child < length) {

            if( less(_data[child], _data[min]) )

              min=child;

          }

          if( less(_data[min], p) ) {

            move(_data[min], hole);

            hole = min;

          }

        }

      }

    ok:

      move(p, hole);

    }

    void move(const Pair &p, int i) {

      _data[i] = p;

      _iim.set(p.first, i);

    }

  public:

    /// \brief Insert a pair of item and priority into the heap.

    ///

    /// This function inserts \c p.first to the heap with priority

    /// \c p.second.

    /// \param p The pair to insert.

    /// \pre \c p.first must not be stored in the heap.

    void push(const Pair &p) {

      int n = _data.size();

      _data.resize(n+1);

      bubbleUp(n, p);

    }

    /// \brief Insert an item into the heap with the given priority.

    ///

    /// This function inserts the given item into the heap with the

    /// given priority.

    /// \param i The item to insert.

    /// \param p The priority of the item.

    /// \pre \e i must not be stored in the heap.

    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }

    /// \brief Return the item having minimum priority.

    ///

    /// This function returns the item having minimum priority.

    /// \pre The heap must be non-empty.

    Item top() const { return _data[0].first; }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

    /// \pre The heap must be non-empty.

    Prio prio() const { return _data[0].second; }

    /// \brief Remove the item having minimum priority.

    ///

    /// This function removes the item having minimum priority.

    /// \pre The heap must be non-empty.

    void pop() {

      int n = _data.size()-1;

      _iim.set(_data[0].first, POST_HEAP);

      if (n>0) bubbleDown(0, _data[n], n);

      _data.pop_back();

    }

    /// \brief Remove the given item from the heap.

    ///

    /// This function removes the given item from the heap if it is

    /// already stored.

    /// \param i The item to delete.

    /// \pre \e i must be in the heap.

    void erase(const Item &i) {

      int h = _iim[i];

      int n = _data.size()-1;

      _iim.set(_data[h].first, POST_HEAP);

      if( h<n ) {

        if( less(_data[parent(h)], _data[n]) )

          bubbleDown(h, _data[n], n);

        else

          bubbleUp(h, _data[n]);

      }

      _data.pop_back();

    }

    /// \brief The priority of the given item.

    ///

    /// This function returns the priority of the given item.

    /// \param i The item.

    /// \pre \e i must be in the heap.

    Prio operator[](const Item &i) const {

      int idx = _iim[i];

      return _data[idx].second;

    }

    /// \brief Set the priority of an item or insert it, if it is

    /// not stored in the heap.

    ///

    /// This method sets the priority of the given item if it is

    /// already stored in the heap. Otherwise it inserts the given

    /// item into the heap with the given priority.

    /// \param i The item.

    /// \param p The priority.

    void set(const Item &i, const Prio &p) {

      int idx = _iim[i];

      if( idx<0 )

        push(i,p);

      else if( _comp(p, _data[idx].second) )

        bubbleUp(idx, Pair(i,p));

      else

        bubbleDown(idx, Pair(i,p), _data.size());

    }

    /// \brief Decrease the priority of an item to the given value.

    ///

    /// This function decreases the priority of an item to the given value.

    /// \param i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at least \e p.

    void decrease(const Item &i, const Prio &p) {

      int idx = _iim[i];

      bubbleUp(idx, Pair(i,p));

    }

    /// \brief Increase the priority of an item to the given value.

    ///

    /// This function increases the priority of an item to the given value.

    /// \param i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at most \e p.

    void increase(const Item &i, const Prio &p) {

      int idx = _iim[i];

      bubbleDown(idx, Pair(i,p), _data.size());

    }

    /// \brief Return the state of an item.

    ///

    /// This method returns \c PRE_HEAP if the given item has never

    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,

    /// and \c POST_HEAP otherwise.

    /// In the latter case it is possible that the item will get back

    /// to the heap again.

    /// \param i The item.

    State state(const Item &i) const {

      int s = _iim[i];

      if (s>=0) s=0;

      return State(s);

    }

    /// \brief Set the state of an item in the heap.

    ///

    /// This function sets the state of the given item in the heap.

    /// It can be used to manually clear the heap when it is important

    /// to achive better time complexity.

    /// \param i The item.

    /// \param st The state. It should not be \c IN_HEAP.

    void state(const Item& i, State st) {

      switch (st) {

        case POST_HEAP:

        case PRE_HEAP:

          if (state(i) == IN_HEAP) erase(i);

          _iim[i] = st;

          break;

        case IN_HEAP:

          break;

      }

    }

    /// \brief Replace an item in the heap.

    ///

    /// This function replaces item \c i with item \c j.

    /// Item \c i must be in the heap, while \c j must be out of the heap.

    /// After calling this method, item \c i will be out of the

    /// heap and \c j will be in the heap with the same prioriority

    /// as item \c i had before.

    void replace(const Item& i, const Item& j) {

      int idx=_iim[i];

      _iim.set(i, _iim[j]);

      _iim.set(j, idx);

      _data[idx].first=j;

    }

} // namespace lemon

/* -*- 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.

 *

 */

///\ingroup heaps

///\file

#include <vector>

#include <utility>

#include <functional>

namespace lemon {

  /// \ingroup heaps

  ///

  ///

  /// It fully conforms to the \ref concepts::Heap "heap concept".

  ///

  /// but its nodes have at most four children, instead of two.

  ///

  /// \tparam PR Type of the priorities of the items.

  /// \tparam IM A read-writable item map with \c int values, used

  /// internally to handle the cross references.

  /// \tparam CMP A functor class for comparing the priorities.

  /// The default is \c std::less<PR>.

  ///

  ///\sa BinHeap

#ifdef DOXYGEN

  template <typename PR, typename IM, typename CMP>

#else

  template <typename PR, typename IM, typename CMP = std::less<PR> >

#endif

  public:

    /// Type of the item-int map.

    typedef IM ItemIntMap;

    /// Type of the priorities.

    typedef PR Prio;

    /// Type of the items stored in the heap.

    typedef typename ItemIntMap::Key Item;

    /// Type of the item-priority pairs.

    typedef std::pair<Item,Prio> Pair;

    /// Functor type for comparing the priorities.

    typedef CMP Compare;

    /// \brief Type to represent the states of the items.

    ///

    /// Each item has a state associated to it. It can be "in heap",

    /// "pre-heap" or "post-heap". The latter two are indifferent from the

    /// heap's point of view, but may be useful to the user.

    ///

    /// The item-int map must be initialized in such way that it assigns

    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.

    enum State {

      IN_HEAP = 0,    ///< = 0.

      PRE_HEAP = -1,  ///< = -1.

      POST_HEAP = -2  ///< = -2.

    };

  private:

    std::vector<Pair> _data;

    Compare _comp;

    ItemIntMap &_iim;

  public:

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    /// \param comp The function object used for comparing the priorities.

      : _iim(map), _comp(comp) {}

    /// \brief The number of items stored in the heap.

    ///

    /// This function returns the number of items stored in the heap.

    int size() const { return _data.size(); }

    /// \brief Check if the heap is empty.

    ///

    /// This function returns \c true if the heap is empty.

    bool empty() const { return _data.empty(); }

    /// \brief Make the heap empty.

    ///

    /// This functon makes the heap empty.

    /// It does not change the cross reference map. If you want to reuse

    /// a heap that is not surely empty, you should first clear it and

    /// then you should set the cross reference map to \c PRE_HEAP

    /// for each item.

    void clear() { _data.clear(); }

  private:

    static int parent(int i) { return (i-1)/4; }

    static int firstChild(int i) { return 4*i+1; }

    bool less(const Pair &p1, const Pair &p2) const {

      return _comp(p1.second, p2.second);

    }

    void bubbleUp(int hole, Pair p) {

      int par = parent(hole);

      while( hole>0 && less(p,_data[par]) ) {

        move(_data[par],hole);

        hole = par;

        par = parent(hole);

      }

      move(p, hole);

    }

    void bubbleDown(int hole, Pair p, int length) {

      if( length>1 ) {

        int child = firstChild(hole);

        while( child+3<length ) {

          int min=child;

          if( less(_data[++child], _data[min]) ) min=child;

          if( less(_data[++child], _data[min]) ) min=child;

          if( less(_data[++child], _data[min]) ) min=child;

          if( !less(_data[min], p) )

            goto ok;

          move(_data[min], hole);

          hole = min;

          child = firstChild(hole);

        }

        if ( child<length ) {

          int min = child;

          if( ++child<length && less(_data[child], _data[min]) ) min=child;

          if( ++child<length && less(_data[child], _data[min]) ) min=child;

          if( less(_data[min], p) ) {

            move(_data[min], hole);

            hole = min;

          }

        }

      }

    ok:

      move(p, hole);

    }

    void move(const Pair &p, int i) {

      _data[i] = p;

      _iim.set(p.first, i);

    }

  public:

    /// \brief Insert a pair of item and priority into the heap.

    ///

    /// This function inserts \c p.first to the heap with priority

    /// \c p.second.

    /// \param p The pair to insert.

    /// \pre \c p.first must not be stored in the heap.

    void push(const Pair &p) {

      int n = _data.size();

      _data.resize(n+1);

      bubbleUp(n, p);

    }

    /// \brief Insert an item into the heap with the given priority.

    ///

    /// This function inserts the given item into the heap with the

    /// given priority.

    /// \param i The item to insert.

    /// \param p The priority of the item.

    /// \pre \e i must not be stored in the heap.

    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }

    /// \brief Return the item having minimum priority.

    ///

    ///

    /// This function returns the priority of the given item.

    /// \param i The item.

    /// \pre \e i must be in the heap.

    Prio operator[](const Item &i) const {

      int idx = _iim[i];

      return _data[idx].second;

    }

    /// \brief Set the priority of an item or insert it, if it is

    /// not stored in the heap.

    ///

    /// This method sets the priority of the given item if it is

    /// already stored in the heap. Otherwise it inserts the given

    /// item into the heap with the given priority.

    /// \param i The item.

    /// \param p The priority.

    void set(const Item &i, const Prio &p) {

      int idx = _iim[i];

      if( idx < 0 )

        push(i,p);

      else if( _comp(p, _data[idx].second) )

        bubbleUp(idx, Pair(i,p));

      else

        bubbleDown(idx, Pair(i,p), _data.size());

    }

    /// \brief Decrease the priority of an item to the given value.

    ///

    /// This function decreases the priority of an item to the given value.

    /// \param i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at least \e p.

    void decrease(const Item &i, const Prio &p) {

      int idx = _iim[i];

      bubbleUp(idx, Pair(i,p));

    }

    /// \brief Increase the priority of an item to the given value.