lemon/bin_heap.h
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 04 Aug 2011 22:00:57 +0200
changeset 924 3dcb45a871c3
parent 157 2ccc1afc2c52
child 440 88ed40ad0d4f
permissions -rw-r--r--
Update the AUTHORS file
     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) 2003-2008
     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. 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. \c Compare specifies the ordering of the priorities. In a heap
    40   ///one can change the priority of an item, add or erase an item, etc.
    41   ///
    42   ///\tparam _Prio Type of the priority of the items.
    43   ///\tparam _ItemIntMap A read and writable Item int map, used internally
    44   ///to handle the cross references.
    45   ///\tparam _Compare A class for the ordering of the priorities. The
    46   ///default is \c std::less<_Prio>.
    47   ///
    48   ///\sa FibHeap
    49   ///\sa Dijkstra
    50   template <typename _Prio, typename _ItemIntMap,
    51             typename _Compare = std::less<_Prio> >
    52   class BinHeap {
    53 
    54   public:
    55     ///\e
    56     typedef _ItemIntMap ItemIntMap;
    57     ///\e
    58     typedef _Prio Prio;
    59     ///\e
    60     typedef typename ItemIntMap::Key Item;
    61     ///\e
    62     typedef std::pair<Item,Prio> Pair;
    63     ///\e
    64     typedef _Compare Compare;
    65 
    66     /// \brief Type to represent the items states.
    67     ///
    68     /// Each Item element have a state associated to it. It may be "in heap",
    69     /// "pre heap" or "post heap". The latter two are indifferent from the
    70     /// heap's point of view, but may be useful to the user.
    71     ///
    72     /// The ItemIntMap \e should be initialized in such way that it maps
    73     /// PRE_HEAP (-1) to any element to be put in the heap...
    74     enum State {
    75       IN_HEAP = 0,
    76       PRE_HEAP = -1,
    77       POST_HEAP = -2
    78     };
    79 
    80   private:
    81     std::vector<Pair> data;
    82     Compare comp;
    83     ItemIntMap &iim;
    84 
    85   public:
    86     /// \brief The constructor.
    87     ///
    88     /// The constructor.
    89     /// \param _iim should be given to the constructor, since it is used
    90     /// internally to handle the cross references. The value of the map
    91     /// should be PRE_HEAP (-1) for each element.
    92     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
    93 
    94     /// \brief The constructor.
    95     ///
    96     /// The constructor.
    97     /// \param _iim should be given to the constructor, since it is used
    98     /// internally to handle the cross references. The value of the map
    99     /// should be PRE_HEAP (-1) for each element.
   100     ///
   101     /// \param _comp The comparator function object.
   102     BinHeap(ItemIntMap &_iim, const Compare &_comp)
   103       : iim(_iim), comp(_comp) {}
   104 
   105 
   106     /// The number of items stored in the heap.
   107     ///
   108     /// \brief Returns the number of items stored in the heap.
   109     int size() const { return data.size(); }
   110 
   111     /// \brief Checks if the heap stores no items.
   112     ///
   113     /// Returns \c true if and only if the heap stores no items.
   114     bool empty() const { return data.empty(); }
   115 
   116     /// \brief Make empty this heap.
   117     ///
   118     /// Make empty this heap. It does not change the cross reference map.
   119     /// If you want to reuse what is not surely empty you should first clear
   120     /// the heap and after that you should set the cross reference map for
   121     /// each item to \c PRE_HEAP.
   122     void clear() {
   123       data.clear();
   124     }
   125 
   126   private:
   127     static int parent(int i) { return (i-1)/2; }
   128 
   129     static int second_child(int i) { return 2*i+2; }
   130     bool less(const Pair &p1, const Pair &p2) const {
   131       return comp(p1.second, p2.second);
   132     }
   133 
   134     int bubble_up(int hole, Pair p) {
   135       int par = parent(hole);
   136       while( hole>0 && less(p,data[par]) ) {
   137         move(data[par],hole);
   138         hole = par;
   139         par = parent(hole);
   140       }
   141       move(p, hole);
   142       return hole;
   143     }
   144 
   145     int bubble_down(int hole, Pair p, int length) {
   146       int child = second_child(hole);
   147       while(child < length) {
   148         if( less(data[child-1], data[child]) ) {
   149           --child;
   150         }
   151         if( !less(data[child], p) )
   152           goto ok;
   153         move(data[child], hole);
   154         hole = child;
   155         child = second_child(hole);
   156       }
   157       child--;
   158       if( child<length && less(data[child], p) ) {
   159         move(data[child], hole);
   160         hole=child;
   161       }
   162     ok:
   163       move(p, hole);
   164       return hole;
   165     }
   166 
   167     void move(const Pair &p, int i) {
   168       data[i] = p;
   169       iim.set(p.first, i);
   170     }
   171 
   172   public:
   173     /// \brief Insert a pair of item and priority into the heap.
   174     ///
   175     /// Adds \c p.first to the heap with priority \c p.second.
   176     /// \param p The pair to insert.
   177     void push(const Pair &p) {
   178       int n = data.size();
   179       data.resize(n+1);
   180       bubble_up(n, p);
   181     }
   182 
   183     /// \brief Insert an item into the heap with the given heap.
   184     ///
   185     /// Adds \c i to the heap with priority \c p.
   186     /// \param i The item to insert.
   187     /// \param p The priority of the item.
   188     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
   189 
   190     /// \brief Returns the item with minimum priority relative to \c Compare.
   191     ///
   192     /// This method returns the item with minimum priority relative to \c
   193     /// Compare.
   194     /// \pre The heap must be nonempty.
   195     Item top() const {
   196       return data[0].first;
   197     }
   198 
   199     /// \brief Returns the minimum priority relative to \c Compare.
   200     ///
   201     /// It returns the minimum priority relative to \c Compare.
   202     /// \pre The heap must be nonempty.
   203     Prio prio() const {
   204       return data[0].second;
   205     }
   206 
   207     /// \brief Deletes the item with minimum priority relative to \c Compare.
   208     ///
   209     /// This method deletes the item with minimum priority relative to \c
   210     /// Compare from the heap.
   211     /// \pre The heap must be non-empty.
   212     void pop() {
   213       int n = data.size()-1;
   214       iim.set(data[0].first, POST_HEAP);
   215       if (n > 0) {
   216         bubble_down(0, data[n], n);
   217       }
   218       data.pop_back();
   219     }
   220 
   221     /// \brief Deletes \c i from the heap.
   222     ///
   223     /// This method deletes item \c i from the heap.
   224     /// \param i The item to erase.
   225     /// \pre The item should be in the heap.
   226     void erase(const Item &i) {
   227       int h = iim[i];
   228       int n = data.size()-1;
   229       iim.set(data[h].first, POST_HEAP);
   230       if( h < n ) {
   231         if ( bubble_up(h, data[n]) == h) {
   232           bubble_down(h, data[n], n);
   233         }
   234       }
   235       data.pop_back();
   236     }
   237 
   238 
   239     /// \brief Returns the priority of \c i.
   240     ///
   241     /// This function returns the priority of item \c i.
   242     /// \pre \c i must be in the heap.
   243     /// \param i The item.
   244     Prio operator[](const Item &i) const {
   245       int idx = iim[i];
   246       return data[idx].second;
   247     }
   248 
   249     /// \brief \c i gets to the heap with priority \c p independently
   250     /// if \c i was already there.
   251     ///
   252     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   253     /// in the heap and sets the priority of \c i to \c p otherwise.
   254     /// \param i The item.
   255     /// \param p The priority.
   256     void set(const Item &i, const Prio &p) {
   257       int idx = iim[i];
   258       if( idx < 0 ) {
   259         push(i,p);
   260       }
   261       else if( comp(p, data[idx].second) ) {
   262         bubble_up(idx, Pair(i,p));
   263       }
   264       else {
   265         bubble_down(idx, Pair(i,p), data.size());
   266       }
   267     }
   268 
   269     /// \brief Decreases the priority of \c i to \c p.
   270     ///
   271     /// This method decreases the priority of item \c i to \c p.
   272     /// \pre \c i must be stored in the heap with priority at least \c
   273     /// p relative to \c Compare.
   274     /// \param i The item.
   275     /// \param p The priority.
   276     void decrease(const Item &i, const Prio &p) {
   277       int idx = iim[i];
   278       bubble_up(idx, Pair(i,p));
   279     }
   280 
   281     /// \brief Increases the priority of \c i to \c p.
   282     ///
   283     /// This method sets the priority of item \c i to \c p.
   284     /// \pre \c i must be stored in the heap with priority at most \c
   285     /// p relative to \c Compare.
   286     /// \param i The item.
   287     /// \param p The priority.
   288     void increase(const Item &i, const Prio &p) {
   289       int idx = iim[i];
   290       bubble_down(idx, Pair(i,p), data.size());
   291     }
   292 
   293     /// \brief Returns if \c item is in, has already been in, or has
   294     /// never been in the heap.
   295     ///
   296     /// This method returns PRE_HEAP if \c item has never been in the
   297     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   298     /// otherwise. In the latter case it is possible that \c item will
   299     /// get back to the heap again.
   300     /// \param i The item.
   301     State state(const Item &i) const {
   302       int s = iim[i];
   303       if( s>=0 )
   304         s=0;
   305       return State(s);
   306     }
   307 
   308     /// \brief Sets the state of the \c item in the heap.
   309     ///
   310     /// Sets the state of the \c item in the heap. It can be used to
   311     /// manually clear the heap when it is important to achive the
   312     /// better time complexity.
   313     /// \param i The item.
   314     /// \param st The state. It should not be \c IN_HEAP.
   315     void state(const Item& i, State st) {
   316       switch (st) {
   317       case POST_HEAP:
   318       case PRE_HEAP:
   319         if (state(i) == IN_HEAP) {
   320           erase(i);
   321         }
   322         iim[i] = st;
   323         break;
   324       case IN_HEAP:
   325         break;
   326       }
   327     }
   328 
   329     /// \brief Replaces an item in the heap.
   330     ///
   331     /// The \c i item is replaced with \c j item. The \c i item should
   332     /// be in the heap, while the \c j should be out of the heap. The
   333     /// \c i item will out of the heap and \c j will be in the heap
   334     /// with the same prioriority as prevoiusly the \c i item.
   335     void replace(const Item& i, const Item& j) {
   336       int idx = iim[i];
   337       iim.set(i, iim[j]);
   338       iim.set(j, idx);
   339       data[idx].first = j;
   340     }
   341 
   342   }; // class BinHeap
   343 
   344 } // namespace lemon
   345 
   346 #endif // LEMON_BIN_HEAP_H