lemon/kary_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 24 Jul 2009 01:07:45 +0200
changeset 707 3887d6f994d7
parent 704 7124b2581f72
permissions -rw-r--r--
Much faster implementation for BinomHeap (#301)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_KARY_HEAP_H
    20 #define LEMON_KARY_HEAP_H
    21 
    22 ///\ingroup heaps
    23 ///\file
    24 ///\brief Fourary heap implementation.
    25 
    26 #include <vector>
    27 #include <utility>
    28 #include <functional>
    29 
    30 namespace lemon {
    31 
    32   /// \ingroup heaps
    33   ///
    34   ///\brief K-ary heap data structure.
    35   ///
    36   /// This class implements the \e K-ary \e heap data structure.
    37   /// It fully conforms to the \ref concepts::Heap "heap concept".
    38   ///
    39   /// The \ref KaryHeap "K-ary heap" is a generalization of the
    40   /// \ref BinHeap "binary heap" structure, its nodes have at most
    41   /// \c K children, instead of two.
    42   /// \ref BinHeap and \ref FouraryHeap are specialized implementations
    43   /// of this structure for <tt>K=2</tt> and <tt>K=4</tt>, respectively.
    44   ///
    45   /// \tparam PR Type of the priorities of the items.
    46   /// \tparam IM A read-writable item map with \c int values, used
    47   /// internally to handle the cross references.
    48   /// \tparam K The degree of the heap, each node have at most \e K
    49   /// children. The default is 16. Powers of two are suggested to use
    50   /// so that the multiplications and divisions needed to traverse the
    51   /// nodes of the heap could be performed faster.
    52   /// \tparam CMP A functor class for comparing the priorities.
    53   /// The default is \c std::less<PR>.
    54   ///
    55   ///\sa BinHeap
    56   ///\sa FouraryHeap
    57 #ifdef DOXYGEN
    58   template <typename PR, typename IM, int K, typename CMP>
    59 #else
    60   template <typename PR, typename IM, int K = 16,
    61             typename CMP = std::less<PR> >
    62 #endif
    63   class KaryHeap {
    64   public:
    65     /// Type of the item-int map.
    66     typedef IM ItemIntMap;
    67     /// Type of the priorities.
    68     typedef PR Prio;
    69     /// Type of the items stored in the heap.
    70     typedef typename ItemIntMap::Key Item;
    71     /// Type of the item-priority pairs.
    72     typedef std::pair<Item,Prio> Pair;
    73     /// Functor type for comparing the priorities.
    74     typedef CMP Compare;
    75 
    76     /// \brief Type to represent the states of the items.
    77     ///
    78     /// Each item has a state associated to it. It can be "in heap",
    79     /// "pre-heap" or "post-heap". The latter two are indifferent from the
    80     /// heap's point of view, but may be useful to the user.
    81     ///
    82     /// The item-int map must be initialized in such way that it assigns
    83     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    84     enum State {
    85       IN_HEAP = 0,    ///< = 0.
    86       PRE_HEAP = -1,  ///< = -1.
    87       POST_HEAP = -2  ///< = -2.
    88     };
    89 
    90   private:
    91     std::vector<Pair> _data;
    92     Compare _comp;
    93     ItemIntMap &_iim;
    94 
    95   public:
    96     /// \brief Constructor.
    97     ///
    98     /// Constructor.
    99     /// \param map A map that assigns \c int values to the items.
   100     /// It is used internally to handle the cross references.
   101     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   102     explicit KaryHeap(ItemIntMap &map) : _iim(map) {}
   103 
   104     /// \brief Constructor.
   105     ///
   106     /// Constructor.
   107     /// \param map A map that assigns \c int values to the items.
   108     /// It is used internally to handle the cross references.
   109     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   110     /// \param comp The function object used for comparing the priorities.
   111     KaryHeap(ItemIntMap &map, const Compare &comp)
   112       : _iim(map), _comp(comp) {}
   113 
   114     /// \brief The number of items stored in the heap.
   115     ///
   116     /// This function returns the number of items stored in the heap.
   117     int size() const { return _data.size(); }
   118 
   119     /// \brief Check if the heap is empty.
   120     ///
   121     /// This function returns \c true if the heap is empty.
   122     bool empty() const { return _data.empty(); }
   123 
   124     /// \brief Make the heap empty.
   125     ///
   126     /// This functon makes the heap empty.
   127     /// It does not change the cross reference map. If you want to reuse
   128     /// a heap that is not surely empty, you should first clear it and
   129     /// then you should set the cross reference map to \c PRE_HEAP
   130     /// for each item.
   131     void clear() { _data.clear(); }
   132 
   133   private:
   134     int parent(int i) { return (i-1)/K; }
   135     int firstChild(int i) { return K*i+1; }
   136 
   137     bool less(const Pair &p1, const Pair &p2) const {
   138       return _comp(p1.second, p2.second);
   139     }
   140 
   141     void bubbleUp(int hole, Pair p) {
   142       int par = parent(hole);
   143       while( hole>0 && less(p,_data[par]) ) {
   144         move(_data[par],hole);
   145         hole = par;
   146         par = parent(hole);
   147       }
   148       move(p, hole);
   149     }
   150 
   151     void bubbleDown(int hole, Pair p, int length) {
   152       if( length>1 ) {
   153         int child = firstChild(hole);
   154         while( child+K<=length ) {
   155           int min=child;
   156           for (int i=1; i<K; ++i) {
   157             if( less(_data[child+i], _data[min]) )
   158               min=child+i;
   159           }
   160           if( !less(_data[min], p) )
   161             goto ok;
   162           move(_data[min], hole);
   163           hole = min;
   164           child = firstChild(hole);
   165         }
   166         if ( child<length ) {
   167           int min = child;
   168           while (++child < length) {
   169             if( less(_data[child], _data[min]) )
   170               min=child;
   171           }
   172           if( less(_data[min], p) ) {
   173             move(_data[min], hole);
   174             hole = min;
   175           }
   176         }
   177       }
   178     ok:
   179       move(p, hole);
   180     }
   181 
   182     void move(const Pair &p, int i) {
   183       _data[i] = p;
   184       _iim.set(p.first, i);
   185     }
   186 
   187   public:
   188     /// \brief Insert a pair of item and priority into the heap.
   189     ///
   190     /// This function inserts \c p.first to the heap with priority
   191     /// \c p.second.
   192     /// \param p The pair to insert.
   193     /// \pre \c p.first must not be stored in the heap.
   194     void push(const Pair &p) {
   195       int n = _data.size();
   196       _data.resize(n+1);
   197       bubbleUp(n, p);
   198     }
   199 
   200     /// \brief Insert an item into the heap with the given priority.
   201     ///
   202     /// This function inserts the given item into the heap with the
   203     /// given priority.
   204     /// \param i The item to insert.
   205     /// \param p The priority of the item.
   206     /// \pre \e i must not be stored in the heap.
   207     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
   208 
   209     /// \brief Return the item having minimum priority.
   210     ///
   211     /// This function returns the item having minimum priority.
   212     /// \pre The heap must be non-empty.
   213     Item top() const { return _data[0].first; }
   214 
   215     /// \brief The minimum priority.
   216     ///
   217     /// This function returns the minimum priority.
   218     /// \pre The heap must be non-empty.
   219     Prio prio() const { return _data[0].second; }
   220 
   221     /// \brief Remove the item having minimum priority.
   222     ///
   223     /// This function removes the item having minimum priority.
   224     /// \pre The heap must be non-empty.
   225     void pop() {
   226       int n = _data.size()-1;
   227       _iim.set(_data[0].first, POST_HEAP);
   228       if (n>0) bubbleDown(0, _data[n], n);
   229       _data.pop_back();
   230     }
   231 
   232     /// \brief Remove the given item from the heap.
   233     ///
   234     /// This function removes the given item from the heap if it is
   235     /// already stored.
   236     /// \param i The item to delete.
   237     /// \pre \e i must be in the heap.
   238     void erase(const Item &i) {
   239       int h = _iim[i];
   240       int n = _data.size()-1;
   241       _iim.set(_data[h].first, POST_HEAP);
   242       if( h<n ) {
   243         if( less(_data[parent(h)], _data[n]) )
   244           bubbleDown(h, _data[n], n);
   245         else
   246           bubbleUp(h, _data[n]);
   247       }
   248       _data.pop_back();
   249     }
   250 
   251     /// \brief The priority of the given item.
   252     ///
   253     /// This function returns the priority of the given item.
   254     /// \param i The item.
   255     /// \pre \e i must be in the heap.
   256     Prio operator[](const Item &i) const {
   257       int idx = _iim[i];
   258       return _data[idx].second;
   259     }
   260 
   261     /// \brief Set the priority of an item or insert it, if it is
   262     /// not stored in the heap.
   263     ///
   264     /// This method sets the priority of the given item if it is
   265     /// already stored in the heap. Otherwise it inserts the given
   266     /// item into the heap with the given priority.
   267     /// \param i The item.
   268     /// \param p The priority.
   269     void set(const Item &i, const Prio &p) {
   270       int idx = _iim[i];
   271       if( idx<0 )
   272         push(i,p);
   273       else if( _comp(p, _data[idx].second) )
   274         bubbleUp(idx, Pair(i,p));
   275       else
   276         bubbleDown(idx, Pair(i,p), _data.size());
   277     }
   278 
   279     /// \brief Decrease the priority of an item to the given value.
   280     ///
   281     /// This function decreases the priority of an item to the given value.
   282     /// \param i The item.
   283     /// \param p The priority.
   284     /// \pre \e i must be stored in the heap with priority at least \e p.
   285     void decrease(const Item &i, const Prio &p) {
   286       int idx = _iim[i];
   287       bubbleUp(idx, Pair(i,p));
   288     }
   289 
   290     /// \brief Increase the priority of an item to the given value.
   291     ///
   292     /// This function increases the priority of an item to the given value.
   293     /// \param i The item.
   294     /// \param p The priority.
   295     /// \pre \e i must be stored in the heap with priority at most \e p.
   296     void increase(const Item &i, const Prio &p) {
   297       int idx = _iim[i];
   298       bubbleDown(idx, Pair(i,p), _data.size());
   299     }
   300 
   301     /// \brief Return the state of an item.
   302     ///
   303     /// This method returns \c PRE_HEAP if the given item has never
   304     /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
   305     /// and \c POST_HEAP otherwise.
   306     /// In the latter case it is possible that the item will get back
   307     /// to the heap again.
   308     /// \param i The item.
   309     State state(const Item &i) const {
   310       int s = _iim[i];
   311       if (s>=0) s=0;
   312       return State(s);
   313     }
   314 
   315     /// \brief Set the state of an item in the heap.
   316     ///
   317     /// This function sets the state of the given item in the heap.
   318     /// It can be used to manually clear the heap when it is important
   319     /// to achive better time complexity.
   320     /// \param i The item.
   321     /// \param st The state. It should not be \c IN_HEAP.
   322     void state(const Item& i, State st) {
   323       switch (st) {
   324         case POST_HEAP:
   325         case PRE_HEAP:
   326           if (state(i) == IN_HEAP) erase(i);
   327           _iim[i] = st;
   328           break;
   329         case IN_HEAP:
   330           break;
   331       }
   332     }
   333 
   334     /// \brief Replace an item in the heap.
   335     ///
   336     /// This function replaces item \c i with item \c j.
   337     /// Item \c i must be in the heap, while \c j must be out of the heap.
   338     /// After calling this method, item \c i will be out of the
   339     /// heap and \c j will be in the heap with the same prioriority
   340     /// as item \c i had before.
   341     void replace(const Item& i, const Item& j) {
   342       int idx=_iim[i];
   343       _iim.set(i, _iim[j]);
   344       _iim.set(j, idx);
   345       _data[idx].first=j;
   346     }
   347 
   348   }; // class KaryHeap
   349 
   350 } // namespace lemon
   351 
   352 #endif // LEMON_KARY_HEAP_H