lemon/fib_heap.h
author Balazs Dezso <deba@inf.elte.hu>
Thu, 11 Jun 2009 22:11:29 +0200
changeset 728 532697c9fa53
child 730 9f529abcaebf
permissions -rw-r--r--
Port remaining heaps from SVN -r 3509 (#50)

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