lemon/bin_heap.h
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     1 /* -*- C++ -*-
       
     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   ///\param _Prio Type of the priority of the items.
       
    43   ///\param _ItemIntMap A read and writable Item int map, used internally
       
    44   ///to handle the cross references.
       
    45   ///\param _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