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  • lemon/bin_heap.h

    r463 r758  
    2020#define LEMON_BIN_HEAP_H
    2121
    22 ///\ingroup auxdat
     22///\ingroup heaps
    2323///\file
    24 ///\brief Binary Heap implementation.
     24///\brief Binary heap implementation.
    2525
    2626#include <vector>
    … …  
    3030namespace lemon {
    3131
    32   ///\ingroup auxdat
     32  /// \ingroup heaps
    3333  ///
    34   ///\brief A Binary Heap implementation.
     34  /// \brief Binary heap data structure.
    3535  ///
    36   ///This class implements the \e binary \e heap data structure. A \e heap
    37   ///is a data structure for storing items with specified values called \e
    38   ///priorities in such a way that finding the item with minimum priority is
    39   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
    40   ///one can change the priority of an item, add or erase an item, etc.
     36  /// This class implements the \e binary \e heap data structure.
     37  /// It fully conforms to the \ref concepts::Heap "heap concept".
    4138  ///
    42   ///\tparam _Prio Type of the priority of the items.
    43   ///\tparam _ItemIntMap A read and writable Item int map, used internally
    44   ///to handle the cross references.
    45   ///\tparam _Compare A class for the ordering of the priorities. The
    46   ///default is \c std::less<_Prio>.
    47   ///
    48   ///\sa FibHeap
    49   ///\sa Dijkstra
    50   template <typename _Prio, typename _ItemIntMap,
    51             typename _Compare = std::less<_Prio> >
     39  /// \tparam PR Type of the priorities of the items.
     40  /// \tparam IM A read-writable item map with \c int values, used
     41  /// internally to handle the cross references.
     42  /// \tparam CMP A functor class for comparing the priorities.
     43  /// The default is \c std::less<PR>.
     44#ifdef DOXYGEN
     45  template <typename PR, typename IM, typename CMP>
     46#else
     47  template <typename PR, typename IM, typename CMP = std::less<PR> >
     48#endif
    5249  class BinHeap {
    53 
    5450  public:
    55     ///\e
    56     typedef _ItemIntMap ItemIntMap;
    57     ///\e
    58     typedef _Prio Prio;
    59     ///\e
     51
     52    /// Type of the item-int map.
     53    typedef IM ItemIntMap;
     54    /// Type of the priorities.
     55    typedef PR Prio;
     56    /// Type of the items stored in the heap.
    6057    typedef typename ItemIntMap::Key Item;
    61     ///\e
     58    /// Type of the item-priority pairs.
    6259    typedef std::pair<Item,Prio> Pair;
    63     ///\e
    64     typedef _Compare Compare;
    65 
    66     /// \brief Type to represent the items states.
    67     ///
    68     /// Each Item element have a state associated to it. It may be "in heap",
    69     /// "pre heap" or "post heap". The latter two are indifferent from the
     60    /// Functor type for comparing the priorities.
     61    typedef CMP Compare;
     62
     63    /// \brief Type to represent the states of the items.
     64    ///
     65    /// Each item has a state associated to it. It can be "in heap",
     66    /// "pre-heap" or "post-heap". The latter two are indifferent from the
    7067    /// heap's point of view, but may be useful to the user.
    7168    ///
    72     /// The ItemIntMap \e should be initialized in such way that it maps
    73     /// PRE_HEAP (-1) to any element to be put in the heap...
     69    /// The item-int map must be initialized in such way that it assigns
     70    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    7471    enum State {
    75       IN_HEAP = 0,
    76       PRE_HEAP = -1,
    77       POST_HEAP = -2
     72      IN_HEAP = 0,    ///< = 0.
     73      PRE_HEAP = -1,  ///< = -1.
     74      POST_HEAP = -2  ///< = -2.
    7875    };
    7976
    8077  private:
    81     std::vector<Pair> data;
    82     Compare comp;
    83     ItemIntMap &iim;
     78    std::vector<Pair> _data;
     79    Compare _comp;
     80    ItemIntMap &_iim;
    8481
    8582  public:
    86     /// \brief The constructor.
    87     ///
    88     /// The constructor.
    89     /// \param _iim should be given to the constructor, since it is used
    90     /// internally to handle the cross references. The value of the map
    91     /// should be PRE_HEAP (-1) for each element.
    92     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
    93 
    94     /// \brief The constructor.
    95     ///
    96     /// The constructor.
    97     /// \param _iim should be given to the constructor, since it is used
    98     /// internally to handle the cross references. The value of the map
    99     /// should be PRE_HEAP (-1) for each element.
    100     ///
    101     /// \param _comp The comparator function object.
    102     BinHeap(ItemIntMap &_iim, const Compare &_comp)
    103       : iim(_iim), comp(_comp) {}
    104 
    105 
    106     /// The number of items stored in the heap.
    107     ///
    108     /// \brief Returns the number of items stored in the heap.
    109     int size() const { return data.size(); }
    110 
    111     /// \brief Checks if the heap stores no items.
    112     ///
    113     /// Returns \c true if and only if the heap stores no items.
    114     bool empty() const { return data.empty(); }
    115 
    116     /// \brief Make empty this heap.
    117     ///
    118     /// Make empty this heap. It does not change the cross reference map.
    119     /// If you want to reuse what is not surely empty you should first clear
    120     /// the heap and after that you should set the cross reference map for
    121     /// each item to \c PRE_HEAP.
     83
     84    /// \brief Constructor.
     85    ///
     86    /// Constructor.
     87    /// \param map A map that assigns \c int values to the items.
     88    /// It is used internally to handle the cross references.
     89    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
     90    explicit BinHeap(ItemIntMap &map) : _iim(map) {}
     91
     92    /// \brief Constructor.
     93    ///
     94    /// Constructor.
     95    /// \param map A map that assigns \c int values to the items.
     96    /// It is used internally to handle the cross references.
     97    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
     98    /// \param comp The function object used for comparing the priorities.
     99    BinHeap(ItemIntMap &map, const Compare &comp)
     100      : _iim(map), _comp(comp) {}
     101
     102
     103    /// \brief The number of items stored in the heap.
     104    ///
     105    /// This function returns the number of items stored in the heap.
     106    int size() const { return _data.size(); }
     107
     108    /// \brief Check if the heap is empty.
     109    ///
     110    /// This function returns \c true if the heap is empty.
     111    bool empty() const { return _data.empty(); }
     112
     113    /// \brief Make the heap empty.
     114    ///
     115    /// This functon makes the heap empty.
     116    /// It does not change the cross reference map. If you want to reuse
     117    /// a heap that is not surely empty, you should first clear it and
     118    /// then you should set the cross reference map to \c PRE_HEAP
     119    /// for each item.
    122120    void clear() {
    123       data.clear();
     121      _data.clear();
    124122    }
    125123
    … …  
    127125    static int parent(int i) { return (i-1)/2; }
    128126
    129     static int second_child(int i) { return 2*i+2; }
     127    static int secondChild(int i) { return 2*i+2; }
    130128    bool less(const Pair &p1, const Pair &p2) const {
    131       return comp(p1.second, p2.second);
    132     }
    133 
    134     int bubble_up(int hole, Pair p) {
     129      return _comp(p1.second, p2.second);
     130    }
     131
     132    int bubbleUp(int hole, Pair p) {
    135133      int par = parent(hole);
    136       while( hole>0 && less(p,data[par]) ) {
    137         move(data[par],hole);
     134      while( hole>0 && less(p,_data[par]) ) {
     135        move(_data[par],hole);
    138136        hole = par;
    139137        par = parent(hole);
    … …  
    143141    }
    144142
    145     int bubble_down(int hole, Pair p, int length) {
    146       int child = second_child(hole);
     143    int bubbleDown(int hole, Pair p, int length) {
     144      int child = secondChild(hole);
    147145      while(child < length) {
    148         if( less(data[child-1], data[child]) ) {
     146        if( less(_data[child-1], _data[child]) ) {
    149147          --child;
    150148        }
    151         if( !less(data[child], p) )
     149        if( !less(_data[child], p) )
    152150          goto ok;
    153         move(data[child], hole);
     151        move(_data[child], hole);
    154152        hole = child;
    155         child = second_child(hole);
     153        child = secondChild(hole);
    156154      }
    157155      child--;
    158       if( child<length && less(data[child], p) ) {
    159         move(data[child], hole);
     156      if( child<length && less(_data[child], p) ) {
     157        move(_data[child], hole);
    160158        hole=child;
    161159      }
    … …  
    166164
    167165    void move(const Pair &p, int i) {
    168       data[i] = p;
    169       iim.set(p.first, i);
     166      _data[i] = p;
     167      _iim.set(p.first, i);
    170168    }
    171169
    172170  public:
     171
    173172    /// \brief Insert a pair of item and priority into the heap.
    174173    ///
    175     /// Adds \c p.first to the heap with priority \c p.second.
     174    /// This function inserts \c p.first to the heap with priority
     175    /// \c p.second.
    176176    /// \param p The pair to insert.
     177    /// \pre \c p.first must not be stored in the heap.
    177178    void push(const Pair &p) {
    178       int n = data.size();
    179       data.resize(n+1);
    180       bubble_up(n, p);
    181     }
    182 
    183     /// \brief Insert an item into the heap with the given heap.
    184     ///
    185     /// Adds \c i to the heap with priority \c p.
     179      int n = _data.size();
     180      _data.resize(n+1);
     181      bubbleUp(n, p);
     182    }
     183
     184    /// \brief Insert an item into the heap with the given priority.
     185    ///
     186    /// This function inserts the given item into the heap with the
     187    /// given priority.
    186188    /// \param i The item to insert.
    187189    /// \param p The priority of the item.
     190    /// \pre \e i must not be stored in the heap.
    188191    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
    189192
    190     /// \brief Returns the item with minimum priority relative to \c Compare.
    191     ///
    192     /// This method returns the item with minimum priority relative to \c
    193     /// Compare.
    194     /// \pre The heap must be nonempty.
     193    /// \brief Return the item having minimum priority.
     194    ///
     195    /// This function returns the item having minimum priority.
     196    /// \pre The heap must be non-empty.
    195197    Item top() const {
    196       return data[0].first;
    197     }
    198 
    199     /// \brief Returns the minimum priority relative to \c Compare.
    200     ///
    201     /// It returns the minimum priority relative to \c Compare.
    202     /// \pre The heap must be nonempty.
     198      return _data[0].first;
     199    }
     200
     201    /// \brief The minimum priority.
     202    ///
     203    /// This function returns the minimum priority.
     204    /// \pre The heap must be non-empty.
    203205    Prio prio() const {
    204       return data[0].second;
    205     }
    206 
    207     /// \brief Deletes the item with minimum priority relative to \c Compare.
    208     ///
    209     /// This method deletes the item with minimum priority relative to \c
    210     /// Compare from the heap.
     206      return _data[0].second;
     207    }
     208
     209    /// \brief Remove the item having minimum priority.
     210    ///
     211    /// This function removes the item having minimum priority.
    211212    /// \pre The heap must be non-empty.
    212213    void pop() {
    213       int n = data.size()-1;
    214       iim.set(data[0].first, POST_HEAP);
     214      int n = _data.size()-1;
     215      _iim.set(_data[0].first, POST_HEAP);
    215216      if (n > 0) {
    216         bubble_down(0, data[n], n);
    217       }
    218       data.pop_back();
    219     }
    220 
    221     /// \brief Deletes \c i from the heap.
    222     ///
    223     /// This method deletes item \c i from the heap.
    224     /// \param i The item to erase.
    225     /// \pre The item should be in the heap.
     217        bubbleDown(0, _data[n], n);
     218      }
     219      _data.pop_back();
     220    }
     221
     222    /// \brief Remove the given item from the heap.
     223    ///
     224    /// This function removes the given item from the heap if it is
     225    /// already stored.
     226    /// \param i The item to delete.
     227    /// \pre \e i must be in the heap.
    226228    void erase(const Item &i) {
    227       int h = iim[i];
    228       int n = data.size()-1;
    229       iim.set(data[h].first, POST_HEAP);
     229      int h = _iim[i];
     230      int n = _data.size()-1;
     231      _iim.set(_data[h].first, POST_HEAP);
    230232      if( h < n ) {
    231         if ( bubble_up(h, data[n]) == h) {
    232           bubble_down(h, data[n], n);
     233        if ( bubbleUp(h, _data[n]) == h) {
     234          bubbleDown(h, _data[n], n);
    233235        }
    234236      }
    235       data.pop_back();
    236     }
    237 
    238 
    239     /// \brief Returns the priority of \c i.
    240     ///
    241     /// This function returns the priority of item \c i.
    242     /// \pre \c i must be in the heap.
    243     /// \param i The item.
     237      _data.pop_back();
     238    }
     239
     240    /// \brief The priority of the given item.
     241    ///
     242    /// This function returns the priority of the given item.
     243    /// \param i The item.
     244    /// \pre \e i must be in the heap.
    244245    Prio operator[](const Item &i) const {
    245       int idx = iim[i];
    246       return data[idx].second;
    247     }
    248 
    249     /// \brief \c i gets to the heap with priority \c p independently
    250     /// if \c i was already there.
    251     ///
    252     /// This method calls \ref push(\c i, \c p) if \c i is not stored
    253     /// in the heap and sets the priority of \c i to \c p otherwise.
     246      int idx = _iim[i];
     247      return _data[idx].second;
     248    }
     249
     250    /// \brief Set the priority of an item or insert it, if it is
     251    /// not stored in the heap.
     252    ///
     253    /// This method sets the priority of the given item if it is
     254    /// already stored in the heap. Otherwise it inserts the given
     255    /// item into the heap with the given priority.
    254256    /// \param i The item.
    255257    /// \param p The priority.
    256258    void set(const Item &i, const Prio &p) {
    257       int idx = iim[i];
     259      int idx = _iim[i];
    258260      if( idx < 0 ) {
    259261        push(i,p);
    260262      }
    261       else if( comp(p, data[idx].second) ) {
    262         bubble_up(idx, Pair(i,p));
     263      else if( _comp(p, _data[idx].second) ) {
     264        bubbleUp(idx, Pair(i,p));
    263265      }
    264266      else {
    265         bubble_down(idx, Pair(i,p), data.size());
    266       }
    267     }
    268 
    269     /// \brief Decreases the priority of \c i to \c p.
    270     ///
    271     /// This method decreases the priority of item \c i to \c p.
    272     /// \pre \c i must be stored in the heap with priority at least \c
    273     /// p relative to \c Compare.
     267        bubbleDown(idx, Pair(i,p), _data.size());
     268      }
     269    }
     270
     271    /// \brief Decrease the priority of an item to the given value.
     272    ///
     273    /// This function decreases the priority of an item to the given value.
    274274    /// \param i The item.
    275275    /// \param p The priority.
     276    /// \pre \e i must be stored in the heap with priority at least \e p.
    276277    void decrease(const Item &i, const Prio &p) {
    277       int idx = iim[i];
    278       bubble_up(idx, Pair(i,p));
    279     }
    280 
    281     /// \brief Increases the priority of \c i to \c p.
    282     ///
    283     /// This method sets the priority of item \c i to \c p.
    284     /// \pre \c i must be stored in the heap with priority at most \c
    285     /// p relative to \c Compare.
     278      int idx = _iim[i];
     279      bubbleUp(idx, Pair(i,p));
     280    }
     281
     282    /// \brief Increase the priority of an item to the given value.
     283    ///
     284    /// This function increases the priority of an item to the given value.
    286285    /// \param i The item.
    287286    /// \param p The priority.
     287    /// \pre \e i must be stored in the heap with priority at most \e p.
    288288    void increase(const Item &i, const Prio &p) {
    289       int idx = iim[i];
    290       bubble_down(idx, Pair(i,p), data.size());
    291     }
    292 
    293     /// \brief Returns if \c item is in, has already been in, or has
    294     /// never been in the heap.
    295     ///
    296     /// This method returns PRE_HEAP if \c item has never been in the
    297     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
    298     /// otherwise. In the latter case it is possible that \c item will
    299     /// get back to the heap again.
     289      int idx = _iim[i];
     290      bubbleDown(idx, Pair(i,p), _data.size());
     291    }
     292
     293    /// \brief Return the state of an item.
     294    ///
     295    /// This method returns \c PRE_HEAP if the given item has never
     296    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
     297    /// and \c POST_HEAP otherwise.
     298    /// In the latter case it is possible that the item will get back
     299    /// to the heap again.
    300300    /// \param i The item.
    301301    State state(const Item &i) const {
    302       int s = iim[i];
     302      int s = _iim[i];
    303303      if( s>=0 )
    304304        s=0;
    … …  
    306306    }
    307307
    308     /// \brief Sets the state of the \c item in the heap.
    309     ///
    310     /// Sets the state of the \c item in the heap. It can be used to
    311     /// manually clear the heap when it is important to achive the
    312     /// better time complexity.
     308    /// \brief Set the state of an item in the heap.
     309    ///
     310    /// This function sets the state of the given item in the heap.
     311    /// It can be used to manually clear the heap when it is important
     312    /// to achive better time complexity.
    313313    /// \param i The item.
    314314    /// \param st The state. It should not be \c IN_HEAP.
    … …  
    320320          erase(i);
    321321        }
    322         iim[i] = st;
     322        _iim[i] = st;
    323323        break;
    324324      case IN_HEAP:
    … …  
    327327    }
    328328
    329     /// \brief Replaces an item in the heap.
    330     ///
    331     /// The \c i item is replaced with \c j item. The \c i item should
    332     /// be in the heap, while the \c j should be out of the heap. The
    333     /// \c i item will out of the heap and \c j will be in the heap
    334     /// with the same prioriority as prevoiusly the \c i item.
     329    /// \brief Replace an item in the heap.
     330    ///
     331    /// This function replaces item \c i with item \c j.
     332    /// Item \c i must be in the heap, while \c j must be out of the heap.
     333    /// After calling this method, item \c i will be out of the
     334    /// heap and \c j will be in the heap with the same prioriority
     335    /// as item \c i had before.
    335336    void replace(const Item& i, const Item& j) {
    336       int idx = iim[i];
    337       iim.set(i, iim[j]);
    338       iim.set(j, idx);
    339       data[idx].first = j;
     337      int idx = _iim[i];
     338      _iim.set(i, _iim[j]);
     339      _iim.set(j, idx);
     340      _data[idx].first = j;
    340341    }
    341342
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