LEMON/LEMON-main Changeset - r711:28cfac049a6a

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Changeset - r711:28cfac049a6a

« 710:f1fe0d

712:6d5f54 »

r711:28cfac049a6a

Wed, 08 Jul 2009 17:47:01

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Unify member names in heaps (#299) The following renamings are made. Public members: - UnderFlowPriorityError -> PriorityUnderflowError ("underflow" is only one word) Private members: - bubble_up() -> bubbleUp() - bubble_down() -> bubbleDown() - second_child() -> secondChild() - makeroot() -> makeRoot() - relocate_last() -> relocateLast() - data -> _data - boxes -> _boxes

0 4 0

default

4 files changed with 97 insertions and 97 deletions:

lemon/bin_heap.h

lemon/bucket_heap.h

lemon/fib_heap.h

lemon/radix_heap.h

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lemon/bin_heap.h

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 		/* -*- 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.
+		 *
 		 */
 		#ifndef LEMON_BIN_HEAP_H
 		#define LEMON_BIN_HEAP_H
 		///\ingroup heaps
 		///\file
 		///\brief Binary heap implementation.
 		#include <vector>
 		#include <utility>
 		#include <functional>
 		namespace lemon {
 		  /// \ingroup heaps
 		  ///
 		  /// \brief Binary heap data structure.
 		  ///
 		  /// This class implements the \e binary \e heap data structure.
 		  /// It fully conforms to the \ref concepts::Heap "heap concept".
 		  ///
 		  /// \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
 		  class BinHeap {
 		  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.
 		    explicit BinHeap(ItemIntMap &map) : _iim(map) {}
 		    /// \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.
 		    BinHeap(ItemIntMap &map, const Compare &comp)
 		      : _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)/2; }
-		    static int second_child(int i) { return 2*i+2; }
+		    static int secondChild(int i) { return 2*i+2; }
 		    bool less(const Pair &p1, const Pair &p2) const {
 		      return _comp(p1.second, p2.second);
+		    }
-		    int bubble_up(int hole, Pair p) {
+		    int 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);
 		      return hole;
+		    }
 		    int bubble_down(int hole, Pair p, int length) {
 		      int child = second_child(hole);
 		    int bubbleDown(int hole, Pair p, int length) {
 		      int child = secondChild(hole);
 		      while(child < length) {
 		        if( less(_data[child-1], _data[child]) ) {
 		          --child;
+		        }
 		        if( !less(_data[child], p) )
 		          goto ok;
 		        move(_data[child], hole);
 		        hole = child;
-		        child = second_child(hole);
+		        child = secondChild(hole);
+		      }
 		      child--;
 		      if( child<length && less(_data[child], p) ) {
 		        move(_data[child], hole);
 		        hole=child;
+		      }
 		    ok:
 		      move(p, hole);
 		      return 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);
-		      bubble_up(n, p);
+		      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) {
-		        bubble_down(0, _data[n], n);
+		        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 ( bubble_up(h, _data[n]) == h) {
 		          bubble_down(h, _data[n], n);
 		        if ( bubbleUp(h, _data[n]) == h) {
 		          bubbleDown(h, _data[n], 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) ) {
-		        bubble_up(idx, Pair(i,p));
+		        bubbleUp(idx, Pair(i,p));
+		      }
 		      else {
-		        bubble_down(idx, Pair(i,p), _data.size());
+		        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];
-		      bubble_up(idx, Pair(i,p));
+		      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];
-		      bubble_down(idx, Pair(i,p), _data.size());
+		      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;
+		    }
 		  }; // class BinHeap
 		} // namespace lemon
 		#endif // LEMON_BIN_HEAP_H

lemon/bucket_heap.h

Show inline comments

 		/* -*- 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.
+		 *
 		 */
 		#ifndef LEMON_BUCKET_HEAP_H
 		#define LEMON_BUCKET_HEAP_H
 		///\ingroup heaps
 		///\file
 		///\brief Bucket heap implementation.
 		#include <vector>
 		#include <utility>
 		#include <functional>
 		namespace lemon {
 		  namespace _bucket_heap_bits {
 		    template <bool MIN>
 		    struct DirectionTraits {
 		      static bool less(int left, int right) {
 		        return left < right;
+		      }
 		      static void increase(int& value) {
 		        ++value;
+		      }
 		    };
 		    template <>
 		    struct DirectionTraits<false> {
 		      static bool less(int left, int right) {
 		        return left > right;
+		      }
 		      static void increase(int& value) {
 		        --value;
+		      }
 		    };
+		  }
 		  /// \ingroup heaps
 		  ///
 		  /// \brief Bucket heap data structure.
 		  ///
 		  /// This class implements the \e bucket \e heap data structure.
 		  /// It practically conforms to the \ref concepts::Heap "heap concept",
 		  /// but it has some limitations.
 		  ///
 		  /// The bucket heap is a very simple structure. It can store only
 		  /// \c int priorities and it maintains a list of items for each priority
 		  /// in the range <tt>[0..C)</tt>. So it should only be used when the
 		  /// priorities are small. It is not intended to use as a Dijkstra heap.
 		  ///
 		  /// \tparam IM A read-writable item map with \c int values, used
 		  /// internally to handle the cross references.
 		  /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.
 		  /// The default is \e min-heap. If this parameter is set to \c false,
 		  /// then the comparison is reversed, so the top(), prio() and pop()
 		  /// functions deal with the item having maximum priority instead of the
 		  /// minimum.
 		  ///
 		  /// \sa SimpleBucketHeap
 		  template <typename IM, bool MIN = true>
 		  class BucketHeap {
 		  public:
 		    /// Type of the item-int map.
 		    typedef IM ItemIntMap;
 		    /// Type of the priorities.
 		    typedef int 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;
 		  private:
 		    typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
 		  public:
 		    /// \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.
 		    };
 		  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.
 		    explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(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 _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(); _first.clear(); _minimum = 0;
+		    }
 		  private:
-		    void relocate_last(int idx) {
+		    void relocateLast(int idx) {
 		      if (idx + 1 < int(_data.size())) {
 		        _data[idx] = _data.back();
 		        if (_data[idx].prev != -1) {
 		          _data[_data[idx].prev].next = idx;
 		        } else {
 		          _first[_data[idx].value] = idx;
+		        }
 		        if (_data[idx].next != -1) {
 		          _data[_data[idx].next].prev = idx;
+		        }
 		        _iim[_data[idx].item] = idx;
+		      }
 		      _data.pop_back();
+		    }
 		    void unlace(int idx) {
 		      if (_data[idx].prev != -1) {
 		        _data[_data[idx].prev].next = _data[idx].next;
 		      } else {
 		        _first[_data[idx].value] = _data[idx].next;
+		      }
 		      if (_data[idx].next != -1) {
 		        _data[_data[idx].next].prev = _data[idx].prev;
+		      }
+		    }
 		    void lace(int idx) {
 		      if (int(_first.size()) <= _data[idx].value) {
 		        _first.resize(_data[idx].value + 1, -1);
+		      }
 		      _data[idx].next = _first[_data[idx].value];
 		      if (_data[idx].next != -1) {
 		        _data[_data[idx].next].prev = idx;
+		      }
 		      _first[_data[idx].value] = idx;
 		      _data[idx].prev = -1;
+		    }
 		  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) {
 		      push(p.first, p.second);
+		    }
 		    /// \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) {
 		      int idx = _data.size();
 		      _iim[i] = idx;
 		      _data.push_back(BucketItem(i, p));
 		      lace(idx);
 		      if (Direction::less(p, _minimum)) {
 		        _minimum = 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 {
 		      while (_first[_minimum] == -1) {
 		        Direction::increase(_minimum);
+		      }
 		      return _data[_first[_minimum]].item;
+		    }
 		    /// \brief The minimum priority.
 		    ///
 		    /// This function returns the minimum priority.
 		    /// \pre The heap must be non-empty.
 		    Prio prio() const {
 		      while (_first[_minimum] == -1) {
 		        Direction::increase(_minimum);
+		      }
 		      return _minimum;
+		    }
 		    /// \brief Remove the item having minimum priority.
 		    ///
 		    /// This function removes the item having minimum priority.
 		    /// \pre The heap must be non-empty.
 		    void pop() {
 		      while (_first[_minimum] == -1) {
 		        Direction::increase(_minimum);
+		      }
 		      int idx = _first[_minimum];
 		      _iim[_data[idx].item] = -2;
 		      unlace(idx);
-		      relocate_last(idx);
+		      relocateLast(idx);
+		    }
 		    /// \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 idx = _iim[i];
 		      _iim[_data[idx].item] = -2;
 		      unlace(idx);
-		      relocate_last(idx);
+		      relocateLast(idx);
+		    }
 		    /// \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].value;
+		    }
 		    /// \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 (Direction::less(p, _data[idx].value)) {
 		        decrease(i, p);
 		      } else {
 		        increase(i, p);
+		      }
+		    }
 		    /// \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];
 		      unlace(idx);
 		      _data[idx].value = p;
 		      if (Direction::less(p, _minimum)) {
 		        _minimum = p;
+		      }
 		      lace(idx);
+		    }
 		    /// \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];
 		      unlace(idx);
 		      _data[idx].value = p;
 		      lace(idx);
+		    }
 		    /// \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 idx = _iim[i];
 		      if (idx >= 0) idx = 0;
 		      return State(idx);
+		    }
 		    /// \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;
+		      }
+		    }
 		  private:
 		    struct BucketItem {
 		      BucketItem(const Item& _item, int _value)
 		        : item(_item), value(_value) {}
 		      Item item;
 		      int value;
 		      int prev, next;
 		    };
 		    ItemIntMap& _iim;
 		    std::vector<int> _first;
 		    std::vector<BucketItem> _data;
 		    mutable int _minimum;
 		  }; // class BucketHeap
 		  /// \ingroup heaps
 		  ///
 		  /// \brief Simplified bucket heap data structure.
 		  ///
 		  /// This class implements a simplified \e bucket \e heap data
 		  /// structure. It does not provide some functionality, but it is
 		  /// faster and simpler than BucketHeap. The main difference is
 		  /// that BucketHeap stores a doubly-linked list for each key while
 		  /// this class stores only simply-linked lists. It supports erasing
 		  /// only for the item having minimum priority and it does not support
 		  /// key increasing and decreasing.
 		  ///
 		  /// Note that this implementation does not conform to the
 		  /// \ref concepts::Heap "heap concept" due to the lack of some
 		  /// functionality.
 		  ///
 		  /// \tparam IM A read-writable item map with \c int values, used
 		  /// internally to handle the cross references.
 		  /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.
 		  /// The default is \e min-heap. If this parameter is set to \c false,
 		  /// then the comparison is reversed, so the top(), prio() and pop()
 		  /// functions deal with the item having maximum priority instead of the
 		  /// minimum.
 		  ///
 		  /// \sa BucketHeap
 		  template <typename IM, bool MIN = true >
 		  class SimpleBucketHeap {
 		  public:
 		    /// Type of the item-int map.
 		    typedef IM ItemIntMap;
 		    /// Type of the priorities.
 		    typedef int 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;
 		  private:
 		    typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
 		  public:
 		    /// \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.
 		    };
 		  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.
 		    explicit SimpleBucketHeap(ItemIntMap &map)
 		      : _iim(map), _free(-1), _num(0), _minimum(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; }
 		    /// \brief Check if the heap is empty.
 		    ///
 		    /// This function returns \c true if the heap is empty.
 		    bool empty() const { return _num == 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(); _first.clear(); _free = -1; _num = 0; _minimum = 0;
+		    }
 		    /// \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) {
 		      push(p.first, p.second);
+		    }
 		    /// \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) {
 		      int idx;
 		      if (_free == -1) {
 		        idx = _data.size();
 		        _data.push_back(BucketItem(i));
 		      } else {
 		        idx = _free;
 		        _free = _data[idx].next;
 		        _data[idx].item = i;
+		      }
 		      _iim[i] = idx;
 		      if (p >= int(_first.size())) _first.resize(p + 1, -1);
 		      _data[idx].next = _first[p];
 		      _first[p] = idx;
 		      if (Direction::less(p, _minimum)) {
 		        _minimum = p;
+		      }
 		      ++_num;
+		    }
 		    /// \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 {
 		      while (_first[_minimum] == -1) {
 		        Direction::increase(_minimum);
+		      }
 		      return _data[_first[_minimum]].item;
+		    }
 		    /// \brief The minimum priority.
 		    ///
 		    /// This function returns the minimum priority.
 		    /// \pre The heap must be non-empty.
 		    Prio prio() const {
 		      while (_first[_minimum] == -1) {
 		        Direction::increase(_minimum);
+		      }
 		      return _minimum;
+		    }
 		    /// \brief Remove the item having minimum priority.
 		    ///
 		    /// This function removes the item having minimum priority.
 		    /// \pre The heap must be non-empty.
 		    void pop() {
 		      while (_first[_minimum] == -1) {
 		        Direction::increase(_minimum);
+		      }
 		      int idx = _first[_minimum];
 		      _iim[_data[idx].item] = -2;
 		      _first[_minimum] = _data[idx].next;
 		      _data[idx].next = _free;
 		      _free = idx;
 		      --_num;
+		    }
 		    /// \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.
 		    /// \warning This operator is not a constant time function because
 		    /// it scans the whole data structure to find the proper value.
 		    Prio operator[](const Item &i) const {
 		      for (int k = 0; k < int(_first.size()); ++k) {
 		        int idx = _first[k];
 		        while (idx != -1) {
 		          if (_data[idx].item == i) {
 		            return k;
+		          }
 		          idx = _data[idx].next;
+		        }
+		      }
 		      return -1;
+		    }
 		    /// \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 idx = _iim[i];
 		      if (idx >= 0) idx = 0;
 		      return State(idx);
+		    }
 		  private:
 		    struct BucketItem {
 		      BucketItem(const Item& _item)
 		        : item(_item) {}
 		      Item item;
 		      int next;
 		    };
 		    ItemIntMap& _iim;
 		    std::vector<int> _first;
 		    std::vector<BucketItem> _data;
 		    int _free, _num;
 		    mutable int _minimum;
 		  }; // class SimpleBucketHeap
+		}
 		#endif

lemon/fib_heap.h

Show inline comments

 		/* -*- 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.
+		 *
 		 */
 		#ifndef LEMON_FIB_HEAP_H
 		#define LEMON_FIB_HEAP_H
 		///\file
 		///\ingroup heaps
 		///\brief Fibonacci heap implementation.
 		#include <vector>
 		#include <utility>
 		#include <functional>
 		#include <lemon/math.h>
 		namespace lemon {
 		  /// \ingroup heaps
 		  ///
 		  /// \brief Fibonacci heap data structure.
 		  ///
 		  /// This class implements the \e Fibonacci \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
 		  /// Fibonacci 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
 		  class FibHeap {
 		  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;
 		  private:
 		    class Store;
 		    std::vector<Store> _data;
 		    int _minimum;
 		    ItemIntMap &_iim;
 		    Compare _comp;
 		    int _num;
 		  public:
 		    /// \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.
 		    };
 		    /// \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.
 		    explicit FibHeap(ItemIntMap &map)
 		      : _minimum(0), _iim(map), _num() {}
 		    /// \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.
 		    FibHeap(ItemIntMap &map, const Compare &comp)
 		      : _minimum(0), _iim(map), _comp(comp), _num() {}
 		    /// \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; }
 		    /// \brief Check if the heap is empty.
 		    ///
 		    /// This function returns \c true if the heap is empty.
 		    bool empty() const { return _num==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(); _minimum = 0; _num = 0;
+		    }
 		    /// \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 prio The priority of the item.
 		    /// \pre \e item must not be stored in the heap.
 		    void push (const Item& item, const Prio& prio) {
 		      int i=_iim[item];
 		      if ( i < 0 ) {
 		        int s=_data.size();
 		        _iim.set( item, s );
 		        Store st;
 		        st.name=item;
 		        _data.push_back(st);
 		        i=s;
 		      } else {
 		        _data[i].parent=_data[i].child=-1;
 		        _data[i].degree=0;
 		        _data[i].in=true;
 		        _data[i].marked=false;
+		      }
 		      if ( _num ) {
 		        _data[_data[_minimum].right_neighbor].left_neighbor=i;
 		        _data[i].right_neighbor=_data[_minimum].right_neighbor;
 		        _data[_minimum].right_neighbor=i;
 		        _data[i].left_neighbor=_minimum;
 		        if ( _comp( prio, _data[_minimum].prio) ) _minimum=i;
 		      } else {
 		        _data[i].right_neighbor=_data[i].left_neighbor=i;
 		        _minimum=i;
+		      }
 		      _data[i].prio=prio;
 		      ++_num;
+		    }
 		    /// \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[_minimum].name; }
 		    /// \brief The minimum priority.
 		    ///
 		    /// This function returns the minimum priority.
 		    /// \pre The heap must be non-empty.
 		    Prio prio() const { return _data[_minimum].prio; }
 		    /// \brief Remove the item having minimum priority.
 		    ///
 		    /// This function removes the item having minimum priority.
 		    /// \pre The heap must be non-empty.
 		    void pop() {
 		      /*The first case is that there are only one root.*/
 		      if ( _data[_minimum].left_neighbor==_minimum ) {
 		        _data[_minimum].in=false;
 		        if ( _data[_minimum].degree!=0 ) {
-		          makeroot(_data[_minimum].child);
+		          makeRoot(_data[_minimum].child);
 		          _minimum=_data[_minimum].child;
 		          balance();
+		        }
 		      } else {
 		        int right=_data[_minimum].right_neighbor;
 		        unlace(_minimum);
 		        _data[_minimum].in=false;
 		        if ( _data[_minimum].degree > 0 ) {
 		          int left=_data[_minimum].left_neighbor;
 		          int child=_data[_minimum].child;
 		          int last_child=_data[child].left_neighbor;
-		          makeroot(child);
+		          makeRoot(child);
 		          _data[left].right_neighbor=child;
 		          _data[child].left_neighbor=left;
 		          _data[right].left_neighbor=last_child;
 		          _data[last_child].right_neighbor=right;
+		        }
 		        _minimum=right;
 		        balance();
 		      } // the case where there are more roots
 		      --_num;
+		    }
 		    /// \brief Remove the given item from the heap.
 		    ///
 		    /// This function removes the given item from the heap if it is
 		    /// already stored.
 		    /// \param item The item to delete.
 		    /// \pre \e item must be in the heap.
 		    void erase (const Item& item) {
 		      int i=_iim[item];
 		      if ( i >= 0 && _data[i].in ) {
 		        if ( _data[i].parent!=-1 ) {
 		          int p=_data[i].parent;
 		          cut(i,p);
 		          cascade(p);
+		        }
 		        _minimum=i;     //As if its prio would be -infinity
 		        pop();
+		      }
+		    }
 		    /// \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.
 		    Prio operator[](const Item& item) const {
 		      return _data[_iim[item]].prio;
+		    }
 		    /// \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 prio The priority.
 		    void set (const Item& item, const Prio& prio) {
 		      int i=_iim[item];
 		      if ( i >= 0 && _data[i].in ) {
 		        if ( _comp(prio, _data[i].prio) ) decrease(item, prio);
 		        if ( _comp(_data[i].prio, prio) ) increase(item, prio);
 		      } else push(item, prio);
+		    }
 		    /// \brief Decrease the priority of an item to the given value.
 		    ///
 		    /// This function decreases the priority of an item to the given value.
 		    /// \param item The item.
 		    /// \param prio The priority.
 		    /// \pre \e item must be stored in the heap with priority at least \e prio.
 		    void decrease (const Item& item, const Prio& prio) {
 		      int i=_iim[item];
 		      _data[i].prio=prio;
 		      int p=_data[i].parent;
 		      if ( p!=-1 && _comp(prio, _data[p].prio) ) {
 		        cut(i,p);
 		        cascade(p);
+		      }
 		      if ( _comp(prio, _data[_minimum].prio) ) _minimum=i;
+		    }
 		    /// \brief Increase the priority of an item to the given value.
 		    ///
 		    /// This function increases the priority of an item to the given value.
 		    /// \param item The item.
 		    /// \param prio The priority.
 		    /// \pre \e item must be stored in the heap with priority at most \e prio.
 		    void increase (const Item& item, const Prio& prio) {
 		      erase(item);
 		      push(item, prio);
+		    }
 		    /// \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 item The item.
 		    State state(const Item &item) const {
 		      int i=_iim[item];
 		      if( i>=0 ) {
 		        if ( _data[i].in ) i=0;
 		        else i=-2;
+		      }
 		      return State(i);
+		    }
 		    /// \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;
+		      }
+		    }
 		  private:
 		    void balance() {
 		      int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
 		      std::vector<int> A(maxdeg,-1);
 		      /*
 		       *Recall that now minimum does not point to the minimum prio element.
 		       *We set minimum to this during balance().
 		       */
 		      int anchor=_data[_minimum].left_neighbor;
 		      int next=_minimum;
 		      bool end=false;
 		      do {
 		        int active=next;
 		        if ( anchor==active ) end=true;
 		        int d=_data[active].degree;
 		        next=_data[active].right_neighbor;
 		        while (A[d]!=-1) {
 		          if( _comp(_data[active].prio, _data[A[d]].prio) ) {
 		            fuse(active,A[d]);
 		          } else {
 		            fuse(A[d],active);
 		            active=A[d];
+		          }
 		          A[d]=-1;
 		          ++d;
+		        }
 		        A[d]=active;
 		      } while ( !end );
 		      while ( _data[_minimum].parent >=0 )
 		        _minimum=_data[_minimum].parent;
 		      int s=_minimum;
 		      int m=_minimum;
 		      do {
 		        if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
 		        s=_data[s].right_neighbor;
 		      } while ( s != m );
+		    }
-		    void makeroot(int c) {
+		    void makeRoot(int c) {
 		      int s=c;
 		      do {
 		        _data[s].parent=-1;
 		        s=_data[s].right_neighbor;
 		      } while ( s != c );
+		    }
 		    void cut(int a, int b) {
 		      /*
 		       *Replacing a from the children of b.
 		       */
 		      --_data[b].degree;
 		      if ( _data[b].degree !=0 ) {
 		        int child=_data[b].child;
 		        if ( child==a )
 		          _data[b].child=_data[child].right_neighbor;
 		        unlace(a);
+		      }
 		      /*Lacing a to the roots.*/
 		      int right=_data[_minimum].right_neighbor;
 		      _data[_minimum].right_neighbor=a;
 		      _data[a].left_neighbor=_minimum;
 		      _data[a].right_neighbor=right;
 		      _data[right].left_neighbor=a;
 		      _data[a].parent=-1;
 		      _data[a].marked=false;
+		    }
 		    void cascade(int a) {
 		      if ( _data[a].parent!=-1 ) {
 		        int p=_data[a].parent;
 		        if ( _data[a].marked==false ) _data[a].marked=true;
 		        else {
 		          cut(a,p);
 		          cascade(p);
+		        }
+		      }
+		    }
 		    void fuse(int a, int b) {
 		      unlace(b);
 		      /*Lacing b under a.*/
 		      _data[b].parent=a;
 		      if (_data[a].degree==0) {
 		        _data[b].left_neighbor=b;
 		        _data[b].right_neighbor=b;
 		        _data[a].child=b;
 		      } else {
 		        int child=_data[a].child;
 		        int last_child=_data[child].left_neighbor;
 		        _data[child].left_neighbor=b;
 		        _data[b].right_neighbor=child;
 		        _data[last_child].right_neighbor=b;
 		        _data[b].left_neighbor=last_child;
+		      }
 		      ++_data[a].degree;
 		      _data[b].marked=false;
+		    }
 		    /*
 		     *It is invoked only if a has siblings.
 		     */
 		    void unlace(int a) {
 		      int leftn=_data[a].left_neighbor;
 		      int rightn=_data[a].right_neighbor;
 		      _data[leftn].right_neighbor=rightn;
 		      _data[rightn].left_neighbor=leftn;
+		    }
 		    class Store {
 		      friend class FibHeap;
 		      Item name;
 		      int parent;
 		      int left_neighbor;
 		      int right_neighbor;
 		      int child;
 		      int degree;
 		      bool marked;
 		      bool in;
 		      Prio prio;
 		      Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
 		    };
 		  };
 		} //namespace lemon
 		#endif //LEMON_FIB_HEAP_H

lemon/radix_heap.h

Show inline comments

 		/* -*- 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.
+		 *
 		 */
 		#ifndef LEMON_RADIX_HEAP_H
 		#define LEMON_RADIX_HEAP_H
 		///\ingroup heaps
 		///\file
 		///\brief Radix heap implementation.
 		#include <vector>
 		#include <lemon/error.h>
 		namespace lemon {
 		  /// \ingroup heaps
 		  ///
 		  /// \brief Radix heap data structure.
 		  ///
 		  /// This class implements the \e radix \e heap data structure.
 		  /// It practically conforms to the \ref concepts::Heap "heap concept",
 		  /// but it has some limitations due its special implementation.
 		  /// The type of the priorities must be \c int and the priority of an
 		  /// item cannot be decreased under the priority of the last removed item.
 		  ///
 		  /// \tparam IM A read-writable item map with \c int values, used
 		  /// internally to handle the cross references.
 		  template <typename IM>
 		  class RadixHeap {
 		  public:
 		    /// Type of the item-int map.
 		    typedef IM ItemIntMap;
 		    /// Type of the priorities.
 		    typedef int Prio;
 		    /// Type of the items stored in the heap.
 		    typedef typename ItemIntMap::Key Item;
 		    /// \brief Exception thrown by RadixHeap.
 		    ///
 		    /// This exception is thrown when an item is inserted into a
 		    /// RadixHeap with a priority smaller than the last erased one.
 		    /// \see RadixHeap
-		    class UnderFlowPriorityError : public Exception {
+		    class PriorityUnderflowError : public Exception {
 		    public:
 		      virtual const char* what() const throw() {
-		        return "lemon::RadixHeap::UnderFlowPriorityError";
+		        return "lemon::RadixHeap::PriorityUnderflowError";
+		      }
 		    };
 		    /// \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:
 		    struct RadixItem {
 		      int prev, next, box;
 		      Item item;
 		      int prio;
 		      RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
 		    };
 		    struct RadixBox {
 		      int first;
 		      int min, size;
 		      RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
 		    };
 		    std::vector<RadixItem> data;
 		    std::vector<RadixBox> boxes;
 		    std::vector<RadixItem> _data;
 		    std::vector<RadixBox> _boxes;
 		    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.
 		    /// \param minimum The initial minimum value of the heap.
 		    /// \param capacity The initial capacity of the heap.
 		    RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0)
 		      : _iim(map)
+		    {
 		      boxes.push_back(RadixBox(minimum, 1));
 		      boxes.push_back(RadixBox(minimum + 1, 1));
-		      while (lower(boxes.size() - 1, capacity + minimum - 1)) {
+		      _boxes.push_back(RadixBox(minimum, 1));
 		      _boxes.push_back(RadixBox(minimum + 1, 1));
 		      while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
 		        extend();
+		      }
+		    }
 		    /// \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(); }
+		    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(); }
+		    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.
 		    /// \param minimum The minimum value of the heap.
 		    /// \param capacity The capacity of the heap.
 		    void clear(int minimum = 0, int capacity = 0) {
 		      data.clear(); boxes.clear();
 		      boxes.push_back(RadixBox(minimum, 1));
 		      boxes.push_back(RadixBox(minimum + 1, 1));
 		      while (lower(boxes.size() - 1, capacity + minimum - 1)) {
 		      _data.clear(); _boxes.clear();
 		      _boxes.push_back(RadixBox(minimum, 1));
 		      _boxes.push_back(RadixBox(minimum + 1, 1));
 		      while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
 		        extend();
+		      }
+		    }
 		  private:
 		    bool upper(int box, Prio pr) {
-		      return pr < boxes[box].min;
+		      return pr < _boxes[box].min;
+		    }
 		    bool lower(int box, Prio pr) {
-		      return pr >= boxes[box].min + boxes[box].size;
+		      return pr >= _boxes[box].min + _boxes[box].size;
+		    }
 		    // Remove item from the box list
 		    void remove(int index) {
 		      if (data[index].prev >= 0) {
 		        data[data[index].prev].next = data[index].next;
 		      if (_data[index].prev >= 0) {
 		        _data[_data[index].prev].next = _data[index].next;
 		      } else {
-		        boxes[data[index].box].first = data[index].next;
+		        _boxes[_data[index].box].first = _data[index].next;
+		      }
 		      if (data[index].next >= 0) {
 		        data[data[index].next].prev = data[index].prev;
 		      if (_data[index].next >= 0) {
 		        _data[_data[index].next].prev = _data[index].prev;
+		      }
+		    }
 		    // Insert item into the box list
 		    void insert(int box, int index) {
 		      if (boxes[box].first == -1) {
 		        boxes[box].first = index;
-		        data[index].next = data[index].prev = -1;
+		      if (_boxes[box].first == -1) {
 		        _boxes[box].first = index;
 		        _data[index].next = _data[index].prev = -1;
 		      } else {
 		        data[index].next = boxes[box].first;
 		        data[boxes[box].first].prev = index;
 		        data[index].prev = -1;
 		        boxes[box].first = index;
 		        _data[index].next = _boxes[box].first;
 		        _data[_boxes[box].first].prev = index;
 		        _data[index].prev = -1;
 		        _boxes[box].first = index;
+		      }
-		      data[index].box = box;
+		      _data[index].box = box;
+		    }
 		    // Add a new box to the box list
 		    void extend() {
 		      int min = boxes.back().min + boxes.back().size;
 		      int bs = 2 * boxes.back().size;
-		      boxes.push_back(RadixBox(min, bs));
+		      int min = _boxes.back().min + _boxes.back().size;
 		      int bs = 2 * _boxes.back().size;
 		      _boxes.push_back(RadixBox(min, bs));
+		    }
 		    // Move an item up into the proper box.
 		    void bubble_up(int index) {
 		      if (!lower(data[index].box, data[index].prio)) return;
 		    void bubbleUp(int index) {
 		      if (!lower(_data[index].box, _data[index].prio)) return;
 		      remove(index);
-		      int box = findUp(data[index].box, data[index].prio);
+		      int box = findUp(_data[index].box, _data[index].prio);
 		      insert(box, index);
+		    }
 		    // Find up the proper box for the item with the given priority
 		    int findUp(int start, int pr) {
 		      while (lower(start, pr)) {
-		        if (++start == int(boxes.size())) {
+		        if (++start == int(_boxes.size())) {
 		          extend();
+		        }
+		      }
 		      return start;
+		    }
 		    // Move an item down into the proper box
 		    void bubble_down(int index) {
 		      if (!upper(data[index].box, data[index].prio)) return;
 		    void bubbleDown(int index) {
 		      if (!upper(_data[index].box, _data[index].prio)) return;
 		      remove(index);
-		      int box = findDown(data[index].box, data[index].prio);
+		      int box = findDown(_data[index].box, _data[index].prio);
 		      insert(box, index);
+		    }
 		    // Find down the proper box for the item with the given priority
 		    int findDown(int start, int pr) {
 		      while (upper(start, pr)) {
-		        if (--start < 0) throw UnderFlowPriorityError();
+		        if (--start < 0) throw PriorityUnderflowError();
+		      }
 		      return start;
+		    }
 		    // Find the first non-empty box
 		    int findFirst() {
 		      int first = 0;
-		      while (boxes[first].first == -1) ++first;
+		      while (_boxes[first].first == -1) ++first;
 		      return first;
+		    }
 		    // Gives back the minimum priority of the given box
 		    int minValue(int box) {
 		      int min = data[boxes[box].first].prio;
 		      for (int k = boxes[box].first; k != -1; k = data[k].next) {
-		        if (data[k].prio < min) min = data[k].prio;
+		      int min = _data[_boxes[box].first].prio;
 		      for (int k = _boxes[box].first; k != -1; k = _data[k].next) {
 		        if (_data[k].prio < min) min = _data[k].prio;
+		      }
 		      return min;
+		    }
 		    // Rearrange the items of the heap and make the first box non-empty
 		    void moveDown() {
 		      int box = findFirst();
 		      if (box == 0) return;
 		      int min = minValue(box);
 		      for (int i = 0; i <= box; ++i) {
 		        boxes[i].min = min;
 		        min += boxes[i].size;
 		        _boxes[i].min = min;
 		        min += _boxes[i].size;
+		      }
-		      int curr = boxes[box].first, next;
+		      int curr = _boxes[box].first, next;
 		      while (curr != -1) {
 		        next = data[curr].next;
 		        bubble_down(curr);
 		        next = _data[curr].next;
 		        bubbleDown(curr);
 		        curr = next;
+		      }
+		    }
 		    void relocate_last(int index) {
 		      if (index != int(data.size()) - 1) {
 		        data[index] = data.back();
 		        if (data[index].prev != -1) {
-		          data[data[index].prev].next = index;
+		    void relocateLast(int index) {
 		      if (index != int(_data.size()) - 1) {
 		        _data[index] = _data.back();
 		        if (_data[index].prev != -1) {
 		          _data[_data[index].prev].next = index;
 		        } else {
-		          boxes[data[index].box].first = index;
+		          _boxes[_data[index].box].first = index;
+		        }
 		        if (data[index].next != -1) {
 		          data[data[index].next].prev = index;
 		        if (_data[index].next != -1) {
 		          _data[_data[index].next].prev = index;
+		        }
-		        _iim[data[index].item] = index;
+		        _iim[_data[index].item] = index;
+		      }
-		      data.pop_back();
+		      _data.pop_back();
+		    }
 		  public:
 		    /// \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.
 		    /// \warning This method may throw an \c UnderFlowPriorityException.
 		    void push(const Item &i, const Prio &p) {
-		      int n = data.size();
+		      int n = _data.size();
 		      _iim.set(i, n);
 		      data.push_back(RadixItem(i, p));
 		      while (lower(boxes.size() - 1, p)) {
 		      _data.push_back(RadixItem(i, p));
 		      while (lower(_boxes.size() - 1, p)) {
 		        extend();
+		      }
-		      int box = findDown(boxes.size() - 1, p);
+		      int box = findDown(_boxes.size() - 1, p);
 		      insert(box, n);
+		    }
 		    /// \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 {
 		      const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
-		      return data[boxes[0].first].item;
+		      return _data[_boxes[0].first].item;
+		    }
 		    /// \brief The minimum priority.
 		    ///
 		    /// This function returns the minimum priority.
 		    /// \pre The heap must be non-empty.
 		    Prio prio() const {
 		      const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
-		      return data[boxes[0].first].prio;
+		      return _data[_boxes[0].first].prio;
+		     }
 		    /// \brief Remove the item having minimum priority.
 		    ///
 		    /// This function removes the item having minimum priority.
 		    /// \pre The heap must be non-empty.
 		    void pop() {
 		      moveDown();
 		      int index = boxes[0].first;
 		      _iim[data[index].item] = POST_HEAP;
 		      int index = _boxes[0].first;
 		      _iim[_data[index].item] = POST_HEAP;
 		      remove(index);
-		      relocate_last(index);
+		      relocateLast(index);
+		    }
 		    /// \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 index = _iim[i];
 		      _iim[i] = POST_HEAP;
 		      remove(index);
-		      relocate_last(index);
+		      relocateLast(index);
+		   }
 		    /// \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].prio;
+		      return _data[idx].prio;
+		    }
 		    /// \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.
 		    /// \pre \e i must be in the heap.
 		    /// \warning This method may throw an \c UnderFlowPriorityException.
 		    void set(const Item &i, const Prio &p) {
 		      int idx = _iim[i];
 		      if( idx < 0 ) {
 		        push(i, p);
+		      }
 		      else if( p >= data[idx].prio ) {
 		        data[idx].prio = p;
-		        bubble_up(idx);
+		      else if( p >= _data[idx].prio ) {
 		        _data[idx].prio = p;
 		        bubbleUp(idx);
 		      } else {
 		        data[idx].prio = p;
 		        bubble_down(idx);
 		        _data[idx].prio = p;
 		        bubbleDown(idx);
+		      }
+		    }
 		    /// \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.
 		    /// \warning This method may throw an \c UnderFlowPriorityException.
 		    void decrease(const Item &i, const Prio &p) {
 		      int idx = _iim[i];
 		      data[idx].prio = p;
 		      bubble_down(idx);
 		      _data[idx].prio = p;
 		      bubbleDown(idx);
+		    }
 		    /// \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];
 		      data[idx].prio = p;
 		      bubble_up(idx);
 		      _data[idx].prio = p;
 		      bubbleUp(idx);
+		    }
 		    /// \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;
+		      }
+		    }
 		  }; // class RadixHeap
 		} // namespace lemon
 		#endif // LEMON_RADIX_HEAP_H

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