deba@728: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@728:  *
deba@728:  * This file is a part of LEMON, a generic C++ optimization library.
deba@728:  *
deba@728:  * Copyright (C) 2003-2009
deba@728:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@728:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@728:  *
deba@728:  * Permission to use, modify and distribute this software is granted
deba@728:  * provided that this copyright notice appears in all copies. For
deba@728:  * precise terms see the accompanying LICENSE file.
deba@728:  *
deba@728:  * This software is provided "AS IS" with no warranty of any kind,
deba@728:  * express or implied, and with no claim as to its suitability for any
deba@728:  * purpose.
deba@728:  *
deba@728:  */
deba@728: 
deba@728: #ifndef LEMON_BUCKET_HEAP_H
deba@728: #define LEMON_BUCKET_HEAP_H
deba@728: 
kpeter@757: ///\ingroup heaps
deba@728: ///\file
kpeter@756: ///\brief Bucket heap implementation.
deba@728: 
deba@728: #include <vector>
deba@728: #include <utility>
deba@728: #include <functional>
deba@728: 
deba@728: namespace lemon {
deba@728: 
deba@729:   namespace _bucket_heap_bits {
deba@729: 
deba@730:     template <bool MIN>
deba@729:     struct DirectionTraits {
deba@729:       static bool less(int left, int right) {
deba@729:         return left < right;
deba@729:       }
deba@729:       static void increase(int& value) {
deba@729:         ++value;
deba@729:       }
deba@729:     };
deba@729: 
deba@729:     template <>
deba@729:     struct DirectionTraits<false> {
deba@729:       static bool less(int left, int right) {
deba@729:         return left > right;
deba@729:       }
deba@729:       static void increase(int& value) {
deba@729:         --value;
deba@729:       }
deba@729:     };
deba@729: 
deba@729:   }
deba@729: 
kpeter@757:   /// \ingroup heaps
deba@728:   ///
kpeter@756:   /// \brief Bucket heap data structure.
deba@728:   ///
kpeter@756:   /// This class implements the \e bucket \e heap data structure.
kpeter@756:   /// It practically conforms to the \ref concepts::Heap "heap concept",
kpeter@756:   /// but it has some limitations.
deba@728:   ///
kpeter@756:   /// The bucket heap is a very simple structure. It can store only
kpeter@756:   /// \c int priorities and it maintains a list of items for each priority
kpeter@756:   /// in the range <tt>[0..C)</tt>. So it should only be used when the
kpeter@756:   /// priorities are small. It is not intended to use as a Dijkstra heap.
kpeter@756:   ///
kpeter@756:   /// \tparam IM A read-writable item map with \c int values, used
kpeter@756:   /// internally to handle the cross references.
kpeter@756:   /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.
kpeter@756:   /// The default is \e min-heap. If this parameter is set to \c false,
kpeter@756:   /// then the comparison is reversed, so the top(), prio() and pop()
kpeter@756:   /// functions deal with the item having maximum priority instead of the
kpeter@756:   /// minimum.
kpeter@756:   ///
kpeter@756:   /// \sa SimpleBucketHeap
deba@730:   template <typename IM, bool MIN = true>
deba@728:   class BucketHeap {
deba@728: 
deba@728:   public:
kpeter@756: 
kpeter@756:     /// Type of the item-int map.
kpeter@756:     typedef IM ItemIntMap;
kpeter@756:     /// Type of the priorities.
deba@728:     typedef int Prio;
kpeter@756:     /// Type of the items stored in the heap.
kpeter@756:     typedef typename ItemIntMap::Key Item;
kpeter@756:     /// Type of the item-priority pairs.
kpeter@756:     typedef std::pair<Item,Prio> Pair;
deba@728: 
deba@729:   private:
deba@729: 
deba@730:     typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
deba@729: 
deba@729:   public:
deba@729: 
kpeter@756:     /// \brief Type to represent the states of the items.
deba@728:     ///
kpeter@756:     /// Each item has a state associated to it. It can be "in heap",
kpeter@756:     /// "pre-heap" or "post-heap". The latter two are indifferent from the
deba@728:     /// heap's point of view, but may be useful to the user.
deba@728:     ///
deba@730:     /// The item-int map must be initialized in such way that it assigns
deba@730:     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
deba@728:     enum State {
deba@730:       IN_HEAP = 0,    ///< = 0.
deba@730:       PRE_HEAP = -1,  ///< = -1.
deba@730:       POST_HEAP = -2  ///< = -2.
deba@728:     };
deba@728: 
deba@728:   public:
kpeter@756: 
kpeter@756:     /// \brief Constructor.
deba@728:     ///
kpeter@756:     /// Constructor.
kpeter@756:     /// \param map A map that assigns \c int values to the items.
kpeter@756:     /// It is used internally to handle the cross references.
kpeter@756:     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
deba@730:     explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {}
deba@728: 
kpeter@756:     /// \brief The number of items stored in the heap.
deba@728:     ///
kpeter@756:     /// This function returns the number of items stored in the heap.
deba@730:     int size() const { return _data.size(); }
deba@728: 
kpeter@756:     /// \brief Check if the heap is empty.
deba@728:     ///
kpeter@756:     /// This function returns \c true if the heap is empty.
deba@730:     bool empty() const { return _data.empty(); }
deba@728: 
kpeter@756:     /// \brief Make the heap empty.
deba@728:     ///
kpeter@756:     /// This functon makes the heap empty.
kpeter@756:     /// It does not change the cross reference map. If you want to reuse
kpeter@756:     /// a heap that is not surely empty, you should first clear it and
kpeter@756:     /// then you should set the cross reference map to \c PRE_HEAP
kpeter@756:     /// for each item.
deba@728:     void clear() {
deba@730:       _data.clear(); _first.clear(); _minimum = 0;
deba@728:     }
deba@728: 
deba@728:   private:
deba@728: 
deba@728:     void relocate_last(int idx) {
deba@730:       if (idx + 1 < int(_data.size())) {
deba@730:         _data[idx] = _data.back();
deba@730:         if (_data[idx].prev != -1) {
deba@730:           _data[_data[idx].prev].next = idx;
deba@728:         } else {
deba@730:           _first[_data[idx].value] = idx;
deba@728:         }
deba@730:         if (_data[idx].next != -1) {
deba@730:           _data[_data[idx].next].prev = idx;
deba@728:         }
deba@730:         _iim[_data[idx].item] = idx;
deba@728:       }
deba@730:       _data.pop_back();
deba@728:     }
deba@728: 
deba@728:     void unlace(int idx) {
deba@730:       if (_data[idx].prev != -1) {
deba@730:         _data[_data[idx].prev].next = _data[idx].next;
deba@728:       } else {
deba@730:         _first[_data[idx].value] = _data[idx].next;
deba@728:       }
deba@730:       if (_data[idx].next != -1) {
deba@730:         _data[_data[idx].next].prev = _data[idx].prev;
deba@728:       }
deba@728:     }
deba@728: 
deba@728:     void lace(int idx) {
deba@730:       if (int(_first.size()) <= _data[idx].value) {
deba@730:         _first.resize(_data[idx].value + 1, -1);
deba@728:       }
deba@730:       _data[idx].next = _first[_data[idx].value];
deba@730:       if (_data[idx].next != -1) {
deba@730:         _data[_data[idx].next].prev = idx;
deba@728:       }
deba@730:       _first[_data[idx].value] = idx;
deba@730:       _data[idx].prev = -1;
deba@728:     }
deba@728: 
deba@728:   public:
kpeter@756: 
deba@728:     /// \brief Insert a pair of item and priority into the heap.
deba@728:     ///
kpeter@756:     /// This function inserts \c p.first to the heap with priority
kpeter@756:     /// \c p.second.
deba@728:     /// \param p The pair to insert.
kpeter@756:     /// \pre \c p.first must not be stored in the heap.
deba@728:     void push(const Pair& p) {
deba@728:       push(p.first, p.second);
deba@728:     }
deba@728: 
deba@728:     /// \brief Insert an item into the heap with the given priority.
deba@728:     ///
kpeter@756:     /// This function inserts the given item into the heap with the
kpeter@756:     /// given priority.
deba@728:     /// \param i The item to insert.
deba@728:     /// \param p The priority of the item.
kpeter@756:     /// \pre \e i must not be stored in the heap.
deba@728:     void push(const Item &i, const Prio &p) {
deba@730:       int idx = _data.size();
deba@730:       _iim[i] = idx;
deba@730:       _data.push_back(BucketItem(i, p));
deba@728:       lace(idx);
deba@730:       if (Direction::less(p, _minimum)) {
deba@730:         _minimum = p;
deba@728:       }
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Return the item having minimum priority.
deba@728:     ///
kpeter@756:     /// This function returns the item having minimum priority.
kpeter@756:     /// \pre The heap must be non-empty.
deba@728:     Item top() const {
deba@730:       while (_first[_minimum] == -1) {
deba@730:         Direction::increase(_minimum);
deba@728:       }
deba@730:       return _data[_first[_minimum]].item;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief The minimum priority.
deba@728:     ///
kpeter@756:     /// This function returns the minimum priority.
kpeter@756:     /// \pre The heap must be non-empty.
deba@728:     Prio prio() const {
deba@730:       while (_first[_minimum] == -1) {
deba@730:         Direction::increase(_minimum);
deba@728:       }
deba@730:       return _minimum;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Remove the item having minimum priority.
deba@728:     ///
kpeter@756:     /// This function removes the item having minimum priority.
deba@728:     /// \pre The heap must be non-empty.
deba@728:     void pop() {
deba@730:       while (_first[_minimum] == -1) {
deba@730:         Direction::increase(_minimum);
deba@728:       }
deba@730:       int idx = _first[_minimum];
deba@730:       _iim[_data[idx].item] = -2;
deba@728:       unlace(idx);
deba@728:       relocate_last(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Remove the given item from the heap.
deba@728:     ///
kpeter@756:     /// This function removes the given item from the heap if it is
kpeter@756:     /// already stored.
kpeter@756:     /// \param i The item to delete.
kpeter@756:     /// \pre \e i must be in the heap.
deba@728:     void erase(const Item &i) {
deba@730:       int idx = _iim[i];
deba@730:       _iim[_data[idx].item] = -2;
deba@728:       unlace(idx);
deba@728:       relocate_last(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief The priority of the given item.
deba@728:     ///
kpeter@756:     /// This function returns the priority of the given item.
deba@728:     /// \param i The item.
kpeter@756:     /// \pre \e i must be in the heap.
deba@728:     Prio operator[](const Item &i) const {
deba@730:       int idx = _iim[i];
deba@730:       return _data[idx].value;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Set the priority of an item or insert it, if it is
kpeter@756:     /// not stored in the heap.
deba@728:     ///
kpeter@756:     /// This method sets the priority of the given item if it is
kpeter@756:     /// already stored in the heap. Otherwise it inserts the given
kpeter@756:     /// item into the heap with the given priority.
deba@728:     /// \param i The item.
deba@728:     /// \param p The priority.
deba@728:     void set(const Item &i, const Prio &p) {
deba@730:       int idx = _iim[i];
deba@728:       if (idx < 0) {
deba@729:         push(i, p);
deba@730:       } else if (Direction::less(p, _data[idx].value)) {
deba@729:         decrease(i, p);
deba@729:       } else {
deba@728:         increase(i, p);
deba@728:       }
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Decrease the priority of an item to the given value.
deba@728:     ///
kpeter@756:     /// This function decreases the priority of an item to the given value.
deba@728:     /// \param i The item.
deba@728:     /// \param p The priority.
kpeter@756:     /// \pre \e i must be stored in the heap with priority at least \e p.
deba@728:     void decrease(const Item &i, const Prio &p) {
deba@730:       int idx = _iim[i];
deba@728:       unlace(idx);
deba@730:       _data[idx].value = p;
deba@730:       if (Direction::less(p, _minimum)) {
deba@730:         _minimum = p;
deba@728:       }
deba@728:       lace(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Increase the priority of an item to the given value.
deba@728:     ///
kpeter@756:     /// This function increases the priority of an item to the given value.
deba@728:     /// \param i The item.
deba@728:     /// \param p The priority.
kpeter@756:     /// \pre \e i must be stored in the heap with priority at most \e p.
deba@728:     void increase(const Item &i, const Prio &p) {
deba@730:       int idx = _iim[i];
deba@728:       unlace(idx);
deba@730:       _data[idx].value = p;
deba@728:       lace(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Return the state of an item.
deba@728:     ///
kpeter@756:     /// This method returns \c PRE_HEAP if the given item has never
kpeter@756:     /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@756:     /// and \c POST_HEAP otherwise.
kpeter@756:     /// In the latter case it is possible that the item will get back
kpeter@756:     /// to the heap again.
deba@728:     /// \param i The item.
deba@728:     State state(const Item &i) const {
deba@730:       int idx = _iim[i];
deba@728:       if (idx >= 0) idx = 0;
deba@728:       return State(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Set the state of an item in the heap.
deba@728:     ///
kpeter@756:     /// This function sets the state of the given item in the heap.
kpeter@756:     /// It can be used to manually clear the heap when it is important
kpeter@756:     /// to achive better time complexity.
deba@728:     /// \param i The item.
deba@728:     /// \param st The state. It should not be \c IN_HEAP.
deba@728:     void state(const Item& i, State st) {
deba@728:       switch (st) {
deba@728:       case POST_HEAP:
deba@728:       case PRE_HEAP:
deba@728:         if (state(i) == IN_HEAP) {
deba@728:           erase(i);
deba@728:         }
deba@730:         _iim[i] = st;
deba@728:         break;
deba@728:       case IN_HEAP:
deba@728:         break;
deba@728:       }
deba@728:     }
deba@728: 
deba@728:   private:
deba@728: 
deba@728:     struct BucketItem {
deba@728:       BucketItem(const Item& _item, int _value)
deba@728:         : item(_item), value(_value) {}
deba@728: 
deba@728:       Item item;
deba@728:       int value;
deba@728: 
deba@728:       int prev, next;
deba@728:     };
deba@728: 
deba@730:     ItemIntMap& _iim;
deba@730:     std::vector<int> _first;
deba@730:     std::vector<BucketItem> _data;
deba@730:     mutable int _minimum;
deba@728: 
deba@728:   }; // class BucketHeap
deba@728: 
kpeter@757:   /// \ingroup heaps
deba@728:   ///
kpeter@756:   /// \brief Simplified bucket heap data structure.
deba@728:   ///
deba@728:   /// This class implements a simplified \e bucket \e heap data
kpeter@756:   /// structure. It does not provide some functionality, but it is
kpeter@756:   /// faster and simpler than BucketHeap. The main difference is
kpeter@756:   /// that BucketHeap stores a doubly-linked list for each key while
kpeter@756:   /// this class stores only simply-linked lists. It supports erasing
kpeter@756:   /// only for the item having minimum priority and it does not support
kpeter@756:   /// key increasing and decreasing.
deba@728:   ///
kpeter@756:   /// Note that this implementation does not conform to the
kpeter@756:   /// \ref concepts::Heap "heap concept" due to the lack of some 
kpeter@756:   /// functionality.
kpeter@756:   ///
kpeter@756:   /// \tparam IM A read-writable item map with \c int values, used
kpeter@756:   /// internally to handle the cross references.
kpeter@756:   /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.
kpeter@756:   /// The default is \e min-heap. If this parameter is set to \c false,
kpeter@756:   /// then the comparison is reversed, so the top(), prio() and pop()
kpeter@756:   /// functions deal with the item having maximum priority instead of the
kpeter@756:   /// minimum.
deba@728:   ///
deba@728:   /// \sa BucketHeap
deba@730:   template <typename IM, bool MIN = true >
deba@728:   class SimpleBucketHeap {
deba@728: 
deba@728:   public:
kpeter@756: 
kpeter@756:     /// Type of the item-int map.
kpeter@756:     typedef IM ItemIntMap;
kpeter@756:     /// Type of the priorities.
deba@728:     typedef int Prio;
kpeter@756:     /// Type of the items stored in the heap.
kpeter@756:     typedef typename ItemIntMap::Key Item;
kpeter@756:     /// Type of the item-priority pairs.
kpeter@756:     typedef std::pair<Item,Prio> Pair;
deba@728: 
deba@729:   private:
deba@729: 
deba@730:     typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
deba@729: 
deba@729:   public:
deba@729: 
kpeter@756:     /// \brief Type to represent the states of the items.
deba@728:     ///
kpeter@756:     /// Each item has a state associated to it. It can be "in heap",
kpeter@756:     /// "pre-heap" or "post-heap". The latter two are indifferent from the
deba@728:     /// heap's point of view, but may be useful to the user.
deba@728:     ///
deba@730:     /// The item-int map must be initialized in such way that it assigns
deba@730:     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
deba@728:     enum State {
deba@730:       IN_HEAP = 0,    ///< = 0.
deba@730:       PRE_HEAP = -1,  ///< = -1.
deba@730:       POST_HEAP = -2  ///< = -2.
deba@728:     };
deba@728: 
deba@728:   public:
deba@728: 
kpeter@756:     /// \brief Constructor.
deba@728:     ///
kpeter@756:     /// Constructor.
kpeter@756:     /// \param map A map that assigns \c int values to the items.
kpeter@756:     /// It is used internally to handle the cross references.
kpeter@756:     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
deba@730:     explicit SimpleBucketHeap(ItemIntMap &map)
deba@730:       : _iim(map), _free(-1), _num(0), _minimum(0) {}
deba@728: 
kpeter@756:     /// \brief The number of items stored in the heap.
deba@728:     ///
kpeter@756:     /// This function returns the number of items stored in the heap.
deba@730:     int size() const { return _num; }
deba@728: 
kpeter@756:     /// \brief Check if the heap is empty.
deba@728:     ///
kpeter@756:     /// This function returns \c true if the heap is empty.
deba@730:     bool empty() const { return _num == 0; }
deba@728: 
kpeter@756:     /// \brief Make the heap empty.
deba@728:     ///
kpeter@756:     /// This functon makes the heap empty.
kpeter@756:     /// It does not change the cross reference map. If you want to reuse
kpeter@756:     /// a heap that is not surely empty, you should first clear it and
kpeter@756:     /// then you should set the cross reference map to \c PRE_HEAP
kpeter@756:     /// for each item.
deba@728:     void clear() {
deba@730:       _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0;
deba@728:     }
deba@728: 
deba@728:     /// \brief Insert a pair of item and priority into the heap.
deba@728:     ///
kpeter@756:     /// This function inserts \c p.first to the heap with priority
kpeter@756:     /// \c p.second.
deba@728:     /// \param p The pair to insert.
kpeter@756:     /// \pre \c p.first must not be stored in the heap.
deba@728:     void push(const Pair& p) {
deba@728:       push(p.first, p.second);
deba@728:     }
deba@728: 
deba@728:     /// \brief Insert an item into the heap with the given priority.
deba@728:     ///
kpeter@756:     /// This function inserts the given item into the heap with the
kpeter@756:     /// given priority.
deba@728:     /// \param i The item to insert.
deba@728:     /// \param p The priority of the item.
kpeter@756:     /// \pre \e i must not be stored in the heap.
deba@728:     void push(const Item &i, const Prio &p) {
deba@728:       int idx;
deba@730:       if (_free == -1) {
deba@730:         idx = _data.size();
deba@730:         _data.push_back(BucketItem(i));
deba@728:       } else {
deba@730:         idx = _free;
deba@730:         _free = _data[idx].next;
deba@730:         _data[idx].item = i;
deba@728:       }
deba@730:       _iim[i] = idx;
deba@730:       if (p >= int(_first.size())) _first.resize(p + 1, -1);
deba@730:       _data[idx].next = _first[p];
deba@730:       _first[p] = idx;
deba@730:       if (Direction::less(p, _minimum)) {
deba@730:         _minimum = p;
deba@728:       }
deba@730:       ++_num;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Return the item having minimum priority.
deba@728:     ///
kpeter@756:     /// This function returns the item having minimum priority.
kpeter@756:     /// \pre The heap must be non-empty.
deba@728:     Item top() const {
deba@730:       while (_first[_minimum] == -1) {
deba@730:         Direction::increase(_minimum);
deba@728:       }
deba@730:       return _data[_first[_minimum]].item;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief The minimum priority.
deba@728:     ///
kpeter@756:     /// This function returns the minimum priority.
kpeter@756:     /// \pre The heap must be non-empty.
deba@728:     Prio prio() const {
deba@730:       while (_first[_minimum] == -1) {
deba@730:         Direction::increase(_minimum);
deba@728:       }
deba@730:       return _minimum;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Remove the item having minimum priority.
deba@728:     ///
kpeter@756:     /// This function removes the item having minimum priority.
deba@728:     /// \pre The heap must be non-empty.
deba@728:     void pop() {
deba@730:       while (_first[_minimum] == -1) {
deba@730:         Direction::increase(_minimum);
deba@728:       }
deba@730:       int idx = _first[_minimum];
deba@730:       _iim[_data[idx].item] = -2;
deba@730:       _first[_minimum] = _data[idx].next;
deba@730:       _data[idx].next = _free;
deba@730:       _free = idx;
deba@730:       --_num;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief The priority of the given item.
deba@728:     ///
kpeter@756:     /// This function returns the priority of the given item.
deba@728:     /// \param i The item.
kpeter@756:     /// \pre \e i must be in the heap.
kpeter@756:     /// \warning This operator is not a constant time function because
kpeter@756:     /// it scans the whole data structure to find the proper value.
deba@728:     Prio operator[](const Item &i) const {
kpeter@756:       for (int k = 0; k < int(_first.size()); ++k) {
deba@730:         int idx = _first[k];
deba@728:         while (idx != -1) {
deba@730:           if (_data[idx].item == i) {
deba@728:             return k;
deba@728:           }
deba@730:           idx = _data[idx].next;
deba@728:         }
deba@728:       }
deba@728:       return -1;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Return the state of an item.
deba@728:     ///
kpeter@756:     /// This method returns \c PRE_HEAP if the given item has never
kpeter@756:     /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@756:     /// and \c POST_HEAP otherwise.
kpeter@756:     /// In the latter case it is possible that the item will get back
kpeter@756:     /// to the heap again.
deba@728:     /// \param i The item.
deba@728:     State state(const Item &i) const {
deba@730:       int idx = _iim[i];
deba@728:       if (idx >= 0) idx = 0;
deba@728:       return State(idx);
deba@728:     }
deba@728: 
deba@728:   private:
deba@728: 
deba@728:     struct BucketItem {
deba@728:       BucketItem(const Item& _item)
deba@728:         : item(_item) {}
deba@728: 
deba@728:       Item item;
deba@728:       int next;
deba@728:     };
deba@728: 
deba@730:     ItemIntMap& _iim;
deba@730:     std::vector<int> _first;
deba@730:     std::vector<BucketItem> _data;
deba@730:     int _free, _num;
deba@730:     mutable int _minimum;
deba@728: 
deba@728:   }; // class SimpleBucketHeap
deba@728: 
deba@728: }
deba@728: 
deba@728: #endif