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lemon/fib_heap.h
changeset 988 8d281761dea4
parent 681 532697c9fa53
child 709 0747f332c478
equal deleted inserted replaced
0:ecddf211311d 1:a79efae23ee0 
    34   ///\brief Fibonacci Heap.
 
    34   ///\brief Fibonacci Heap.
 
    35   ///
 
    35   ///
 
    36   ///This class implements the \e Fibonacci \e heap data structure. A \e heap
 
    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
 
    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
 
    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
 
    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.
 
    40   ///one can change the priority of an item, add or erase an item, etc.
 
    41   ///
 
    41   ///
 
    42   ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
 
    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
 
    43   ///heap. In case of many calls to these operations, it is better to use a
 
    44   ///\ref BinHeap "binary heap".
 
    44   ///\ref BinHeap "binary heap".
 
    45   ///
 
    45   ///
 
    46   ///\param _Prio Type of the priority of the items.
 
    46   ///\param PRIO Type of the priority of the items.
 
    47   ///\param _ItemIntMap A read and writable Item int map, used internally
 
    47   ///\param IM A read and writable Item int map, used internally
 
    48   ///to handle the cross references.
 
    48   ///to handle the cross references.
 
    49   ///\param _Compare A class for the ordering of the priorities. The
 
    49   ///\param CMP A class for the ordering of the priorities. The
 
    50   ///default is \c std::less<_Prio>.
 
    50   ///default is \c std::less<PRIO>.
 
    51   ///
 
    51   ///
 
    52   ///\sa BinHeap
 
    52   ///\sa BinHeap
 
    53   ///\sa Dijkstra
 
    53   ///\sa Dijkstra
 
    54 #ifdef DOXYGEN
 
    54 #ifdef DOXYGEN
 
    55   template <typename _Prio,
 
    55   template <typename PRIO, typename IM, typename CMP>
 
    56             typename _ItemIntMap,
 
       
    57             typename _Compare>
 
       
    58 #else
 
    56 #else
 
    59   template <typename _Prio,
 
    57   template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
 
    60             typename _ItemIntMap,
 
       
    61             typename _Compare = std::less<_Prio> >
 
       
    62 #endif
 
    58 #endif
 
    63   class FibHeap {
 
    59   class FibHeap {
 
    64   public:
 
    60   public:
 
    65     ///\e
 
    61     ///\e
 
    66     typedef _ItemIntMap ItemIntMap;
 
    62     typedef IM ItemIntMap;
 
    67     ///\e
 
    63     ///\e
 
    68     typedef _Prio Prio;
 
    64     typedef PRIO Prio;
 
    69     ///\e
 
    65     ///\e
 
    70     typedef typename ItemIntMap::Key Item;
 
    66     typedef typename ItemIntMap::Key Item;
 
    71     ///\e
 
    67     ///\e
 
    72     typedef std::pair<Item,Prio> Pair;
 
    68     typedef std::pair<Item,Prio> Pair;
 
    73     ///\e
 
    69     ///\e
 
    74     typedef _Compare Compare;
 
    70     typedef CMP Compare;
 
    75 
    71 
    76   private:
 
    72   private:
 
    77     class store;
 
    73     class Store;
 
    78 
    74 
    79     std::vector<store> container;
 
    75     std::vector<Store> _data;
 
    80     int minimum;
 
    76     int _minimum;
 
    81     ItemIntMap &iimap;
 
    77     ItemIntMap &_iim;
 
    82     Compare comp;
 
    78     Compare _comp;
 
    83     int num_items;
 
    79     int _num;
 
    84 
    80 
    85   public:
 
    81   public:
 
    86     ///Status of the nodes
 
    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.
 
    87     enum State {
 
    91     enum State {
 
    88       ///The node is in the heap
 
    92       IN_HEAP = 0,    ///< = 0.
 
    89       IN_HEAP = 0,
 
    93       PRE_HEAP = -1,  ///< = -1.
 
    90       ///The node has never been in the heap
 
    94       POST_HEAP = -2  ///< = -2.
 
    91       PRE_HEAP = -1,
 
       
    92       ///The node was in the heap but it got out of it
 
       
    93       POST_HEAP = -2
 
       
    94     };
 
    95     };
 
    95 
    96 
    96     /// \brief The constructor
 
    97     /// \brief The constructor
 
    97     ///
 
    98     ///
 
    98     /// \c _iimap should be given to the constructor, since it is
 
    99     /// \c map should be given to the constructor, since it is
 
    99     ///   used internally to handle the cross references.
 
   100     ///   used internally to handle the cross references.
 
   100     explicit FibHeap(ItemIntMap &_iimap)
 
   101     explicit FibHeap(ItemIntMap &map)
 
   101       : minimum(0), iimap(_iimap), num_items() {}
 
   102       : _minimum(0), _iim(map), _num() {}
 
   102 
   103 
   103     /// \brief The constructor
 
   104     /// \brief The constructor
 
   104     ///
 
   105     ///
 
   105     /// \c _iimap should be given to the constructor, since it is used
 
   106     /// \c map should be given to the constructor, since it is used
 
   106     /// internally to handle the cross references. \c _comp is an
 
   107     /// internally to handle the cross references. \c comp is an
 
   107     /// object for ordering of the priorities.
 
   108     /// object for ordering of the priorities.
 
   108     FibHeap(ItemIntMap &_iimap, const Compare &_comp)
 
   109     FibHeap(ItemIntMap &map, const Compare &comp)
 
   109       : minimum(0), iimap(_iimap), comp(_comp), num_items() {}
 
   110       : _minimum(0), _iim(map), _comp(comp), _num() {}
 
   110 
   111 
   111     /// \brief The number of items stored in the heap.
 
   112     /// \brief The number of items stored in the heap.
 
   112     ///
 
   113     ///
 
   113     /// Returns the number of items stored in the heap.
 
   114     /// Returns the number of items stored in the heap.
 
   114     int size() const { return num_items; }
 
   115     int size() const { return _num; }
 
   115 
   116 
   116     /// \brief Checks if the heap stores no items.
 
   117     /// \brief Checks if the heap stores no items.
 
   117     ///
 
   118     ///
 
   118     ///   Returns \c true if and only if the heap stores no items.
 
   119     ///   Returns \c true if and only if the heap stores no items.
 
   119     bool empty() const { return num_items==0; }
 
   120     bool empty() const { return _num==0; }
 
   120 
   121 
   121     /// \brief Make empty this heap.
 
   122     /// \brief Make empty this heap.
 
   122     ///
 
   123     ///
 
   123     /// Make empty this heap. It does not change the cross reference
 
   124     /// 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     /// 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     /// should first clear the heap and after that you should set the
 
   126     /// cross reference map for each item to \c PRE_HEAP.
 
   127     /// cross reference map for each item to \c PRE_HEAP.
 
   127     void clear() {
 
   128     void clear() {
 
   128       container.clear(); minimum = 0; num_items = 0;
 
   129       _data.clear(); _minimum = 0; _num = 0;
 
   129     }
 
   130     }
 
   130 
   131 
   131     /// \brief \c item gets to the heap with priority \c value independently
 
   132     /// \brief \c item gets to the heap with priority \c value independently
 
   132     /// if \c item was already there.
 
   133     /// if \c item was already there.
 
   133     ///
 
   134     ///
 
   134     /// This method calls \ref push(\c item, \c value) if \c item is not
 
   135     /// 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     /// stored in the heap and it calls \ref decrease(\c item, \c value) or
 
   136     /// \ref increase(\c item, \c value) otherwise.
 
   137     /// \ref increase(\c item, \c value) otherwise.
 
   137     void set (const Item& item, const Prio& value) {
 
   138     void set (const Item& item, const Prio& value) {
 
   138       int i=iimap[item];
 
   139       int i=_iim[item];
 
   139       if ( i >= 0 && container[i].in ) {
 
   140       if ( i >= 0 && _data[i].in ) {
 
   140         if ( comp(value, container[i].prio) ) decrease(item, value);
 
   141         if ( _comp(value, _data[i].prio) ) decrease(item, value);
 
   141         if ( comp(container[i].prio, value) ) increase(item, value);
 
   142         if ( _comp(_data[i].prio, value) ) increase(item, value);
 
   142       } else push(item, value);
 
   143       } else push(item, value);
 
   143     }
 
   144     }
 
   144 
   145 
   145     /// \brief Adds \c item to the heap with priority \c value.
 
   146     /// \brief Adds \c item to the heap with priority \c value.
 
   146     ///
 
   147     ///
 
   147     /// Adds \c item to the heap with priority \c value.
 
   148     /// Adds \c item to the heap with priority \c value.
 
   148     /// \pre \c item must not be stored in the heap.
 
   149     /// \pre \c item must not be stored in the heap.
 
   149     void push (const Item& item, const Prio& value) {
 
   150     void push (const Item& item, const Prio& value) {
 
   150       int i=iimap[item];
 
   151       int i=_iim[item];
 
   151       if ( i < 0 ) {
 
   152       if ( i < 0 ) {
 
   152         int s=container.size();
 
   153         int s=_data.size();
 
   153         iimap.set( item, s );
 
   154         _iim.set( item, s );
 
   154         store st;
 
   155         Store st;
 
   155         st.name=item;
 
   156         st.name=item;
 
   156         container.push_back(st);
 
   157         _data.push_back(st);
 
   157         i=s;
 
   158         i=s;
 
   158       } else {
 
   159       } else {
 
   159         container[i].parent=container[i].child=-1;
 
   160         _data[i].parent=_data[i].child=-1;
 
   160         container[i].degree=0;
 
   161         _data[i].degree=0;
 
   161         container[i].in=true;
 
   162         _data[i].in=true;
 
   162         container[i].marked=false;
 
   163         _data[i].marked=false;
 
   163       }
 
   164       }
 
   164 
   165 
   165       if ( num_items ) {
 
   166       if ( _num ) {
 
   166         container[container[minimum].right_neighbor].left_neighbor=i;
 
   167         _data[_data[_minimum].right_neighbor].left_neighbor=i;
 
   167         container[i].right_neighbor=container[minimum].right_neighbor;
 
   168         _data[i].right_neighbor=_data[_minimum].right_neighbor;
 
   168         container[minimum].right_neighbor=i;
 
   169         _data[_minimum].right_neighbor=i;
 
   169         container[i].left_neighbor=minimum;
 
   170         _data[i].left_neighbor=_minimum;
 
   170         if ( comp( value, container[minimum].prio) ) minimum=i;
 
   171         if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
 
   171       } else {
 
   172       } else {
 
   172         container[i].right_neighbor=container[i].left_neighbor=i;
 
   173         _data[i].right_neighbor=_data[i].left_neighbor=i;
 
   173         minimum=i;
 
   174         _minimum=i;
 
   174       }
 
   175       }
 
   175       container[i].prio=value;
 
   176       _data[i].prio=value;
 
   176       ++num_items;
 
   177       ++_num;
 
   177     }
 
   178     }
 
   178 
   179 
   179     /// \brief Returns the item with minimum priority relative to \c Compare.
 
   180     /// \brief Returns the item with minimum priority relative to \c Compare.
 
   180     ///
 
   181     ///
 
   181     /// This method returns the item with minimum priority relative to \c
 
   182     /// This method returns the item with minimum priority relative to \c
 
   182     /// Compare.
 
   183     /// Compare.
 
   183     /// \pre The heap must be nonempty.
 
   184     /// \pre The heap must be nonempty.
 
   184     Item top() const { return container[minimum].name; }
 
   185     Item top() const { return _data[_minimum].name; }
 
   185 
   186 
   186     /// \brief Returns the minimum priority relative to \c Compare.
 
   187     /// \brief Returns the minimum priority relative to \c Compare.
 
   187     ///
 
   188     ///
 
   188     /// It returns the minimum priority relative to \c Compare.
 
   189     /// It returns the minimum priority relative to \c Compare.
 
   189     /// \pre The heap must be nonempty.
 
   190     /// \pre The heap must be nonempty.
 
   190     const Prio& prio() const { return container[minimum].prio; }
 
   191     const Prio& prio() const { return _data[_minimum].prio; }
 
   191 
   192 
   192     /// \brief Returns the priority of \c item.
 
   193     /// \brief Returns the priority of \c item.
 
   193     ///
 
   194     ///
 
   194     /// It returns the priority of \c item.
 
   195     /// It returns the priority of \c item.
 
   195     /// \pre \c item must be in the heap.
 
   196     /// \pre \c item must be in the heap.
 
   196     const Prio& operator[](const Item& item) const {
 
   197     const Prio& operator[](const Item& item) const {
 
   197       return container[iimap[item]].prio;
 
   198       return _data[_iim[item]].prio;
 
   198     }
 
   199     }
 
   199 
   200 
   200     /// \brief Deletes the item with minimum priority relative to \c Compare.
 
   201     /// \brief Deletes the item with minimum priority relative to \c Compare.
 
   201     ///
 
   202     ///
 
   202     /// This method deletes the item with minimum priority relative to \c
 
   203     /// This method deletes the item with minimum priority relative to \c
 
   203     /// Compare from the heap.
 
   204     /// Compare from the heap.
 
   204     /// \pre The heap must be non-empty.
 
   205     /// \pre The heap must be non-empty.
 
   205     void pop() {
 
   206     void pop() {
 
   206       /*The first case is that there are only one root.*/
 
   207       /*The first case is that there are only one root.*/
 
   207       if ( container[minimum].left_neighbor==minimum ) {
 
   208       if ( _data[_minimum].left_neighbor==_minimum ) {
 
   208         container[minimum].in=false;
 
   209         _data[_minimum].in=false;
 
   209         if ( container[minimum].degree!=0 ) {
 
   210         if ( _data[_minimum].degree!=0 ) {
 
   210           makeroot(container[minimum].child);
 
   211           makeroot(_data[_minimum].child);
 
   211           minimum=container[minimum].child;
 
   212           _minimum=_data[_minimum].child;
 
   212           balance();
 
   213           balance();
 
   213         }
 
   214         }
 
   214       } else {
 
   215       } else {
 
   215         int right=container[minimum].right_neighbor;
 
   216         int right=_data[_minimum].right_neighbor;
 
   216         unlace(minimum);
 
   217         unlace(_minimum);
 
   217         container[minimum].in=false;
 
   218         _data[_minimum].in=false;
 
   218         if ( container[minimum].degree > 0 ) {
 
   219         if ( _data[_minimum].degree > 0 ) {
 
   219           int left=container[minimum].left_neighbor;
 
   220           int left=_data[_minimum].left_neighbor;
 
   220           int child=container[minimum].child;
 
   221           int child=_data[_minimum].child;
 
   221           int last_child=container[child].left_neighbor;
 
   222           int last_child=_data[child].left_neighbor;
 
   222 
   223 
   223           makeroot(child);
 
   224           makeroot(child);
 
   224 
   225 
   225           container[left].right_neighbor=child;
 
   226           _data[left].right_neighbor=child;
 
   226           container[child].left_neighbor=left;
 
   227           _data[child].left_neighbor=left;
 
   227           container[right].left_neighbor=last_child;
 
   228           _data[right].left_neighbor=last_child;
 
   228           container[last_child].right_neighbor=right;
 
   229           _data[last_child].right_neighbor=right;
 
   229         }
 
   230         }
 
   230         minimum=right;
 
   231         _minimum=right;
 
   231         balance();
 
   232         balance();
 
   232       } // the case where there are more roots
 
   233       } // the case where there are more roots
 
   233       --num_items;
 
   234       --_num;
 
   234     }
 
   235     }
 
   235 
   236 
   236     /// \brief Deletes \c item from the heap.
 
   237     /// \brief Deletes \c item from the heap.
 
   237     ///
 
   238     ///
 
   238     /// This method deletes \c item from the heap, if \c item was already
 
   239     /// 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     /// stored in the heap. It is quite inefficient in Fibonacci heaps.
 
   240     void erase (const Item& item) {
 
   241     void erase (const Item& item) {
 
   241       int i=iimap[item];
 
   242       int i=_iim[item];
 
   242 
   243 
   243       if ( i >= 0 && container[i].in ) {
 
   244       if ( i >= 0 && _data[i].in ) {
 
   244         if ( container[i].parent!=-1 ) {
 
   245         if ( _data[i].parent!=-1 ) {
 
   245           int p=container[i].parent;
 
   246           int p=_data[i].parent;
 
   246           cut(i,p);
 
   247           cut(i,p);
 
   247           cascade(p);
 
   248           cascade(p);
 
   248         }
 
   249         }
 
   249         minimum=i;     //As if its prio would be -infinity
 
   250         _minimum=i;     //As if its prio would be -infinity
 
   250         pop();
 
   251         pop();
 
   251       }
 
   252       }
 
   252     }
 
   253     }
 
   253 
   254 
   254     /// \brief Decreases the priority of \c item to \c value.
 
   255     /// \brief Decreases the priority of \c item to \c value.
 
   255     ///
 
   256     ///
 
   256     /// This method decreases the priority of \c item to \c value.
 
   257     /// 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     /// \pre \c item must be stored in the heap with priority at least \c
 
   258     ///   value relative to \c Compare.
 
   259     ///   value relative to \c Compare.
 
   259     void decrease (Item item, const Prio& value) {
 
   260     void decrease (Item item, const Prio& value) {
 
   260       int i=iimap[item];
 
   261       int i=_iim[item];
 
   261       container[i].prio=value;
 
   262       _data[i].prio=value;
 
   262       int p=container[i].parent;
 
   263       int p=_data[i].parent;
 
   263 
   264 
   264       if ( p!=-1 && comp(value, container[p].prio) ) {
 
   265       if ( p!=-1 && _comp(value, _data[p].prio) ) {
 
   265         cut(i,p);
 
   266         cut(i,p);
 
   266         cascade(p);
 
   267         cascade(p);
 
   267       }
 
   268       }
 
   268       if ( comp(value, container[minimum].prio) ) minimum=i;
 
   269       if ( _comp(value, _data[_minimum].prio) ) _minimum=i;
 
   269     }
 
   270     }
 
   270 
   271 
   271     /// \brief Increases the priority of \c item to \c value.
 
   272     /// \brief Increases the priority of \c item to \c value.
 
   272     ///
 
   273     ///
 
   273     /// This method sets the priority of \c item to \c value. Though
 
   274     /// This method sets the priority of \c item to \c value. Though
 
   287     /// This method returns PRE_HEAP if \c item has never been in the
 
   288     /// 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     /// 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     /// otherwise. In the latter case it is possible that \c item will
 
   290     /// get back to the heap again.
 
   291     /// get back to the heap again.
 
   291     State state(const Item &item) const {
 
   292     State state(const Item &item) const {
 
   292       int i=iimap[item];
 
   293       int i=_iim[item];
 
   293       if( i>=0 ) {
 
   294       if( i>=0 ) {
 
   294         if ( container[i].in ) i=0;
 
   295         if ( _data[i].in ) i=0;
 
   295         else i=-2;
 
   296         else i=-2;
 
   296       }
 
   297       }
 
   297       return State(i);
 
   298       return State(i);
 
   298     }
 
   299     }
 
   299 
   300 
   300     /// \brief Sets the state of the \c item in the heap.
 
   301     /// \brief Sets the state of the \c item in the heap.
 
   301     ///
 
   302     ///
 
   302     /// Sets the state of the \c item in the heap. It can be used to
 
   303     /// 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     /// manually clear the heap when it is important to achive the
 
   304     /// better time complexity.
 
   305     /// better time _complexity.
 
   305     /// \param i The item.
 
   306     /// \param i The item.
 
   306     /// \param st The state. It should not be \c IN_HEAP.
 
   307     /// \param st The state. It should not be \c IN_HEAP.
 
   307     void state(const Item& i, State st) {
 
   308     void state(const Item& i, State st) {
 
   308       switch (st) {
 
   309       switch (st) {
 
   309       case POST_HEAP:
 
   310       case POST_HEAP:
 
   310       case PRE_HEAP:
 
   311       case PRE_HEAP:
 
   311         if (state(i) == IN_HEAP) {
 
   312         if (state(i) == IN_HEAP) {
 
   312           erase(i);
 
   313           erase(i);
 
   313         }
 
   314         }
 
   314         iimap[i] = st;
 
   315         _iim[i] = st;
 
   315         break;
 
   316         break;
 
   316       case IN_HEAP:
 
   317       case IN_HEAP:
 
   317         break;
 
   318         break;
 
   318       }
 
   319       }
 
   319     }
 
   320     }
 
   320 
   321 
   321   private:
 
   322   private:
 
   322 
   323 
   323     void balance() {
 
   324     void balance() {
 
   324 
   325 
   325       int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1;
 
   326       int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
 
   326 
   327 
   327       std::vector<int> A(maxdeg,-1);
 
   328       std::vector<int> A(maxdeg,-1);
 
   328 
   329 
   329       /*
 
   330       /*
 
   330        *Recall that now minimum does not point to the minimum prio element.
 
   331        *Recall that now minimum does not point to the minimum prio element.
 
   331        *We set minimum to this during balance().
 
   332        *We set minimum to this during balance().
 
   332        */
 
   333        */
 
   333       int anchor=container[minimum].left_neighbor;
 
   334       int anchor=_data[_minimum].left_neighbor;
 
   334       int next=minimum;
 
   335       int next=_minimum;
 
   335       bool end=false;
 
   336       bool end=false;
 
   336 
   337 
   337       do {
 
   338       do {
 
   338         int active=next;
 
   339         int active=next;
 
   339         if ( anchor==active ) end=true;
 
   340         if ( anchor==active ) end=true;
 
   340         int d=container[active].degree;
 
   341         int d=_data[active].degree;
 
   341         next=container[active].right_neighbor;
 
   342         next=_data[active].right_neighbor;
 
   342 
   343 
   343         while (A[d]!=-1) {
 
   344         while (A[d]!=-1) {
 
   344           if( comp(container[active].prio, container[A[d]].prio) ) {
 
   345           if( _comp(_data[active].prio, _data[A[d]].prio) ) {
 
   345             fuse(active,A[d]);
 
   346             fuse(active,A[d]);
 
   346           } else {
 
   347           } else {
 
   347             fuse(A[d],active);
 
   348             fuse(A[d],active);
 
   348             active=A[d];
 
   349             active=A[d];
 
   349           }
 
   350           }
 
   352         }
 
   353         }
 
   353         A[d]=active;
 
   354         A[d]=active;
 
   354       } while ( !end );
 
   355       } while ( !end );
 
   355 
   356 
   356 
   357 
   357       while ( container[minimum].parent >=0 )
 
   358       while ( _data[_minimum].parent >=0 )
 
   358         minimum=container[minimum].parent;
 
   359         _minimum=_data[_minimum].parent;
 
   359       int s=minimum;
 
   360       int s=_minimum;
 
   360       int m=minimum;
 
   361       int m=_minimum;
 
   361       do {
 
   362       do {
 
   362         if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
 
   363         if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
 
   363         s=container[s].right_neighbor;
 
   364         s=_data[s].right_neighbor;
 
   364       } while ( s != m );
 
   365       } while ( s != m );
 
   365     }
 
   366     }
 
   366 
   367 
   367     void makeroot(int c) {
 
   368     void makeroot(int c) {
 
   368       int s=c;
 
   369       int s=c;
 
   369       do {
 
   370       do {
 
   370         container[s].parent=-1;
 
   371         _data[s].parent=-1;
 
   371         s=container[s].right_neighbor;
 
   372         s=_data[s].right_neighbor;
 
   372       } while ( s != c );
 
   373       } while ( s != c );
 
   373     }
 
   374     }
 
   374 
   375 
   375     void cut(int a, int b) {
 
   376     void cut(int a, int b) {
 
   376       /*
 
   377       /*
 
   377        *Replacing a from the children of b.
 
   378        *Replacing a from the children of b.
 
   378        */
 
   379        */
 
   379       --container[b].degree;
 
   380       --_data[b].degree;
 
   380 
   381 
   381       if ( container[b].degree !=0 ) {
 
   382       if ( _data[b].degree !=0 ) {
 
   382         int child=container[b].child;
 
   383         int child=_data[b].child;
 
   383         if ( child==a )
 
   384         if ( child==a )
 
   384           container[b].child=container[child].right_neighbor;
 
   385           _data[b].child=_data[child].right_neighbor;
 
   385         unlace(a);
 
   386         unlace(a);
 
   386       }
 
   387       }
 
   387 
   388 
   388 
   389 
   389       /*Lacing a to the roots.*/
 
   390       /*Lacing a to the roots.*/
 
   390       int right=container[minimum].right_neighbor;
 
   391       int right=_data[_minimum].right_neighbor;
 
   391       container[minimum].right_neighbor=a;
 
   392       _data[_minimum].right_neighbor=a;
 
   392       container[a].left_neighbor=minimum;
 
   393       _data[a].left_neighbor=_minimum;
 
   393       container[a].right_neighbor=right;
 
   394       _data[a].right_neighbor=right;
 
   394       container[right].left_neighbor=a;
 
   395       _data[right].left_neighbor=a;
 
   395 
   396 
   396       container[a].parent=-1;
 
   397       _data[a].parent=-1;
 
   397       container[a].marked=false;
 
   398       _data[a].marked=false;
 
   398     }
 
   399     }
 
   399 
   400 
   400     void cascade(int a) {
 
   401     void cascade(int a) {
 
   401       if ( container[a].parent!=-1 ) {
 
   402       if ( _data[a].parent!=-1 ) {
 
   402         int p=container[a].parent;
 
   403         int p=_data[a].parent;
 
   403 
   404 
   404         if ( container[a].marked==false ) container[a].marked=true;
 
   405         if ( _data[a].marked==false ) _data[a].marked=true;
 
   405         else {
 
   406         else {
 
   406           cut(a,p);
 
   407           cut(a,p);
 
   407           cascade(p);
 
   408           cascade(p);
 
   408         }
 
   409         }
 
   409       }
 
   410       }
 
   411 
   412 
   412     void fuse(int a, int b) {
 
   413     void fuse(int a, int b) {
 
   413       unlace(b);
 
   414       unlace(b);
 
   414 
   415 
   415       /*Lacing b under a.*/
 
   416       /*Lacing b under a.*/
 
   416       container[b].parent=a;
 
   417       _data[b].parent=a;
 
   417 
   418 
   418       if (container[a].degree==0) {
 
   419       if (_data[a].degree==0) {
 
   419         container[b].left_neighbor=b;
 
   420         _data[b].left_neighbor=b;
 
   420         container[b].right_neighbor=b;
 
   421         _data[b].right_neighbor=b;
 
   421         container[a].child=b;
 
   422         _data[a].child=b;
 
   422       } else {
 
   423       } else {
 
   423         int child=container[a].child;
 
   424         int child=_data[a].child;
 
   424         int last_child=container[child].left_neighbor;
 
   425         int last_child=_data[child].left_neighbor;
 
   425         container[child].left_neighbor=b;
 
   426         _data[child].left_neighbor=b;
 
   426         container[b].right_neighbor=child;
 
   427         _data[b].right_neighbor=child;
 
   427         container[last_child].right_neighbor=b;
 
   428         _data[last_child].right_neighbor=b;
 
   428         container[b].left_neighbor=last_child;
 
   429         _data[b].left_neighbor=last_child;
 
   429       }
 
   430       }
 
   430 
   431 
   431       ++container[a].degree;
 
   432       ++_data[a].degree;
 
   432 
   433 
   433       container[b].marked=false;
 
   434       _data[b].marked=false;
 
   434     }
 
   435     }
 
   435 
   436 
   436     /*
 
   437     /*
 
   437      *It is invoked only if a has siblings.
 
   438      *It is invoked only if a has siblings.
 
   438      */
 
   439      */
 
   439     void unlace(int a) {
 
   440     void unlace(int a) {
 
   440       int leftn=container[a].left_neighbor;
 
   441       int leftn=_data[a].left_neighbor;
 
   441       int rightn=container[a].right_neighbor;
 
   442       int rightn=_data[a].right_neighbor;
 
   442       container[leftn].right_neighbor=rightn;
 
   443       _data[leftn].right_neighbor=rightn;
 
   443       container[rightn].left_neighbor=leftn;
 
   444       _data[rightn].left_neighbor=leftn;
 
   444     }
 
   445     }
 
   445 
   446 
   446 
   447 
   447     class store {
 
   448     class Store {
 
   448       friend class FibHeap;
 
   449       friend class FibHeap;
 
   449 
   450 
   450       Item name;
 
   451       Item name;
 
   451       int parent;
 
   452       int parent;
 
   452       int left_neighbor;
 
   453       int left_neighbor;
 
   455       int degree;
 
   456       int degree;
 
   456       bool marked;
 
   457       bool marked;
 
   457       bool in;
 
   458       bool in;
 
   458       Prio prio;
 
   459       Prio prio;
 
   459 
   460 
   460       store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
 
   461       Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
 
   461     };
 
   462     };
 
   462   };
 
   463   };
 
   463 
   464 
   464 } //namespace lemon
 
   465 } //namespace lemon
 
   465 
   466
lemon-main