lemon/quad_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 08 Jan 2011 22:49:09 +0100
changeset 1032 62ba43576f85
parent 706 9314d9339475
permissions -rw-r--r--
Doc group for TSP algorithms (#386)
     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_QUAD_HEAP_H
    20 #define LEMON_QUAD_HEAP_H
    21 
    22 ///\ingroup heaps
    23 ///\file
    24 ///\brief Fourary (quaternary) heap implementation.
    25 
    26 #include <vector>
    27 #include <utility>
    28 #include <functional>
    29 
    30 namespace lemon {
    31 
    32   /// \ingroup heaps
    33   ///
    34   ///\brief Fourary (quaternary) heap data structure.
    35   ///
    36   /// This class implements the \e Fourary (\e quaternary) \e heap
    37   /// data structure.
    38   /// It fully conforms to the \ref concepts::Heap "heap concept".
    39   ///
    40   /// The fourary heap is a specialization of the \ref DHeap "D-ary heap"
    41   /// for <tt>D=4</tt>. It is similar to the \ref BinHeap "binary heap",
    42   /// but its nodes have at most four children, instead of two.
    43   ///
    44   /// \tparam PR Type of the priorities of the items.
    45   /// \tparam IM A read-writable item map with \c int values, used
    46   /// internally to handle the cross references.
    47   /// \tparam CMP A functor class for comparing the priorities.
    48   /// The default is \c std::less<PR>.
    49   ///
    50   ///\sa BinHeap
    51   ///\sa DHeap
    52 #ifdef DOXYGEN
    53   template <typename PR, typename IM, typename CMP>
    54 #else
    55   template <typename PR, typename IM, typename CMP = std::less<PR> >
    56 #endif
    57   class QuadHeap {
    58   public:
    59     /// Type of the item-int map.
    60     typedef IM ItemIntMap;
    61     /// Type of the priorities.
    62     typedef PR Prio;
    63     /// Type of the items stored in the heap.
    64     typedef typename ItemIntMap::Key Item;
    65     /// Type of the item-priority pairs.
    66     typedef std::pair<Item,Prio> Pair;
    67     /// Functor type for comparing the priorities.
    68     typedef CMP Compare;
    69 
    70     /// \brief Type to represent the states of the items.
    71     ///
    72     /// Each item has a state associated to it. It can be "in heap",
    73     /// "pre-heap" or "post-heap". The latter two are indifferent from the
    74     /// heap's point of view, but may be useful to the user.
    75     ///
    76     /// The item-int map must be initialized in such way that it assigns
    77     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    78     enum State {
    79       IN_HEAP = 0,    ///< = 0.
    80       PRE_HEAP = -1,  ///< = -1.
    81       POST_HEAP = -2  ///< = -2.
    82     };
    83 
    84   private:
    85     std::vector<Pair> _data;
    86     Compare _comp;
    87     ItemIntMap &_iim;
    88 
    89   public:
    90     /// \brief Constructor.
    91     ///
    92     /// Constructor.
    93     /// \param map A map that assigns \c int values to the items.
    94     /// It is used internally to handle the cross references.
    95     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
    96     explicit QuadHeap(ItemIntMap &map) : _iim(map) {}
    97 
    98     /// \brief Constructor.
    99     ///
   100     /// Constructor.
   101     /// \param map A map that assigns \c int values to the items.
   102     /// It is used internally to handle the cross references.
   103     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   104     /// \param comp The function object used for comparing the priorities.
   105     QuadHeap(ItemIntMap &map, const Compare &comp)
   106       : _iim(map), _comp(comp) {}
   107 
   108     /// \brief The number of items stored in the heap.
   109     ///
   110     /// This function returns the number of items stored in the heap.
   111     int size() const { return _data.size(); }
   112 
   113     /// \brief Check if the heap is empty.
   114     ///
   115     /// This function returns \c true if the heap is empty.
   116     bool empty() const { return _data.empty(); }
   117 
   118     /// \brief Make the heap empty.
   119     ///
   120     /// This functon makes the heap empty.
   121     /// It does not change the cross reference map. If you want to reuse
   122     /// a heap that is not surely empty, you should first clear it and
   123     /// then you should set the cross reference map to \c PRE_HEAP
   124     /// for each item.
   125     void clear() { _data.clear(); }
   126 
   127   private:
   128     static int parent(int i) { return (i-1)/4; }
   129     static int firstChild(int i) { return 4*i+1; }
   130 
   131     bool less(const Pair &p1, const Pair &p2) const {
   132       return _comp(p1.second, p2.second);
   133     }
   134 
   135     void bubbleUp(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     }
   144 
   145     void bubbleDown(int hole, Pair p, int length) {
   146       if( length>1 ) {
   147         int child = firstChild(hole);
   148         while( child+3<length ) {
   149           int min=child;
   150           if( less(_data[++child], _data[min]) ) min=child;
   151           if( less(_data[++child], _data[min]) ) min=child;
   152           if( less(_data[++child], _data[min]) ) min=child;
   153           if( !less(_data[min], p) )
   154             goto ok;
   155           move(_data[min], hole);
   156           hole = min;
   157           child = firstChild(hole);
   158         }
   159         if ( child<length ) {
   160           int min = child;
   161           if( ++child<length && less(_data[child], _data[min]) ) min=child;
   162           if( ++child<length && less(_data[child], _data[min]) ) min=child;
   163           if( less(_data[min], p) ) {
   164             move(_data[min], hole);
   165             hole = min;
   166           }
   167         }
   168       }
   169     ok:
   170       move(p, hole);
   171     }
   172 
   173     void move(const Pair &p, int i) {
   174       _data[i] = p;
   175       _iim.set(p.first, i);
   176     }
   177 
   178   public:
   179     /// \brief Insert a pair of item and priority into the heap.
   180     ///
   181     /// This function inserts \c p.first to the heap with priority
   182     /// \c p.second.
   183     /// \param p The pair to insert.
   184     /// \pre \c p.first must not be stored in the heap.
   185     void push(const Pair &p) {
   186       int n = _data.size();
   187       _data.resize(n+1);
   188       bubbleUp(n, p);
   189     }
   190 
   191     /// \brief Insert an item into the heap with the given priority.
   192     ///
   193     /// This function inserts the given item into the heap with the
   194     /// given priority.
   195     /// \param i The item to insert.
   196     /// \param p The priority of the item.
   197     /// \pre \e i must not be stored in the heap.
   198     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
   199 
   200     /// \brief Return the item having minimum priority.
   201     ///
   202     /// This function returns the item having minimum priority.
   203     /// \pre The heap must be non-empty.
   204     Item top() const { return _data[0].first; }
   205 
   206     /// \brief The minimum priority.
   207     ///
   208     /// This function returns the minimum priority.
   209     /// \pre The heap must be non-empty.
   210     Prio prio() const { return _data[0].second; }
   211 
   212     /// \brief Remove the item having minimum priority.
   213     ///
   214     /// This function removes the item having minimum priority.
   215     /// \pre The heap must be non-empty.
   216     void pop() {
   217       int n = _data.size()-1;
   218       _iim.set(_data[0].first, POST_HEAP);
   219       if (n>0) bubbleDown(0, _data[n], n);
   220       _data.pop_back();
   221     }
   222 
   223     /// \brief Remove the given item from the heap.
   224     ///
   225     /// This function removes the given item from the heap if it is
   226     /// already stored.
   227     /// \param i The item to delete.
   228     /// \pre \e i must be in the heap.
   229     void erase(const Item &i) {
   230       int h = _iim[i];
   231       int n = _data.size()-1;
   232       _iim.set(_data[h].first, POST_HEAP);
   233       if( h<n ) {
   234         if( less(_data[parent(h)], _data[n]) )
   235           bubbleDown(h, _data[n], n);
   236         else
   237           bubbleUp(h, _data[n]);
   238       }
   239       _data.pop_back();
   240     }
   241 
   242     /// \brief The priority of the given item.
   243     ///
   244     /// This function returns the priority of the given item.
   245     /// \param i The item.
   246     /// \pre \e i must be in the heap.
   247     Prio operator[](const Item &i) const {
   248       int idx = _iim[i];
   249       return _data[idx].second;
   250     }
   251 
   252     /// \brief Set the priority of an item or insert it, if it is
   253     /// not stored in the heap.
   254     ///
   255     /// This method sets the priority of the given item if it is
   256     /// already stored in the heap. Otherwise it inserts the given
   257     /// item into the heap with the given priority.
   258     /// \param i The item.
   259     /// \param p The priority.
   260     void set(const Item &i, const Prio &p) {
   261       int idx = _iim[i];
   262       if( idx < 0 )
   263         push(i,p);
   264       else if( _comp(p, _data[idx].second) )
   265         bubbleUp(idx, Pair(i,p));
   266       else
   267         bubbleDown(idx, Pair(i,p), _data.size());
   268     }
   269 
   270     /// \brief Decrease the priority of an item to the given value.
   271     ///
   272     /// This function decreases the priority of an item to the given value.
   273     /// \param i The item.
   274     /// \param p The priority.
   275     /// \pre \e i must be stored in the heap with priority at least \e p.
   276     void decrease(const Item &i, const Prio &p) {
   277       int idx = _iim[i];
   278       bubbleUp(idx, Pair(i,p));
   279     }
   280 
   281     /// \brief Increase the priority of an item to the given value.
   282     ///
   283     /// This function increases the priority of an item to the given value.
   284     /// \param i The item.
   285     /// \param p The priority.
   286     /// \pre \e i must be stored in the heap with priority at most \e p.
   287     void increase(const Item &i, const Prio &p) {
   288       int idx = _iim[i];
   289       bubbleDown(idx, Pair(i,p), _data.size());
   290     }
   291 
   292     /// \brief Return the state of an item.
   293     ///
   294     /// This method returns \c PRE_HEAP if the given item has never
   295     /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
   296     /// and \c POST_HEAP otherwise.
   297     /// In the latter case it is possible that the item will get back
   298     /// to the heap again.
   299     /// \param i The item.
   300     State state(const Item &i) const {
   301       int s = _iim[i];
   302       if (s>=0) s=0;
   303       return State(s);
   304     }
   305 
   306     /// \brief Set the state of an item in the heap.
   307     ///
   308     /// This function sets the state of the given item in the heap.
   309     /// It can be used to manually clear the heap when it is important
   310     /// to achive better time complexity.
   311     /// \param i The item.
   312     /// \param st The state. It should not be \c IN_HEAP.
   313     void state(const Item& i, State st) {
   314       switch (st) {
   315         case POST_HEAP:
   316         case PRE_HEAP:
   317           if (state(i) == IN_HEAP) erase(i);
   318           _iim[i] = st;
   319           break;
   320         case IN_HEAP:
   321           break;
   322       }
   323     }
   324 
   325     /// \brief Replace an item in the heap.
   326     ///
   327     /// This function replaces item \c i with item \c j.
   328     /// Item \c i must be in the heap, while \c j must be out of the heap.
   329     /// After calling this method, item \c i will be out of the
   330     /// heap and \c j will be in the heap with the same prioriority
   331     /// as item \c i had before.
   332     void replace(const Item& i, const Item& j) {
   333       int idx = _iim[i];
   334       _iim.set(i, _iim[j]);
   335       _iim.set(j, idx);
   336       _data[idx].first = j;
   337     }
   338 
   339   }; // class QuadHeap
   340 
   341 } // namespace lemon
   342 
   343 #endif // LEMON_FOURARY_HEAP_H