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  • lemon/bin_heap.h

    r758 r209  
    33 * This file is a part of LEMON, a generic C++ optimization library.
    44 *
    5  * Copyright (C) 2003-2009
     5 * Copyright (C) 2003-2008
    66 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    77 * (Egervary Research Group on Combinatorial Optimization, EGRES).
    … …  
    2020#define LEMON_BIN_HEAP_H
    2121
    22 ///\ingroup heaps
     22///\ingroup auxdat
    2323///\file
    24 ///\brief Binary heap implementation.
     24///\brief Binary Heap implementation.
    2525
    2626#include <vector>
    … …  
    3030namespace lemon {
    3131
    32   /// \ingroup heaps
     32  ///\ingroup auxdat
    3333  ///
    34   /// \brief Binary heap data structure.
     34  ///\brief A Binary Heap implementation.
    3535  ///
    36   /// This class implements the \e binary \e heap data structure.
    37   /// It fully conforms to the \ref concepts::Heap "heap concept".
     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.
    3841  ///
    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
     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> >
    4952  class BinHeap {
     53
    5054  public:
    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.
     55    ///\e
     56    typedef _ItemIntMap ItemIntMap;
     57    ///\e
     58    typedef _Prio Prio;
     59    ///\e
    5760    typedef typename ItemIntMap::Key Item;
    58     /// Type of the item-priority pairs.
     61    ///\e
    5962    typedef std::pair<Item,Prio> Pair;
    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
     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
    6770    /// heap's point of view, but may be useful to the user.
    6871    ///
    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.
     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...
    7174    enum State {
    72       IN_HEAP = 0,    ///< = 0.
    73       PRE_HEAP = -1,  ///< = -1.
    74       POST_HEAP = -2  ///< = -2.
     75      IN_HEAP = 0,
     76      PRE_HEAP = -1,
     77      POST_HEAP = -2
    7578    };
    7679
    7780  private:
    78     std::vector<Pair> _data;
    79     Compare _comp;
    80     ItemIntMap &_iim;
     81    std::vector<Pair> data;
     82    Compare comp;
     83    ItemIntMap &iim;
    8184
    8285  public:
    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.
     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.
    120122    void clear() {
    121       _data.clear();
     123      data.clear();
    122124    }
    123125
    … …  
    125127    static int parent(int i) { return (i-1)/2; }
    126128
    127     static int secondChild(int i) { return 2*i+2; }
     129    static int second_child(int i) { return 2*i+2; }
    128130    bool less(const Pair &p1, const Pair &p2) const {
    129       return _comp(p1.second, p2.second);
    130     }
    131 
    132     int bubbleUp(int hole, Pair p) {
     131      return comp(p1.second, p2.second);
     132    }
     133
     134    int bubble_up(int hole, Pair p) {
    133135      int par = parent(hole);
    134       while( hole>0 && less(p,_data[par]) ) {
    135         move(_data[par],hole);
     136      while( hole>0 && less(p,data[par]) ) {
     137        move(data[par],hole);
    136138        hole = par;
    137139        par = parent(hole);
    … …  
    141143    }
    142144
    143     int bubbleDown(int hole, Pair p, int length) {
    144       int child = secondChild(hole);
     145    int bubble_down(int hole, Pair p, int length) {
     146      int child = second_child(hole);
    145147      while(child < length) {
    146         if( less(_data[child-1], _data[child]) ) {
     148        if( less(data[child-1], data[child]) ) {
    147149          --child;
    148150        }
    149         if( !less(_data[child], p) )
     151        if( !less(data[child], p) )
    150152          goto ok;
    151         move(_data[child], hole);
     153        move(data[child], hole);
    152154        hole = child;
    153         child = secondChild(hole);
     155        child = second_child(hole);
    154156      }
    155157      child--;
    156       if( child<length && less(_data[child], p) ) {
    157         move(_data[child], hole);
     158      if( child<length && less(data[child], p) ) {
     159        move(data[child], hole);
    158160        hole=child;
    159161      }
    … …  
    164166
    165167    void move(const Pair &p, int i) {
    166       _data[i] = p;
    167       _iim.set(p.first, i);
     168      data[i] = p;
     169      iim.set(p.first, i);
    168170    }
    169171
    170172  public:
    171 
    172173    /// \brief Insert a pair of item and priority into the heap.
    173174    ///
    174     /// This function inserts \c p.first to the heap with priority
    175     /// \c p.second.
     175    /// Adds \c p.first to the heap with priority \c p.second.
    176176    /// \param p The pair to insert.
    177     /// \pre \c p.first must not be stored in the heap.
    178177    void push(const Pair &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.
     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.
    188186    /// \param i The item to insert.
    189187    /// \param p The priority of the item.
    190     /// \pre \e i must not be stored in the heap.
    191188    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
    192189
    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.
     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.
    197195    Item top() const {
    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.
     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.
    205203    Prio prio() const {
    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.
     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.
    212211    /// \pre The heap must be non-empty.
    213212    void pop() {
    214       int n = _data.size()-1;
    215       _iim.set(_data[0].first, POST_HEAP);
     213      int n = data.size()-1;
     214      iim.set(data[0].first, POST_HEAP);
    216215      if (n > 0) {
    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.
     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.
    228226    void erase(const Item &i) {
    229       int h = _iim[i];
    230       int n = _data.size()-1;
    231       _iim.set(_data[h].first, POST_HEAP);
     227      int h = iim[i];
     228      int n = data.size()-1;
     229      iim.set(data[h].first, POST_HEAP);
    232230      if( h < n ) {
    233         if ( bubbleUp(h, _data[n]) == h) {
    234           bubbleDown(h, _data[n], n);
     231        if ( bubble_up(h, data[n]) == h) {
     232          bubble_down(h, data[n], n);
    235233        }
    236234      }
    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.
     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.
    245244    Prio operator[](const Item &i) const {
    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.
     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.
    256254    /// \param i The item.
    257255    /// \param p The priority.
    258256    void set(const Item &i, const Prio &p) {
    259       int idx = _iim[i];
     257      int idx = iim[i];
    260258      if( idx < 0 ) {
    261259        push(i,p);
    262260      }
    263       else if( _comp(p, _data[idx].second) ) {
    264         bubbleUp(idx, Pair(i,p));
     261      else if( comp(p, data[idx].second) ) {
     262        bubble_up(idx, Pair(i,p));
    265263      }
    266264      else {
    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.
     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.
    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.
    277276    void decrease(const Item &i, const Prio &p) {
    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.
     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.
    285286    /// \param i The item.
    286287    /// \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       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.
     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.
    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 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.
     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.
    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 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.
     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.
    336335    void replace(const Item& i, const Item& j) {
    337       int idx = _iim[i];
    338       _iim.set(i, _iim[j]);
    339       _iim.set(j, idx);
    340       _data[idx].first = j;
     336      int idx = iim[i];
     337      iim.set(i, iim[j]);
     338      iim.set(j, idx);
     339      data[idx].first = j;
    341340    }
    342341
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