lemon/radix_heap.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 20 Dec 2011 17:38:19 +0100
changeset 961 71fd280363d5
parent 681 532697c9fa53
child 709 0747f332c478
permissions -rw-r--r--
Merge
     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_RADIX_HEAP_H
    20 #define LEMON_RADIX_HEAP_H
    21 
    22 ///\ingroup auxdat
    23 ///\file
    24 ///\brief Radix Heap implementation.
    25 
    26 #include <vector>
    27 #include <lemon/error.h>
    28 
    29 namespace lemon {
    30 
    31 
    32   /// \ingroup auxdata
    33   ///
    34   /// \brief A Radix Heap implementation.
    35   ///
    36   /// This class implements the \e radix \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. This heap type can store only items with \e int priority.
    40   /// In a heap one can change the priority of an item, add or erase an
    41   /// item, but the priority cannot be decreased under the last removed
    42   /// item's priority.
    43   ///
    44   /// \param IM A read and writable Item int map, used internally
    45   /// to handle the cross references.
    46   ///
    47   /// \see BinHeap
    48   /// \see Dijkstra
    49   template <typename IM>
    50   class RadixHeap {
    51 
    52   public:
    53     typedef typename IM::Key Item;
    54     typedef int Prio;
    55     typedef IM ItemIntMap;
    56 
    57     /// \brief Exception thrown by RadixHeap.
    58     ///
    59     /// This Exception is thrown when a smaller priority
    60     /// is inserted into the \e RadixHeap then the last time erased.
    61     /// \see RadixHeap
    62 
    63     class UnderFlowPriorityError : public Exception {
    64     public:
    65       virtual const char* what() const throw() {
    66         return "lemon::RadixHeap::UnderFlowPriorityError";
    67       }
    68     };
    69 
    70     /// \brief Type to represent the items states.
    71     ///
    72     /// Each Item element have a state associated to it. It may 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 ItemIntMap \e should be initialized in such way that it maps
    77     /// PRE_HEAP (-1) to any element to be put in the heap...
    78     enum State {
    79       IN_HEAP = 0,
    80       PRE_HEAP = -1,
    81       POST_HEAP = -2
    82     };
    83 
    84   private:
    85 
    86     struct RadixItem {
    87       int prev, next, box;
    88       Item item;
    89       int prio;
    90       RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
    91     };
    92 
    93     struct RadixBox {
    94       int first;
    95       int min, size;
    96       RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
    97     };
    98 
    99     std::vector<RadixItem> data;
   100     std::vector<RadixBox> boxes;
   101 
   102     ItemIntMap &_iim;
   103 
   104 
   105   public:
   106     /// \brief The constructor.
   107     ///
   108     /// The constructor.
   109     ///
   110     /// \param map It 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     ///
   114     /// \param minimal The initial minimal value of the heap.
   115     /// \param capacity It determines the initial capacity of the heap.
   116     RadixHeap(ItemIntMap &map, int minimal = 0, int capacity = 0)
   117       : _iim(map) {
   118       boxes.push_back(RadixBox(minimal, 1));
   119       boxes.push_back(RadixBox(minimal + 1, 1));
   120       while (lower(boxes.size() - 1, capacity + minimal - 1)) {
   121         extend();
   122       }
   123     }
   124 
   125     /// The number of items stored in the heap.
   126     ///
   127     /// \brief Returns the number of items stored in the heap.
   128     int size() const { return data.size(); }
   129     /// \brief Checks if the heap stores no items.
   130     ///
   131     /// Returns \c true if and only if the heap stores no items.
   132     bool empty() const { return data.empty(); }
   133 
   134     /// \brief Make empty this heap.
   135     ///
   136     /// Make empty this heap. It does not change the cross reference
   137     /// map.  If you want to reuse a heap what is not surely empty you
   138     /// should first clear the heap and after that you should set the
   139     /// cross reference map for each item to \c PRE_HEAP.
   140     void clear(int minimal = 0, int capacity = 0) {
   141       data.clear(); boxes.clear();
   142       boxes.push_back(RadixBox(minimal, 1));
   143       boxes.push_back(RadixBox(minimal + 1, 1));
   144       while (lower(boxes.size() - 1, capacity + minimal - 1)) {
   145         extend();
   146       }
   147     }
   148 
   149   private:
   150 
   151     bool upper(int box, Prio pr) {
   152       return pr < boxes[box].min;
   153     }
   154 
   155     bool lower(int box, Prio pr) {
   156       return pr >= boxes[box].min + boxes[box].size;
   157     }
   158 
   159     /// \brief Remove item from the box list.
   160     void remove(int index) {
   161       if (data[index].prev >= 0) {
   162         data[data[index].prev].next = data[index].next;
   163       } else {
   164         boxes[data[index].box].first = data[index].next;
   165       }
   166       if (data[index].next >= 0) {
   167         data[data[index].next].prev = data[index].prev;
   168       }
   169     }
   170 
   171     /// \brief Insert item into the box list.
   172     void insert(int box, int index) {
   173       if (boxes[box].first == -1) {
   174         boxes[box].first = index;
   175         data[index].next = data[index].prev = -1;
   176       } else {
   177         data[index].next = boxes[box].first;
   178         data[boxes[box].first].prev = index;
   179         data[index].prev = -1;
   180         boxes[box].first = index;
   181       }
   182       data[index].box = box;
   183     }
   184 
   185     /// \brief Add a new box to the box list.
   186     void extend() {
   187       int min = boxes.back().min + boxes.back().size;
   188       int bs = 2 * boxes.back().size;
   189       boxes.push_back(RadixBox(min, bs));
   190     }
   191 
   192     /// \brief Move an item up into the proper box.
   193     void bubble_up(int index) {
   194       if (!lower(data[index].box, data[index].prio)) return;
   195       remove(index);
   196       int box = findUp(data[index].box, data[index].prio);
   197       insert(box, index);
   198     }
   199 
   200     /// \brief Find up the proper box for the item with the given prio.
   201     int findUp(int start, int pr) {
   202       while (lower(start, pr)) {
   203         if (++start == int(boxes.size())) {
   204           extend();
   205         }
   206       }
   207       return start;
   208     }
   209 
   210     /// \brief Move an item down into the proper box.
   211     void bubble_down(int index) {
   212       if (!upper(data[index].box, data[index].prio)) return;
   213       remove(index);
   214       int box = findDown(data[index].box, data[index].prio);
   215       insert(box, index);
   216     }
   217 
   218     /// \brief Find up the proper box for the item with the given prio.
   219     int findDown(int start, int pr) {
   220       while (upper(start, pr)) {
   221         if (--start < 0) throw UnderFlowPriorityError();
   222       }
   223       return start;
   224     }
   225 
   226     /// \brief Find the first not empty box.
   227     int findFirst() {
   228       int first = 0;
   229       while (boxes[first].first == -1) ++first;
   230       return first;
   231     }
   232 
   233     /// \brief Gives back the minimal prio of the box.
   234     int minValue(int box) {
   235       int min = data[boxes[box].first].prio;
   236       for (int k = boxes[box].first; k != -1; k = data[k].next) {
   237         if (data[k].prio < min) min = data[k].prio;
   238       }
   239       return min;
   240     }
   241 
   242     /// \brief Rearrange the items of the heap and makes the
   243     /// first box not empty.
   244     void moveDown() {
   245       int box = findFirst();
   246       if (box == 0) return;
   247       int min = minValue(box);
   248       for (int i = 0; i <= box; ++i) {
   249         boxes[i].min = min;
   250         min += boxes[i].size;
   251       }
   252       int curr = boxes[box].first, next;
   253       while (curr != -1) {
   254         next = data[curr].next;
   255         bubble_down(curr);
   256         curr = next;
   257       }
   258     }
   259 
   260     void relocate_last(int index) {
   261       if (index != int(data.size()) - 1) {
   262         data[index] = data.back();
   263         if (data[index].prev != -1) {
   264           data[data[index].prev].next = index;
   265         } else {
   266           boxes[data[index].box].first = index;
   267         }
   268         if (data[index].next != -1) {
   269           data[data[index].next].prev = index;
   270         }
   271         _iim[data[index].item] = index;
   272       }
   273       data.pop_back();
   274     }
   275 
   276   public:
   277 
   278     /// \brief Insert an item into the heap with the given priority.
   279     ///
   280     /// Adds \c i to the heap with priority \c p.
   281     /// \param i The item to insert.
   282     /// \param p The priority of the item.
   283     void push(const Item &i, const Prio &p) {
   284       int n = data.size();
   285       _iim.set(i, n);
   286       data.push_back(RadixItem(i, p));
   287       while (lower(boxes.size() - 1, p)) {
   288         extend();
   289       }
   290       int box = findDown(boxes.size() - 1, p);
   291       insert(box, n);
   292     }
   293 
   294     /// \brief Returns the item with minimum priority.
   295     ///
   296     /// This method returns the item with minimum priority.
   297     /// \pre The heap must be nonempty.
   298     Item top() const {
   299       const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
   300       return data[boxes[0].first].item;
   301     }
   302 
   303     /// \brief Returns the minimum priority.
   304     ///
   305     /// It returns the minimum priority.
   306     /// \pre The heap must be nonempty.
   307     Prio prio() const {
   308       const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
   309       return data[boxes[0].first].prio;
   310      }
   311 
   312     /// \brief Deletes the item with minimum priority.
   313     ///
   314     /// This method deletes the item with minimum priority.
   315     /// \pre The heap must be non-empty.
   316     void pop() {
   317       moveDown();
   318       int index = boxes[0].first;
   319       _iim[data[index].item] = POST_HEAP;
   320       remove(index);
   321       relocate_last(index);
   322     }
   323 
   324     /// \brief Deletes \c i from the heap.
   325     ///
   326     /// This method deletes item \c i from the heap, if \c i was
   327     /// already stored in the heap.
   328     /// \param i The item to erase.
   329     void erase(const Item &i) {
   330       int index = _iim[i];
   331       _iim[i] = POST_HEAP;
   332       remove(index);
   333       relocate_last(index);
   334    }
   335 
   336     /// \brief Returns the priority of \c i.
   337     ///
   338     /// This function returns the priority of item \c i.
   339     /// \pre \c i must be in the heap.
   340     /// \param i The item.
   341     Prio operator[](const Item &i) const {
   342       int idx = _iim[i];
   343       return data[idx].prio;
   344     }
   345 
   346     /// \brief \c i gets to the heap with priority \c p independently
   347     /// if \c i was already there.
   348     ///
   349     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   350     /// in the heap and sets the priority of \c i to \c p otherwise.
   351     /// It may throw an \e UnderFlowPriorityException.
   352     /// \param i The item.
   353     /// \param p The priority.
   354     void set(const Item &i, const Prio &p) {
   355       int idx = _iim[i];
   356       if( idx < 0 ) {
   357         push(i, p);
   358       }
   359       else if( p >= data[idx].prio ) {
   360         data[idx].prio = p;
   361         bubble_up(idx);
   362       } else {
   363         data[idx].prio = p;
   364         bubble_down(idx);
   365       }
   366     }
   367 
   368 
   369     /// \brief Decreases the priority of \c i to \c p.
   370     ///
   371     /// This method decreases the priority of item \c i to \c p.
   372     /// \pre \c i must be stored in the heap with priority at least \c p, and
   373     /// \c should be greater or equal to the last removed item's priority.
   374     /// \param i The item.
   375     /// \param p The priority.
   376     void decrease(const Item &i, const Prio &p) {
   377       int idx = _iim[i];
   378       data[idx].prio = p;
   379       bubble_down(idx);
   380     }
   381 
   382     /// \brief Increases the priority of \c i to \c p.
   383     ///
   384     /// This method sets the priority of item \c i to \c p.
   385     /// \pre \c i must be stored in the heap with priority at most \c p
   386     /// \param i The item.
   387     /// \param p The priority.
   388     void increase(const Item &i, const Prio &p) {
   389       int idx = _iim[i];
   390       data[idx].prio = p;
   391       bubble_up(idx);
   392     }
   393 
   394     /// \brief Returns if \c item is in, has already been in, or has
   395     /// never been in the heap.
   396     ///
   397     /// This method returns PRE_HEAP if \c item has never been in the
   398     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   399     /// otherwise. In the latter case it is possible that \c item will
   400     /// get back to the heap again.
   401     /// \param i The item.
   402     State state(const Item &i) const {
   403       int s = _iim[i];
   404       if( s >= 0 ) s = 0;
   405       return State(s);
   406     }
   407 
   408     /// \brief Sets the state of the \c item in the heap.
   409     ///
   410     /// Sets the state of the \c item in the heap. It can be used to
   411     /// manually clear the heap when it is important to achive the
   412     /// better time complexity.
   413     /// \param i The item.
   414     /// \param st The state. It should not be \c IN_HEAP.
   415     void state(const Item& i, State st) {
   416       switch (st) {
   417       case POST_HEAP:
   418       case PRE_HEAP:
   419         if (state(i) == IN_HEAP) {
   420           erase(i);
   421         }
   422         _iim[i] = st;
   423         break;
   424       case IN_HEAP:
   425         break;
   426       }
   427     }
   428 
   429   }; // class RadixHeap
   430 
   431 } // namespace lemon
   432 
   433 #endif // LEMON_RADIX_HEAP_H