lemon/bin_heap.h
author Balazs Dezso <deba@inf.elte.hu>
Thu, 11 Jun 2009 23:13:24 +0200
changeset 730 9f529abcaebf
parent 631 33c6b6e755cd
child 756 0747f332c478
child 912 37f440367057
permissions -rw-r--r--
Unification of names in heaps (#50)
     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_BIN_HEAP_H
    20 #define LEMON_BIN_HEAP_H
    21 
    22 ///\ingroup auxdat
    23 ///\file
    24 ///\brief Binary Heap implementation.
    25 
    26 #include <vector>
    27 #include <utility>
    28 #include <functional>
    29 
    30 namespace lemon {
    31 
    32   ///\ingroup auxdat
    33   ///
    34   ///\brief A Binary Heap implementation.
    35   ///
    36   ///This class implements the \e binary \e heap data structure.
    37   ///
    38   ///A \e heap is a data structure for storing items with specified values
    39   ///called \e priorities in such a way that finding the item with minimum
    40   ///priority is efficient. \c CMP specifies the ordering of the priorities.
    41   ///In a heap one can change the priority of an item, add or erase an
    42   ///item, etc.
    43   ///
    44   ///\tparam PR Type of the priority of the items.
    45   ///\tparam IM A read and writable item map with int values, used internally
    46   ///to handle the cross references.
    47   ///\tparam CMP A functor class for the ordering of the priorities.
    48   ///The default is \c std::less<PR>.
    49   ///
    50   ///\sa FibHeap
    51   ///\sa Dijkstra
    52   template <typename PR, typename IM, typename CMP = std::less<PR> >
    53   class BinHeap {
    54 
    55   public:
    56     ///\e
    57     typedef IM ItemIntMap;
    58     ///\e
    59     typedef PR Prio;
    60     ///\e
    61     typedef typename ItemIntMap::Key Item;
    62     ///\e
    63     typedef std::pair<Item,Prio> Pair;
    64     ///\e
    65     typedef CMP Compare;
    66 
    67     /// \brief Type to represent the items states.
    68     ///
    69     /// Each Item element have a state associated to it. It may be "in heap",
    70     /// "pre heap" or "post heap". The latter two are indifferent from the
    71     /// heap's point of view, but may be useful to the user.
    72     ///
    73     /// The item-int map must be initialized in such way that it assigns
    74     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    75     enum State {
    76       IN_HEAP = 0,    ///< = 0.
    77       PRE_HEAP = -1,  ///< = -1.
    78       POST_HEAP = -2  ///< = -2.
    79     };
    80 
    81   private:
    82     std::vector<Pair> _data;
    83     Compare _comp;
    84     ItemIntMap &_iim;
    85 
    86   public:
    87     /// \brief The constructor.
    88     ///
    89     /// The constructor.
    90     /// \param map should be given to the constructor, since it is used
    91     /// internally to handle the cross references. The value of the map
    92     /// must be \c PRE_HEAP (<tt>-1</tt>) for every item.
    93     explicit BinHeap(ItemIntMap &map) : _iim(map) {}
    94 
    95     /// \brief The constructor.
    96     ///
    97     /// The constructor.
    98     /// \param map should be given to the constructor, since it is used
    99     /// internally to handle the cross references. The value of the map
   100     /// should be PRE_HEAP (-1) for each element.
   101     ///
   102     /// \param comp The comparator function object.
   103     BinHeap(ItemIntMap &map, const Compare &comp)
   104       : _iim(map), _comp(comp) {}
   105 
   106 
   107     /// The number of items stored in the heap.
   108     ///
   109     /// \brief Returns the number of items stored in the heap.
   110     int size() const { return _data.size(); }
   111 
   112     /// \brief Checks if the heap stores no items.
   113     ///
   114     /// Returns \c true if and only if the heap stores no items.
   115     bool empty() const { return _data.empty(); }
   116 
   117     /// \brief Make empty this heap.
   118     ///
   119     /// Make empty this heap. It does not change the cross reference map.
   120     /// If you want to reuse what is not surely empty you should first clear
   121     /// the heap and after that you should set the cross reference map for
   122     /// each item to \c PRE_HEAP.
   123     void clear() {
   124       _data.clear();
   125     }
   126 
   127   private:
   128     static int parent(int i) { return (i-1)/2; }
   129 
   130     static int second_child(int i) { return 2*i+2; }
   131     bool less(const Pair &p1, const Pair &p2) const {
   132       return _comp(p1.second, p2.second);
   133     }
   134 
   135     int bubble_up(int hole, Pair p) {
   136       int par = parent(hole);
   137       while( hole>0 && less(p,_data[par]) ) {
   138         move(_data[par],hole);
   139         hole = par;
   140         par = parent(hole);
   141       }
   142       move(p, hole);
   143       return hole;
   144     }
   145 
   146     int bubble_down(int hole, Pair p, int length) {
   147       int child = second_child(hole);
   148       while(child < length) {
   149         if( less(_data[child-1], _data[child]) ) {
   150           --child;
   151         }
   152         if( !less(_data[child], p) )
   153           goto ok;
   154         move(_data[child], hole);
   155         hole = child;
   156         child = second_child(hole);
   157       }
   158       child--;
   159       if( child<length && less(_data[child], p) ) {
   160         move(_data[child], hole);
   161         hole=child;
   162       }
   163     ok:
   164       move(p, hole);
   165       return hole;
   166     }
   167 
   168     void move(const Pair &p, int i) {
   169       _data[i] = p;
   170       _iim.set(p.first, i);
   171     }
   172 
   173   public:
   174     /// \brief Insert a pair of item and priority into the heap.
   175     ///
   176     /// Adds \c p.first to the heap with priority \c p.second.
   177     /// \param p The pair to insert.
   178     void push(const Pair &p) {
   179       int n = _data.size();
   180       _data.resize(n+1);
   181       bubble_up(n, p);
   182     }
   183 
   184     /// \brief Insert an item into the heap with the given heap.
   185     ///
   186     /// Adds \c i to the heap with priority \c p.
   187     /// \param i The item to insert.
   188     /// \param p The priority of the item.
   189     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
   190 
   191     /// \brief Returns the item with minimum priority relative to \c Compare.
   192     ///
   193     /// This method returns the item with minimum priority relative to \c
   194     /// Compare.
   195     /// \pre The heap must be nonempty.
   196     Item top() const {
   197       return _data[0].first;
   198     }
   199 
   200     /// \brief Returns the minimum priority relative to \c Compare.
   201     ///
   202     /// It returns the minimum priority relative to \c Compare.
   203     /// \pre The heap must be nonempty.
   204     Prio prio() const {
   205       return _data[0].second;
   206     }
   207 
   208     /// \brief Deletes the item with minimum priority relative to \c Compare.
   209     ///
   210     /// This method deletes the item with minimum priority relative to \c
   211     /// Compare from the heap.
   212     /// \pre The heap must be non-empty.
   213     void pop() {
   214       int n = _data.size()-1;
   215       _iim.set(_data[0].first, POST_HEAP);
   216       if (n > 0) {
   217         bubble_down(0, _data[n], n);
   218       }
   219       _data.pop_back();
   220     }
   221 
   222     /// \brief Deletes \c i from the heap.
   223     ///
   224     /// This method deletes item \c i from the heap.
   225     /// \param i The item to erase.
   226     /// \pre The item should be in the heap.
   227     void erase(const Item &i) {
   228       int h = _iim[i];
   229       int n = _data.size()-1;
   230       _iim.set(_data[h].first, POST_HEAP);
   231       if( h < n ) {
   232         if ( bubble_up(h, _data[n]) == h) {
   233           bubble_down(h, _data[n], n);
   234         }
   235       }
   236       _data.pop_back();
   237     }
   238 
   239 
   240     /// \brief Returns the priority of \c i.
   241     ///
   242     /// This function returns the priority of item \c i.
   243     /// \param i The item.
   244     /// \pre \c i must be in the heap.
   245     Prio operator[](const Item &i) const {
   246       int idx = _iim[i];
   247       return _data[idx].second;
   248     }
   249 
   250     /// \brief \c i gets to the heap with priority \c p independently
   251     /// if \c i was already there.
   252     ///
   253     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   254     /// in the heap and sets the priority of \c i to \c p otherwise.
   255     /// \param i The item.
   256     /// \param p The priority.
   257     void set(const Item &i, const Prio &p) {
   258       int idx = _iim[i];
   259       if( idx < 0 ) {
   260         push(i,p);
   261       }
   262       else if( _comp(p, _data[idx].second) ) {
   263         bubble_up(idx, Pair(i,p));
   264       }
   265       else {
   266         bubble_down(idx, Pair(i,p), _data.size());
   267       }
   268     }
   269 
   270     /// \brief Decreases the priority of \c i to \c p.
   271     ///
   272     /// This method decreases the priority of item \c i to \c p.
   273     /// \param i The item.
   274     /// \param p The priority.
   275     /// \pre \c i must be stored in the heap with priority at least \c
   276     /// p relative to \c Compare.
   277     void decrease(const Item &i, const Prio &p) {
   278       int idx = _iim[i];
   279       bubble_up(idx, Pair(i,p));
   280     }
   281 
   282     /// \brief Increases the priority of \c i to \c p.
   283     ///
   284     /// This method sets the priority of item \c i to \c p.
   285     /// \param i The item.
   286     /// \param p The priority.
   287     /// \pre \c i must be stored in the heap with priority at most \c
   288     /// p relative to \c Compare.
   289     void increase(const Item &i, const Prio &p) {
   290       int idx = _iim[i];
   291       bubble_down(idx, Pair(i,p), _data.size());
   292     }
   293 
   294     /// \brief Returns if \c item is in, has already been in, or has
   295     /// never been in the heap.
   296     ///
   297     /// This method returns PRE_HEAP if \c item has never been in the
   298     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   299     /// otherwise. In the latter case it is possible that \c item will
   300     /// get back to the heap again.
   301     /// \param i The item.
   302     State state(const Item &i) const {
   303       int s = _iim[i];
   304       if( s>=0 )
   305         s=0;
   306       return State(s);
   307     }
   308 
   309     /// \brief Sets the state of the \c item in the heap.
   310     ///
   311     /// Sets the state of the \c item in the heap. It can be used to
   312     /// manually clear the heap when it is important to achive the
   313     /// better time complexity.
   314     /// \param i The item.
   315     /// \param st The state. It should not be \c IN_HEAP.
   316     void state(const Item& i, State st) {
   317       switch (st) {
   318       case POST_HEAP:
   319       case PRE_HEAP:
   320         if (state(i) == IN_HEAP) {
   321           erase(i);
   322         }
   323         _iim[i] = st;
   324         break;
   325       case IN_HEAP:
   326         break;
   327       }
   328     }
   329 
   330     /// \brief Replaces an item in the heap.
   331     ///
   332     /// The \c i item is replaced with \c j item. The \c i item should
   333     /// be in the heap, while the \c j should be out of the heap. The
   334     /// \c i item will out of the heap and \c j will be in the heap
   335     /// with the same prioriority as prevoiusly the \c i item.
   336     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;
   341     }
   342 
   343   }; // class BinHeap
   344 
   345 } // namespace lemon
   346 
   347 #endif // LEMON_BIN_HEAP_H