lemon/bucket_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 24 Jul 2009 01:07:45 +0200
changeset 707 3887d6f994d7
parent 682 bb8c4cd57900
child 709 0747f332c478
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_BUCKET_HEAP_H
    20 #define LEMON_BUCKET_HEAP_H
    21 
    22 ///\ingroup auxdat
    23 ///\file
    24 ///\brief Bucket Heap implementation.
    25 
    26 #include <vector>
    27 #include <utility>
    28 #include <functional>
    29 
    30 namespace lemon {
    31 
    32   namespace _bucket_heap_bits {
    33 
    34     template <bool MIN>
    35     struct DirectionTraits {
    36       static bool less(int left, int right) {
    37         return left < right;
    38       }
    39       static void increase(int& value) {
    40         ++value;
    41       }
    42     };
    43 
    44     template <>
    45     struct DirectionTraits<false> {
    46       static bool less(int left, int right) {
    47         return left > right;
    48       }
    49       static void increase(int& value) {
    50         --value;
    51       }
    52     };
    53 
    54   }
    55 
    56   /// \ingroup auxdat
    57   ///
    58   /// \brief A Bucket Heap implementation.
    59   ///
    60   /// This class implements the \e bucket \e heap data structure. A \e heap
    61   /// is a data structure for storing items with specified values called \e
    62   /// priorities in such a way that finding the item with minimum priority is
    63   /// efficient. The bucket heap is very simple implementation, it can store
    64   /// only integer priorities and it stores for each priority in the
    65   /// \f$ [0..C) \f$ range a list of items. So it should be used only when
    66   /// the priorities are small. It is not intended to use as dijkstra heap.
    67   ///
    68   /// \param IM A read and write Item int map, used internally
    69   /// to handle the cross references.
    70   /// \param MIN If the given parameter is false then instead of the
    71   /// minimum value the maximum can be retrivied with the top() and
    72   /// prio() member functions.
    73   template <typename IM, bool MIN = true>
    74   class BucketHeap {
    75 
    76   public:
    77     /// \e
    78     typedef typename IM::Key Item;
    79     /// \e
    80     typedef int Prio;
    81     /// \e
    82     typedef std::pair<Item, Prio> Pair;
    83     /// \e
    84     typedef IM ItemIntMap;
    85 
    86   private:
    87 
    88     typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
    89 
    90   public:
    91 
    92     /// \brief Type to represent the items states.
    93     ///
    94     /// Each Item element have a state associated to it. It may be "in heap",
    95     /// "pre heap" or "post heap". The latter two are indifferent from the
    96     /// heap's point of view, but may be useful to the user.
    97     ///
    98     /// The item-int map must be initialized in such way that it assigns
    99     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
   100     enum State {
   101       IN_HEAP = 0,    ///< = 0.
   102       PRE_HEAP = -1,  ///< = -1.
   103       POST_HEAP = -2  ///< = -2.
   104     };
   105 
   106   public:
   107     /// \brief The constructor.
   108     ///
   109     /// The constructor.
   110     /// \param map should be given to the constructor, since it is used
   111     /// internally to handle the cross references. The value of the map
   112     /// should be PRE_HEAP (-1) for each element.
   113     explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {}
   114 
   115     /// The number of items stored in the heap.
   116     ///
   117     /// \brief Returns the number of items stored in the heap.
   118     int size() const { return _data.size(); }
   119 
   120     /// \brief Checks if the heap stores no items.
   121     ///
   122     /// Returns \c true if and only if the heap stores no items.
   123     bool empty() const { return _data.empty(); }
   124 
   125     /// \brief Make empty this heap.
   126     ///
   127     /// Make empty this heap. It does not change the cross reference
   128     /// map.  If you want to reuse a heap what is not surely empty you
   129     /// should first clear the heap and after that you should set the
   130     /// cross reference map for each item to \c PRE_HEAP.
   131     void clear() {
   132       _data.clear(); _first.clear(); _minimum = 0;
   133     }
   134 
   135   private:
   136 
   137     void relocate_last(int idx) {
   138       if (idx + 1 < int(_data.size())) {
   139         _data[idx] = _data.back();
   140         if (_data[idx].prev != -1) {
   141           _data[_data[idx].prev].next = idx;
   142         } else {
   143           _first[_data[idx].value] = idx;
   144         }
   145         if (_data[idx].next != -1) {
   146           _data[_data[idx].next].prev = idx;
   147         }
   148         _iim[_data[idx].item] = idx;
   149       }
   150       _data.pop_back();
   151     }
   152 
   153     void unlace(int idx) {
   154       if (_data[idx].prev != -1) {
   155         _data[_data[idx].prev].next = _data[idx].next;
   156       } else {
   157         _first[_data[idx].value] = _data[idx].next;
   158       }
   159       if (_data[idx].next != -1) {
   160         _data[_data[idx].next].prev = _data[idx].prev;
   161       }
   162     }
   163 
   164     void lace(int idx) {
   165       if (int(_first.size()) <= _data[idx].value) {
   166         _first.resize(_data[idx].value + 1, -1);
   167       }
   168       _data[idx].next = _first[_data[idx].value];
   169       if (_data[idx].next != -1) {
   170         _data[_data[idx].next].prev = idx;
   171       }
   172       _first[_data[idx].value] = idx;
   173       _data[idx].prev = -1;
   174     }
   175 
   176   public:
   177     /// \brief Insert a pair of item and priority into the heap.
   178     ///
   179     /// Adds \c p.first to the heap with priority \c p.second.
   180     /// \param p The pair to insert.
   181     void push(const Pair& p) {
   182       push(p.first, p.second);
   183     }
   184 
   185     /// \brief Insert an item into the heap with the given priority.
   186     ///
   187     /// Adds \c i to the heap with priority \c p.
   188     /// \param i The item to insert.
   189     /// \param p The priority of the item.
   190     void push(const Item &i, const Prio &p) {
   191       int idx = _data.size();
   192       _iim[i] = idx;
   193       _data.push_back(BucketItem(i, p));
   194       lace(idx);
   195       if (Direction::less(p, _minimum)) {
   196         _minimum = p;
   197       }
   198     }
   199 
   200     /// \brief Returns the item with minimum priority.
   201     ///
   202     /// This method returns the item with minimum priority.
   203     /// \pre The heap must be nonempty.
   204     Item top() const {
   205       while (_first[_minimum] == -1) {
   206         Direction::increase(_minimum);
   207       }
   208       return _data[_first[_minimum]].item;
   209     }
   210 
   211     /// \brief Returns the minimum priority.
   212     ///
   213     /// It returns the minimum priority.
   214     /// \pre The heap must be nonempty.
   215     Prio prio() const {
   216       while (_first[_minimum] == -1) {
   217         Direction::increase(_minimum);
   218       }
   219       return _minimum;
   220     }
   221 
   222     /// \brief Deletes the item with minimum priority.
   223     ///
   224     /// This method deletes the item with minimum priority from the heap.
   225     /// \pre The heap must be non-empty.
   226     void pop() {
   227       while (_first[_minimum] == -1) {
   228         Direction::increase(_minimum);
   229       }
   230       int idx = _first[_minimum];
   231       _iim[_data[idx].item] = -2;
   232       unlace(idx);
   233       relocate_last(idx);
   234     }
   235 
   236     /// \brief Deletes \c i from the heap.
   237     ///
   238     /// This method deletes item \c i from the heap, if \c i was
   239     /// already stored in the heap.
   240     /// \param i The item to erase.
   241     void erase(const Item &i) {
   242       int idx = _iim[i];
   243       _iim[_data[idx].item] = -2;
   244       unlace(idx);
   245       relocate_last(idx);
   246     }
   247 
   248 
   249     /// \brief Returns the priority of \c i.
   250     ///
   251     /// This function returns the priority of item \c i.
   252     /// \pre \c i must be in the heap.
   253     /// \param i The item.
   254     Prio operator[](const Item &i) const {
   255       int idx = _iim[i];
   256       return _data[idx].value;
   257     }
   258 
   259     /// \brief \c i gets to the heap with priority \c p independently
   260     /// if \c i was already there.
   261     ///
   262     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   263     /// in the heap and sets the priority of \c i to \c p otherwise.
   264     /// \param i The item.
   265     /// \param p The priority.
   266     void set(const Item &i, const Prio &p) {
   267       int idx = _iim[i];
   268       if (idx < 0) {
   269         push(i, p);
   270       } else if (Direction::less(p, _data[idx].value)) {
   271         decrease(i, p);
   272       } else {
   273         increase(i, p);
   274       }
   275     }
   276 
   277     /// \brief Decreases the priority of \c i to \c p.
   278     ///
   279     /// This method decreases the priority of item \c i to \c p.
   280     /// \pre \c i must be stored in the heap with priority at least \c
   281     /// p relative to \c Compare.
   282     /// \param i The item.
   283     /// \param p The priority.
   284     void decrease(const Item &i, const Prio &p) {
   285       int idx = _iim[i];
   286       unlace(idx);
   287       _data[idx].value = p;
   288       if (Direction::less(p, _minimum)) {
   289         _minimum = p;
   290       }
   291       lace(idx);
   292     }
   293 
   294     /// \brief Increases the priority of \c i to \c p.
   295     ///
   296     /// This method sets the priority of item \c i to \c p.
   297     /// \pre \c i must be stored in the heap with priority at most \c
   298     /// p relative to \c Compare.
   299     /// \param i The item.
   300     /// \param p The priority.
   301     void increase(const Item &i, const Prio &p) {
   302       int idx = _iim[i];
   303       unlace(idx);
   304       _data[idx].value = p;
   305       lace(idx);
   306     }
   307 
   308     /// \brief Returns if \c item is in, has already been in, or has
   309     /// never been in the heap.
   310     ///
   311     /// This method returns PRE_HEAP if \c item has never been in the
   312     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   313     /// otherwise. In the latter case it is possible that \c item will
   314     /// get back to the heap again.
   315     /// \param i The item.
   316     State state(const Item &i) const {
   317       int idx = _iim[i];
   318       if (idx >= 0) idx = 0;
   319       return State(idx);
   320     }
   321 
   322     /// \brief Sets the state of the \c item in the heap.
   323     ///
   324     /// Sets the state of the \c item in the heap. It can be used to
   325     /// manually clear the heap when it is important to achive the
   326     /// better time complexity.
   327     /// \param i The item.
   328     /// \param st The state. It should not be \c IN_HEAP.
   329     void state(const Item& i, State st) {
   330       switch (st) {
   331       case POST_HEAP:
   332       case PRE_HEAP:
   333         if (state(i) == IN_HEAP) {
   334           erase(i);
   335         }
   336         _iim[i] = st;
   337         break;
   338       case IN_HEAP:
   339         break;
   340       }
   341     }
   342 
   343   private:
   344 
   345     struct BucketItem {
   346       BucketItem(const Item& _item, int _value)
   347         : item(_item), value(_value) {}
   348 
   349       Item item;
   350       int value;
   351 
   352       int prev, next;
   353     };
   354 
   355     ItemIntMap& _iim;
   356     std::vector<int> _first;
   357     std::vector<BucketItem> _data;
   358     mutable int _minimum;
   359 
   360   }; // class BucketHeap
   361 
   362   /// \ingroup auxdat
   363   ///
   364   /// \brief A Simplified Bucket Heap implementation.
   365   ///
   366   /// This class implements a simplified \e bucket \e heap data
   367   /// structure.  It does not provide some functionality but it faster
   368   /// and simplier data structure than the BucketHeap. The main
   369   /// difference is that the BucketHeap stores for every key a double
   370   /// linked list while this class stores just simple lists. In the
   371   /// other way it does not support erasing each elements just the
   372   /// minimal and it does not supports key increasing, decreasing.
   373   ///
   374   /// \param IM A read and write Item int map, used internally
   375   /// to handle the cross references.
   376   /// \param MIN If the given parameter is false then instead of the
   377   /// minimum value the maximum can be retrivied with the top() and
   378   /// prio() member functions.
   379   ///
   380   /// \sa BucketHeap
   381   template <typename IM, bool MIN = true >
   382   class SimpleBucketHeap {
   383 
   384   public:
   385     typedef typename IM::Key Item;
   386     typedef int Prio;
   387     typedef std::pair<Item, Prio> Pair;
   388     typedef IM ItemIntMap;
   389 
   390   private:
   391 
   392     typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;
   393 
   394   public:
   395 
   396     /// \brief Type to represent the items states.
   397     ///
   398     /// Each Item element have a state associated to it. It may be "in heap",
   399     /// "pre heap" or "post heap". The latter two are indifferent from the
   400     /// heap's point of view, but may be useful to the user.
   401     ///
   402     /// The item-int map must be initialized in such way that it assigns
   403     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
   404     enum State {
   405       IN_HEAP = 0,    ///< = 0.
   406       PRE_HEAP = -1,  ///< = -1.
   407       POST_HEAP = -2  ///< = -2.
   408     };
   409 
   410   public:
   411 
   412     /// \brief The constructor.
   413     ///
   414     /// The constructor.
   415     /// \param map should be given to the constructor, since it is used
   416     /// internally to handle the cross references. The value of the map
   417     /// should be PRE_HEAP (-1) for each element.
   418     explicit SimpleBucketHeap(ItemIntMap &map)
   419       : _iim(map), _free(-1), _num(0), _minimum(0) {}
   420 
   421     /// \brief Returns the number of items stored in the heap.
   422     ///
   423     /// The number of items stored in the heap.
   424     int size() const { return _num; }
   425 
   426     /// \brief Checks if the heap stores no items.
   427     ///
   428     /// Returns \c true if and only if the heap stores no items.
   429     bool empty() const { return _num == 0; }
   430 
   431     /// \brief Make empty this heap.
   432     ///
   433     /// Make empty this heap. It does not change the cross reference
   434     /// map.  If you want to reuse a heap what is not surely empty you
   435     /// should first clear the heap and after that you should set the
   436     /// cross reference map for each item to \c PRE_HEAP.
   437     void clear() {
   438       _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0;
   439     }
   440 
   441     /// \brief Insert a pair of item and priority into the heap.
   442     ///
   443     /// Adds \c p.first to the heap with priority \c p.second.
   444     /// \param p The pair to insert.
   445     void push(const Pair& p) {
   446       push(p.first, p.second);
   447     }
   448 
   449     /// \brief Insert an item into the heap with the given priority.
   450     ///
   451     /// Adds \c i to the heap with priority \c p.
   452     /// \param i The item to insert.
   453     /// \param p The priority of the item.
   454     void push(const Item &i, const Prio &p) {
   455       int idx;
   456       if (_free == -1) {
   457         idx = _data.size();
   458         _data.push_back(BucketItem(i));
   459       } else {
   460         idx = _free;
   461         _free = _data[idx].next;
   462         _data[idx].item = i;
   463       }
   464       _iim[i] = idx;
   465       if (p >= int(_first.size())) _first.resize(p + 1, -1);
   466       _data[idx].next = _first[p];
   467       _first[p] = idx;
   468       if (Direction::less(p, _minimum)) {
   469         _minimum = p;
   470       }
   471       ++_num;
   472     }
   473 
   474     /// \brief Returns the item with minimum priority.
   475     ///
   476     /// This method returns the item with minimum priority.
   477     /// \pre The heap must be nonempty.
   478     Item top() const {
   479       while (_first[_minimum] == -1) {
   480         Direction::increase(_minimum);
   481       }
   482       return _data[_first[_minimum]].item;
   483     }
   484 
   485     /// \brief Returns the minimum priority.
   486     ///
   487     /// It returns the minimum priority.
   488     /// \pre The heap must be nonempty.
   489     Prio prio() const {
   490       while (_first[_minimum] == -1) {
   491         Direction::increase(_minimum);
   492       }
   493       return _minimum;
   494     }
   495 
   496     /// \brief Deletes the item with minimum priority.
   497     ///
   498     /// This method deletes the item with minimum priority from the heap.
   499     /// \pre The heap must be non-empty.
   500     void pop() {
   501       while (_first[_minimum] == -1) {
   502         Direction::increase(_minimum);
   503       }
   504       int idx = _first[_minimum];
   505       _iim[_data[idx].item] = -2;
   506       _first[_minimum] = _data[idx].next;
   507       _data[idx].next = _free;
   508       _free = idx;
   509       --_num;
   510     }
   511 
   512     /// \brief Returns the priority of \c i.
   513     ///
   514     /// This function returns the priority of item \c i.
   515     /// \warning This operator is not a constant time function
   516     /// because it scans the whole data structure to find the proper
   517     /// value.
   518     /// \pre \c i must be in the heap.
   519     /// \param i The item.
   520     Prio operator[](const Item &i) const {
   521       for (int k = 0; k < _first.size(); ++k) {
   522         int idx = _first[k];
   523         while (idx != -1) {
   524           if (_data[idx].item == i) {
   525             return k;
   526           }
   527           idx = _data[idx].next;
   528         }
   529       }
   530       return -1;
   531     }
   532 
   533     /// \brief Returns if \c item is in, has already been in, or has
   534     /// never been in the heap.
   535     ///
   536     /// This method returns PRE_HEAP if \c item has never been in the
   537     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   538     /// otherwise. In the latter case it is possible that \c item will
   539     /// get back to the heap again.
   540     /// \param i The item.
   541     State state(const Item &i) const {
   542       int idx = _iim[i];
   543       if (idx >= 0) idx = 0;
   544       return State(idx);
   545     }
   546 
   547   private:
   548 
   549     struct BucketItem {
   550       BucketItem(const Item& _item)
   551         : item(_item) {}
   552 
   553       Item item;
   554       int next;
   555     };
   556 
   557     ItemIntMap& _iim;
   558     std::vector<int> _first;
   559     std::vector<BucketItem> _data;
   560     int _free, _num;
   561     mutable int _minimum;
   562 
   563   }; // class SimpleBucketHeap
   564 
   565 }
   566 
   567 #endif