lemon/fib_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 02 Aug 2009 13:24:46 +0200
changeset 697 9496ed797f20
parent 681 532697c9fa53
child 709 0747f332c478
permissions -rw-r--r--
Improvements and unifications for BellmanFord (#51)

- Rework the function type interface to fit to dijkstra().
- Rename named template parameters (Def* -> Set*).
- Rename some private member variables
(to start with an underscore).
- Simplify template parameter names.
- Many unifications and improvements in the doc.
     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_FIB_HEAP_H
    20 #define LEMON_FIB_HEAP_H
    21 
    22 ///\file
    23 ///\ingroup auxdat
    24 ///\brief Fibonacci Heap implementation.
    25 
    26 #include <vector>
    27 #include <functional>
    28 #include <lemon/math.h>
    29 
    30 namespace lemon {
    31 
    32   /// \ingroup auxdat
    33   ///
    34   ///\brief Fibonacci Heap.
    35   ///
    36   ///This class implements the \e Fibonacci \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 CMP 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   ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
    43   ///heap. In case of many calls to these operations, it is better to use a
    44   ///\ref BinHeap "binary heap".
    45   ///
    46   ///\param PRIO Type of the priority of the items.
    47   ///\param IM A read and writable Item int map, used internally
    48   ///to handle the cross references.
    49   ///\param CMP A class for the ordering of the priorities. The
    50   ///default is \c std::less<PRIO>.
    51   ///
    52   ///\sa BinHeap
    53   ///\sa Dijkstra
    54 #ifdef DOXYGEN
    55   template <typename PRIO, typename IM, typename CMP>
    56 #else
    57   template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
    58 #endif
    59   class FibHeap {
    60   public:
    61     ///\e
    62     typedef IM ItemIntMap;
    63     ///\e
    64     typedef PRIO Prio;
    65     ///\e
    66     typedef typename ItemIntMap::Key Item;
    67     ///\e
    68     typedef std::pair<Item,Prio> Pair;
    69     ///\e
    70     typedef CMP Compare;
    71 
    72   private:
    73     class Store;
    74 
    75     std::vector<Store> _data;
    76     int _minimum;
    77     ItemIntMap &_iim;
    78     Compare _comp;
    79     int _num;
    80 
    81   public:
    82 
    83     /// \brief Type to represent the items states.
    84     ///
    85     /// Each Item element have a state associated to it. It may be "in heap",
    86     /// "pre heap" or "post heap". The latter two are indifferent from the
    87     /// heap's point of view, but may be useful to the user.
    88     ///
    89     /// The item-int map must be initialized in such way that it assigns
    90     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    91     enum State {
    92       IN_HEAP = 0,    ///< = 0.
    93       PRE_HEAP = -1,  ///< = -1.
    94       POST_HEAP = -2  ///< = -2.
    95     };
    96 
    97     /// \brief The constructor
    98     ///
    99     /// \c map should be given to the constructor, since it is
   100     ///   used internally to handle the cross references.
   101     explicit FibHeap(ItemIntMap &map)
   102       : _minimum(0), _iim(map), _num() {}
   103 
   104     /// \brief The constructor
   105     ///
   106     /// \c map should be given to the constructor, since it is used
   107     /// internally to handle the cross references. \c comp is an
   108     /// object for ordering of the priorities.
   109     FibHeap(ItemIntMap &map, const Compare &comp)
   110       : _minimum(0), _iim(map), _comp(comp), _num() {}
   111 
   112     /// \brief The number of items stored in the heap.
   113     ///
   114     /// Returns the number of items stored in the heap.
   115     int size() const { return _num; }
   116 
   117     /// \brief Checks if the heap stores no items.
   118     ///
   119     ///   Returns \c true if and only if the heap stores no items.
   120     bool empty() const { return _num==0; }
   121 
   122     /// \brief Make empty this heap.
   123     ///
   124     /// Make empty this heap. It does not change the cross reference
   125     /// map.  If you want to reuse a heap what is not surely empty you
   126     /// should first clear the heap and after that you should set the
   127     /// cross reference map for each item to \c PRE_HEAP.
   128     void clear() {
   129       _data.clear(); _minimum = 0; _num = 0;
   130     }
   131 
   132     /// \brief \c item gets to the heap with priority \c value independently
   133     /// if \c item was already there.
   134     ///
   135     /// This method calls \ref push(\c item, \c value) if \c item is not
   136     /// stored in the heap and it calls \ref decrease(\c item, \c value) or
   137     /// \ref increase(\c item, \c value) otherwise.
   138     void set (const Item& item, const Prio& value) {
   139       int i=_iim[item];
   140       if ( i >= 0 && _data[i].in ) {
   141         if ( _comp(value, _data[i].prio) ) decrease(item, value);
   142         if ( _comp(_data[i].prio, value) ) increase(item, value);
   143       } else push(item, value);
   144     }
   145 
   146     /// \brief Adds \c item to the heap with priority \c value.
   147     ///
   148     /// Adds \c item to the heap with priority \c value.
   149     /// \pre \c item must not be stored in the heap.
   150     void push (const Item& item, const Prio& value) {
   151       int i=_iim[item];
   152       if ( i < 0 ) {
   153         int s=_data.size();
   154         _iim.set( item, s );
   155         Store st;
   156         st.name=item;
   157         _data.push_back(st);
   158         i=s;
   159       } else {
   160         _data[i].parent=_data[i].child=-1;
   161         _data[i].degree=0;
   162         _data[i].in=true;
   163         _data[i].marked=false;
   164       }
   165 
   166       if ( _num ) {
   167         _data[_data[_minimum].right_neighbor].left_neighbor=i;
   168         _data[i].right_neighbor=_data[_minimum].right_neighbor;
   169         _data[_minimum].right_neighbor=i;
   170         _data[i].left_neighbor=_minimum;
   171         if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
   172       } else {
   173         _data[i].right_neighbor=_data[i].left_neighbor=i;
   174         _minimum=i;
   175       }
   176       _data[i].prio=value;
   177       ++_num;
   178     }
   179 
   180     /// \brief Returns the item with minimum priority relative to \c Compare.
   181     ///
   182     /// This method returns the item with minimum priority relative to \c
   183     /// Compare.
   184     /// \pre The heap must be nonempty.
   185     Item top() const { return _data[_minimum].name; }
   186 
   187     /// \brief Returns the minimum priority relative to \c Compare.
   188     ///
   189     /// It returns the minimum priority relative to \c Compare.
   190     /// \pre The heap must be nonempty.
   191     const Prio& prio() const { return _data[_minimum].prio; }
   192 
   193     /// \brief Returns the priority of \c item.
   194     ///
   195     /// It returns the priority of \c item.
   196     /// \pre \c item must be in the heap.
   197     const Prio& operator[](const Item& item) const {
   198       return _data[_iim[item]].prio;
   199     }
   200 
   201     /// \brief Deletes the item with minimum priority relative to \c Compare.
   202     ///
   203     /// This method deletes the item with minimum priority relative to \c
   204     /// Compare from the heap.
   205     /// \pre The heap must be non-empty.
   206     void pop() {
   207       /*The first case is that there are only one root.*/
   208       if ( _data[_minimum].left_neighbor==_minimum ) {
   209         _data[_minimum].in=false;
   210         if ( _data[_minimum].degree!=0 ) {
   211           makeroot(_data[_minimum].child);
   212           _minimum=_data[_minimum].child;
   213           balance();
   214         }
   215       } else {
   216         int right=_data[_minimum].right_neighbor;
   217         unlace(_minimum);
   218         _data[_minimum].in=false;
   219         if ( _data[_minimum].degree > 0 ) {
   220           int left=_data[_minimum].left_neighbor;
   221           int child=_data[_minimum].child;
   222           int last_child=_data[child].left_neighbor;
   223 
   224           makeroot(child);
   225 
   226           _data[left].right_neighbor=child;
   227           _data[child].left_neighbor=left;
   228           _data[right].left_neighbor=last_child;
   229           _data[last_child].right_neighbor=right;
   230         }
   231         _minimum=right;
   232         balance();
   233       } // the case where there are more roots
   234       --_num;
   235     }
   236 
   237     /// \brief Deletes \c item from the heap.
   238     ///
   239     /// This method deletes \c item from the heap, if \c item was already
   240     /// stored in the heap. It is quite inefficient in Fibonacci heaps.
   241     void erase (const Item& item) {
   242       int i=_iim[item];
   243 
   244       if ( i >= 0 && _data[i].in ) {
   245         if ( _data[i].parent!=-1 ) {
   246           int p=_data[i].parent;
   247           cut(i,p);
   248           cascade(p);
   249         }
   250         _minimum=i;     //As if its prio would be -infinity
   251         pop();
   252       }
   253     }
   254 
   255     /// \brief Decreases the priority of \c item to \c value.
   256     ///
   257     /// This method decreases the priority of \c item to \c value.
   258     /// \pre \c item must be stored in the heap with priority at least \c
   259     ///   value relative to \c Compare.
   260     void decrease (Item item, const Prio& value) {
   261       int i=_iim[item];
   262       _data[i].prio=value;
   263       int p=_data[i].parent;
   264 
   265       if ( p!=-1 && _comp(value, _data[p].prio) ) {
   266         cut(i,p);
   267         cascade(p);
   268       }
   269       if ( _comp(value, _data[_minimum].prio) ) _minimum=i;
   270     }
   271 
   272     /// \brief Increases the priority of \c item to \c value.
   273     ///
   274     /// This method sets the priority of \c item to \c value. Though
   275     /// there is no precondition on the priority of \c item, this
   276     /// method should be used only if it is indeed necessary to increase
   277     /// (relative to \c Compare) the priority of \c item, because this
   278     /// method is inefficient.
   279     void increase (Item item, const Prio& value) {
   280       erase(item);
   281       push(item, value);
   282     }
   283 
   284 
   285     /// \brief Returns if \c item is in, has already been in, or has never
   286     /// been in the heap.
   287     ///
   288     /// This method returns PRE_HEAP if \c item has never been in the
   289     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   290     /// otherwise. In the latter case it is possible that \c item will
   291     /// get back to the heap again.
   292     State state(const Item &item) const {
   293       int i=_iim[item];
   294       if( i>=0 ) {
   295         if ( _data[i].in ) i=0;
   296         else i=-2;
   297       }
   298       return State(i);
   299     }
   300 
   301     /// \brief Sets the state of the \c item in the heap.
   302     ///
   303     /// Sets the state of the \c item in the heap. It can be used to
   304     /// manually clear the heap when it is important to achive the
   305     /// better time _complexity.
   306     /// \param i The item.
   307     /// \param st The state. It should not be \c IN_HEAP.
   308     void state(const Item& i, State st) {
   309       switch (st) {
   310       case POST_HEAP:
   311       case PRE_HEAP:
   312         if (state(i) == IN_HEAP) {
   313           erase(i);
   314         }
   315         _iim[i] = st;
   316         break;
   317       case IN_HEAP:
   318         break;
   319       }
   320     }
   321 
   322   private:
   323 
   324     void balance() {
   325 
   326       int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
   327 
   328       std::vector<int> A(maxdeg,-1);
   329 
   330       /*
   331        *Recall that now minimum does not point to the minimum prio element.
   332        *We set minimum to this during balance().
   333        */
   334       int anchor=_data[_minimum].left_neighbor;
   335       int next=_minimum;
   336       bool end=false;
   337 
   338       do {
   339         int active=next;
   340         if ( anchor==active ) end=true;
   341         int d=_data[active].degree;
   342         next=_data[active].right_neighbor;
   343 
   344         while (A[d]!=-1) {
   345           if( _comp(_data[active].prio, _data[A[d]].prio) ) {
   346             fuse(active,A[d]);
   347           } else {
   348             fuse(A[d],active);
   349             active=A[d];
   350           }
   351           A[d]=-1;
   352           ++d;
   353         }
   354         A[d]=active;
   355       } while ( !end );
   356 
   357 
   358       while ( _data[_minimum].parent >=0 )
   359         _minimum=_data[_minimum].parent;
   360       int s=_minimum;
   361       int m=_minimum;
   362       do {
   363         if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
   364         s=_data[s].right_neighbor;
   365       } while ( s != m );
   366     }
   367 
   368     void makeroot(int c) {
   369       int s=c;
   370       do {
   371         _data[s].parent=-1;
   372         s=_data[s].right_neighbor;
   373       } while ( s != c );
   374     }
   375 
   376     void cut(int a, int b) {
   377       /*
   378        *Replacing a from the children of b.
   379        */
   380       --_data[b].degree;
   381 
   382       if ( _data[b].degree !=0 ) {
   383         int child=_data[b].child;
   384         if ( child==a )
   385           _data[b].child=_data[child].right_neighbor;
   386         unlace(a);
   387       }
   388 
   389 
   390       /*Lacing a to the roots.*/
   391       int right=_data[_minimum].right_neighbor;
   392       _data[_minimum].right_neighbor=a;
   393       _data[a].left_neighbor=_minimum;
   394       _data[a].right_neighbor=right;
   395       _data[right].left_neighbor=a;
   396 
   397       _data[a].parent=-1;
   398       _data[a].marked=false;
   399     }
   400 
   401     void cascade(int a) {
   402       if ( _data[a].parent!=-1 ) {
   403         int p=_data[a].parent;
   404 
   405         if ( _data[a].marked==false ) _data[a].marked=true;
   406         else {
   407           cut(a,p);
   408           cascade(p);
   409         }
   410       }
   411     }
   412 
   413     void fuse(int a, int b) {
   414       unlace(b);
   415 
   416       /*Lacing b under a.*/
   417       _data[b].parent=a;
   418 
   419       if (_data[a].degree==0) {
   420         _data[b].left_neighbor=b;
   421         _data[b].right_neighbor=b;
   422         _data[a].child=b;
   423       } else {
   424         int child=_data[a].child;
   425         int last_child=_data[child].left_neighbor;
   426         _data[child].left_neighbor=b;
   427         _data[b].right_neighbor=child;
   428         _data[last_child].right_neighbor=b;
   429         _data[b].left_neighbor=last_child;
   430       }
   431 
   432       ++_data[a].degree;
   433 
   434       _data[b].marked=false;
   435     }
   436 
   437     /*
   438      *It is invoked only if a has siblings.
   439      */
   440     void unlace(int a) {
   441       int leftn=_data[a].left_neighbor;
   442       int rightn=_data[a].right_neighbor;
   443       _data[leftn].right_neighbor=rightn;
   444       _data[rightn].left_neighbor=leftn;
   445     }
   446 
   447 
   448     class Store {
   449       friend class FibHeap;
   450 
   451       Item name;
   452       int parent;
   453       int left_neighbor;
   454       int right_neighbor;
   455       int child;
   456       int degree;
   457       bool marked;
   458       bool in;
   459       Prio prio;
   460 
   461       Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
   462     };
   463   };
   464 
   465 } //namespace lemon
   466 
   467 #endif //LEMON_FIB_HEAP_H
   468