lemon/fib_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Thu, 17 Mar 2011 00:35:33 +0100
changeset 931 f112c18bc304
parent 710 f1fe0ddad6f7
permissions -rw-r--r--
Bug fix in CostScaling (#417)
     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 heaps
    24 ///\brief Fibonacci heap implementation.
    25 
    26 #include <vector>
    27 #include <utility>
    28 #include <functional>
    29 #include <lemon/math.h>
    30 
    31 namespace lemon {
    32 
    33   /// \ingroup heaps
    34   ///
    35   /// \brief Fibonacci heap data structure.
    36   ///
    37   /// This class implements the \e Fibonacci \e heap data structure.
    38   /// It fully conforms to the \ref concepts::Heap "heap concept".
    39   ///
    40   /// The methods \ref increase() and \ref erase() are not efficient in a
    41   /// Fibonacci heap. In case of many calls of these operations, it is
    42   /// better to use other heap structure, e.g. \ref BinHeap "binary heap".
    43   ///
    44   /// \tparam PR Type of the priorities of the items.
    45   /// \tparam IM A read-writable item map with \c int values, used
    46   /// internally to handle the cross references.
    47   /// \tparam CMP A functor class for comparing the priorities.
    48   /// The default is \c std::less<PR>.
    49 #ifdef DOXYGEN
    50   template <typename PR, typename IM, typename CMP>
    51 #else
    52   template <typename PR, typename IM, typename CMP = std::less<PR> >
    53 #endif
    54   class FibHeap {
    55   public:
    56 
    57     /// Type of the item-int map.
    58     typedef IM ItemIntMap;
    59     /// Type of the priorities.
    60     typedef PR Prio;
    61     /// Type of the items stored in the heap.
    62     typedef typename ItemIntMap::Key Item;
    63     /// Type of the item-priority pairs.
    64     typedef std::pair<Item,Prio> Pair;
    65     /// Functor type for comparing the priorities.
    66     typedef CMP Compare;
    67 
    68   private:
    69     class Store;
    70 
    71     std::vector<Store> _data;
    72     int _minimum;
    73     ItemIntMap &_iim;
    74     Compare _comp;
    75     int _num;
    76 
    77   public:
    78 
    79     /// \brief Type to represent the states of the items.
    80     ///
    81     /// Each item has a state associated to it. It can be "in heap",
    82     /// "pre-heap" or "post-heap". The latter two are indifferent from the
    83     /// heap's point of view, but may be useful to the user.
    84     ///
    85     /// The item-int map must be initialized in such way that it assigns
    86     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    87     enum State {
    88       IN_HEAP = 0,    ///< = 0.
    89       PRE_HEAP = -1,  ///< = -1.
    90       POST_HEAP = -2  ///< = -2.
    91     };
    92 
    93     /// \brief Constructor.
    94     ///
    95     /// Constructor.
    96     /// \param map A map that assigns \c int values to the items.
    97     /// It is used internally to handle the cross references.
    98     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
    99     explicit FibHeap(ItemIntMap &map)
   100       : _minimum(0), _iim(map), _num() {}
   101 
   102     /// \brief Constructor.
   103     ///
   104     /// Constructor.
   105     /// \param map A map that assigns \c int values to the items.
   106     /// It is used internally to handle the cross references.
   107     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   108     /// \param comp The function object used for comparing 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     /// This function returns the number of items stored in the heap.
   115     int size() const { return _num; }
   116 
   117     /// \brief Check if the heap is empty.
   118     ///
   119     /// This function returns \c true if the heap is empty.
   120     bool empty() const { return _num==0; }
   121 
   122     /// \brief Make the heap empty.
   123     ///
   124     /// This functon makes the heap empty.
   125     /// It does not change the cross reference map. If you want to reuse
   126     /// a heap that is not surely empty, you should first clear it and
   127     /// then you should set the cross reference map to \c PRE_HEAP
   128     /// for each item.
   129     void clear() {
   130       _data.clear(); _minimum = 0; _num = 0;
   131     }
   132 
   133     /// \brief Insert an item into the heap with the given priority.
   134     ///
   135     /// This function inserts the given item into the heap with the
   136     /// given priority.
   137     /// \param item The item to insert.
   138     /// \param prio The priority of the item.
   139     /// \pre \e item must not be stored in the heap.
   140     void push (const Item& item, const Prio& prio) {
   141       int i=_iim[item];
   142       if ( i < 0 ) {
   143         int s=_data.size();
   144         _iim.set( item, s );
   145         Store st;
   146         st.name=item;
   147         _data.push_back(st);
   148         i=s;
   149       } else {
   150         _data[i].parent=_data[i].child=-1;
   151         _data[i].degree=0;
   152         _data[i].in=true;
   153         _data[i].marked=false;
   154       }
   155 
   156       if ( _num ) {
   157         _data[_data[_minimum].right_neighbor].left_neighbor=i;
   158         _data[i].right_neighbor=_data[_minimum].right_neighbor;
   159         _data[_minimum].right_neighbor=i;
   160         _data[i].left_neighbor=_minimum;
   161         if ( _comp( prio, _data[_minimum].prio) ) _minimum=i;
   162       } else {
   163         _data[i].right_neighbor=_data[i].left_neighbor=i;
   164         _minimum=i;
   165       }
   166       _data[i].prio=prio;
   167       ++_num;
   168     }
   169 
   170     /// \brief Return the item having minimum priority.
   171     ///
   172     /// This function returns the item having minimum priority.
   173     /// \pre The heap must be non-empty.
   174     Item top() const { return _data[_minimum].name; }
   175 
   176     /// \brief The minimum priority.
   177     ///
   178     /// This function returns the minimum priority.
   179     /// \pre The heap must be non-empty.
   180     Prio prio() const { return _data[_minimum].prio; }
   181 
   182     /// \brief Remove the item having minimum priority.
   183     ///
   184     /// This function removes the item having minimum priority.
   185     /// \pre The heap must be non-empty.
   186     void pop() {
   187       /*The first case is that there are only one root.*/
   188       if ( _data[_minimum].left_neighbor==_minimum ) {
   189         _data[_minimum].in=false;
   190         if ( _data[_minimum].degree!=0 ) {
   191           makeRoot(_data[_minimum].child);
   192           _minimum=_data[_minimum].child;
   193           balance();
   194         }
   195       } else {
   196         int right=_data[_minimum].right_neighbor;
   197         unlace(_minimum);
   198         _data[_minimum].in=false;
   199         if ( _data[_minimum].degree > 0 ) {
   200           int left=_data[_minimum].left_neighbor;
   201           int child=_data[_minimum].child;
   202           int last_child=_data[child].left_neighbor;
   203 
   204           makeRoot(child);
   205 
   206           _data[left].right_neighbor=child;
   207           _data[child].left_neighbor=left;
   208           _data[right].left_neighbor=last_child;
   209           _data[last_child].right_neighbor=right;
   210         }
   211         _minimum=right;
   212         balance();
   213       } // the case where there are more roots
   214       --_num;
   215     }
   216 
   217     /// \brief Remove the given item from the heap.
   218     ///
   219     /// This function removes the given item from the heap if it is
   220     /// already stored.
   221     /// \param item The item to delete.
   222     /// \pre \e item must be in the heap.
   223     void erase (const Item& item) {
   224       int i=_iim[item];
   225 
   226       if ( i >= 0 && _data[i].in ) {
   227         if ( _data[i].parent!=-1 ) {
   228           int p=_data[i].parent;
   229           cut(i,p);
   230           cascade(p);
   231         }
   232         _minimum=i;     //As if its prio would be -infinity
   233         pop();
   234       }
   235     }
   236 
   237     /// \brief The priority of the given item.
   238     ///
   239     /// This function returns the priority of the given item.
   240     /// \param item The item.
   241     /// \pre \e item must be in the heap.
   242     Prio operator[](const Item& item) const {
   243       return _data[_iim[item]].prio;
   244     }
   245 
   246     /// \brief Set the priority of an item or insert it, if it is
   247     /// not stored in the heap.
   248     ///
   249     /// This method sets the priority of the given item if it is
   250     /// already stored in the heap. Otherwise it inserts the given
   251     /// item into the heap with the given priority.
   252     /// \param item The item.
   253     /// \param prio The priority.
   254     void set (const Item& item, const Prio& prio) {
   255       int i=_iim[item];
   256       if ( i >= 0 && _data[i].in ) {
   257         if ( _comp(prio, _data[i].prio) ) decrease(item, prio);
   258         if ( _comp(_data[i].prio, prio) ) increase(item, prio);
   259       } else push(item, prio);
   260     }
   261 
   262     /// \brief Decrease the priority of an item to the given value.
   263     ///
   264     /// This function decreases the priority of an item to the given value.
   265     /// \param item The item.
   266     /// \param prio The priority.
   267     /// \pre \e item must be stored in the heap with priority at least \e prio.
   268     void decrease (const Item& item, const Prio& prio) {
   269       int i=_iim[item];
   270       _data[i].prio=prio;
   271       int p=_data[i].parent;
   272 
   273       if ( p!=-1 && _comp(prio, _data[p].prio) ) {
   274         cut(i,p);
   275         cascade(p);
   276       }
   277       if ( _comp(prio, _data[_minimum].prio) ) _minimum=i;
   278     }
   279 
   280     /// \brief Increase the priority of an item to the given value.
   281     ///
   282     /// This function increases the priority of an item to the given value.
   283     /// \param item The item.
   284     /// \param prio The priority.
   285     /// \pre \e item must be stored in the heap with priority at most \e prio.
   286     void increase (const Item& item, const Prio& prio) {
   287       erase(item);
   288       push(item, prio);
   289     }
   290 
   291     /// \brief Return the state of an item.
   292     ///
   293     /// This method returns \c PRE_HEAP if the given item has never
   294     /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
   295     /// and \c POST_HEAP otherwise.
   296     /// In the latter case it is possible that the item will get back
   297     /// to the heap again.
   298     /// \param item The item.
   299     State state(const Item &item) const {
   300       int i=_iim[item];
   301       if( i>=0 ) {
   302         if ( _data[i].in ) i=0;
   303         else i=-2;
   304       }
   305       return State(i);
   306     }
   307 
   308     /// \brief Set the state of an item in the heap.
   309     ///
   310     /// This function sets the state of the given item in the heap.
   311     /// It can be used to manually clear the heap when it is important
   312     /// to achive 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   private:
   330 
   331     void balance() {
   332 
   333       int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
   334 
   335       std::vector<int> A(maxdeg,-1);
   336 
   337       /*
   338        *Recall that now minimum does not point to the minimum prio element.
   339        *We set minimum to this during balance().
   340        */
   341       int anchor=_data[_minimum].left_neighbor;
   342       int next=_minimum;
   343       bool end=false;
   344 
   345       do {
   346         int active=next;
   347         if ( anchor==active ) end=true;
   348         int d=_data[active].degree;
   349         next=_data[active].right_neighbor;
   350 
   351         while (A[d]!=-1) {
   352           if( _comp(_data[active].prio, _data[A[d]].prio) ) {
   353             fuse(active,A[d]);
   354           } else {
   355             fuse(A[d],active);
   356             active=A[d];
   357           }
   358           A[d]=-1;
   359           ++d;
   360         }
   361         A[d]=active;
   362       } while ( !end );
   363 
   364 
   365       while ( _data[_minimum].parent >=0 )
   366         _minimum=_data[_minimum].parent;
   367       int s=_minimum;
   368       int m=_minimum;
   369       do {
   370         if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
   371         s=_data[s].right_neighbor;
   372       } while ( s != m );
   373     }
   374 
   375     void makeRoot(int c) {
   376       int s=c;
   377       do {
   378         _data[s].parent=-1;
   379         s=_data[s].right_neighbor;
   380       } while ( s != c );
   381     }
   382 
   383     void cut(int a, int b) {
   384       /*
   385        *Replacing a from the children of b.
   386        */
   387       --_data[b].degree;
   388 
   389       if ( _data[b].degree !=0 ) {
   390         int child=_data[b].child;
   391         if ( child==a )
   392           _data[b].child=_data[child].right_neighbor;
   393         unlace(a);
   394       }
   395 
   396 
   397       /*Lacing a to the roots.*/
   398       int right=_data[_minimum].right_neighbor;
   399       _data[_minimum].right_neighbor=a;
   400       _data[a].left_neighbor=_minimum;
   401       _data[a].right_neighbor=right;
   402       _data[right].left_neighbor=a;
   403 
   404       _data[a].parent=-1;
   405       _data[a].marked=false;
   406     }
   407 
   408     void cascade(int a) {
   409       if ( _data[a].parent!=-1 ) {
   410         int p=_data[a].parent;
   411 
   412         if ( _data[a].marked==false ) _data[a].marked=true;
   413         else {
   414           cut(a,p);
   415           cascade(p);
   416         }
   417       }
   418     }
   419 
   420     void fuse(int a, int b) {
   421       unlace(b);
   422 
   423       /*Lacing b under a.*/
   424       _data[b].parent=a;
   425 
   426       if (_data[a].degree==0) {
   427         _data[b].left_neighbor=b;
   428         _data[b].right_neighbor=b;
   429         _data[a].child=b;
   430       } else {
   431         int child=_data[a].child;
   432         int last_child=_data[child].left_neighbor;
   433         _data[child].left_neighbor=b;
   434         _data[b].right_neighbor=child;
   435         _data[last_child].right_neighbor=b;
   436         _data[b].left_neighbor=last_child;
   437       }
   438 
   439       ++_data[a].degree;
   440 
   441       _data[b].marked=false;
   442     }
   443 
   444     /*
   445      *It is invoked only if a has siblings.
   446      */
   447     void unlace(int a) {
   448       int leftn=_data[a].left_neighbor;
   449       int rightn=_data[a].right_neighbor;
   450       _data[leftn].right_neighbor=rightn;
   451       _data[rightn].left_neighbor=leftn;
   452     }
   453 
   454 
   455     class Store {
   456       friend class FibHeap;
   457 
   458       Item name;
   459       int parent;
   460       int left_neighbor;
   461       int right_neighbor;
   462       int child;
   463       int degree;
   464       bool marked;
   465       bool in;
   466       Prio prio;
   467 
   468       Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
   469     };
   470   };
   471 
   472 } //namespace lemon
   473 
   474 #endif //LEMON_FIB_HEAP_H
   475