diff --git a/lemon/fib_heap.h b/lemon/fib_heap.h --- a/lemon/fib_heap.h +++ b/lemon/fib_heap.h @@ -21,9 +21,10 @@ ///\file ///\ingroup auxdat -///\brief Fibonacci Heap implementation. +///\brief Fibonacci heap implementation. #include +#include #include #include @@ -31,42 +32,37 @@ /// \ingroup auxdat /// - ///\brief Fibonacci Heap. + /// \brief Fibonacci heap data structure. /// - ///This class implements the \e Fibonacci \e heap data structure. A \e heap - ///is a data structure for storing items with specified values called \e - ///priorities in such a way that finding the item with minimum priority is - ///efficient. \c CMP specifies the ordering of the priorities. In a heap - ///one can change the priority of an item, add or erase an item, etc. + /// This class implements the \e Fibonacci \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". /// - ///The methods \ref increase and \ref erase are not efficient in a Fibonacci - ///heap. In case of many calls to these operations, it is better to use a - ///\ref BinHeap "binary heap". + /// The methods \ref increase() and \ref erase() are not efficient in a + /// Fibonacci heap. In case of many calls of these operations, it is + /// better to use other heap structure, e.g. \ref BinHeap "binary heap". /// - ///\param PRIO Type of the priority of the items. - ///\param IM A read and writable Item int map, used internally - ///to handle the cross references. - ///\param CMP A class for the ordering of the priorities. The - ///default is \c std::less. - /// - ///\sa BinHeap - ///\sa Dijkstra + /// \tparam PR Type of the priorities of the items. + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam CMP A functor class for comparing the priorities. + /// The default is \c std::less. #ifdef DOXYGEN - template + template #else - template > + template > #endif class FibHeap { public: - ///\e + + /// Type of the item-int map. typedef IM ItemIntMap; - ///\e - typedef PRIO Prio; - ///\e + /// Type of the priorities. + typedef PR Prio; + /// Type of the items stored in the heap. typedef typename ItemIntMap::Key Item; - ///\e + /// Type of the item-priority pairs. typedef std::pair Pair; - ///\e + /// Functor type for comparing the priorities. typedef CMP Compare; private: @@ -80,10 +76,10 @@ public: - /// \brief Type to represent the items states. + /// \brief Type to represent the states of the items. /// - /// Each Item element have a state associated to it. It may be "in heap", - /// "pre heap" or "post heap". The latter two are indifferent from the + /// Each item has a state associated to it. It can be "in heap", + /// "pre-heap" or "post-heap". The latter two are indifferent from the /// heap's point of view, but may be useful to the user. /// /// The item-int map must be initialized in such way that it assigns @@ -94,60 +90,54 @@ POST_HEAP = -2 ///< = -2. }; - /// \brief The constructor + /// \brief Constructor. /// - /// \c map should be given to the constructor, since it is - /// used internally to handle the cross references. + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (-1) for each item. explicit FibHeap(ItemIntMap &map) : _minimum(0), _iim(map), _num() {} - /// \brief The constructor + /// \brief Constructor. /// - /// \c map should be given to the constructor, since it is used - /// internally to handle the cross references. \c comp is an - /// object for ordering of the priorities. + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (-1) for each item. + /// \param comp The function object used for comparing the priorities. FibHeap(ItemIntMap &map, const Compare &comp) : _minimum(0), _iim(map), _comp(comp), _num() {} /// \brief The number of items stored in the heap. /// - /// Returns the number of items stored in the heap. + /// This function returns the number of items stored in the heap. int size() const { return _num; } - /// \brief Checks if the heap stores no items. + /// \brief Check if the heap is empty. /// - /// Returns \c true if and only if the heap stores no items. + /// This function returns \c true if the heap is empty. bool empty() const { return _num==0; } - /// \brief Make empty this heap. + /// \brief Make the heap empty. /// - /// Make empty this heap. It does not change the cross reference - /// map. If you want to reuse a heap what is not surely empty you - /// should first clear the heap and after that you should set the - /// cross reference map for each item to \c PRE_HEAP. + /// This functon makes the heap empty. + /// It does not change the cross reference map. If you want to reuse + /// a heap that is not surely empty, you should first clear it and + /// then you should set the cross reference map to \c PRE_HEAP + /// for each item. void clear() { _data.clear(); _minimum = 0; _num = 0; } - /// \brief \c item gets to the heap with priority \c value independently - /// if \c item was already there. + /// \brief Insert an item into the heap with the given priority. /// - /// This method calls \ref push(\c item, \c value) if \c item is not - /// stored in the heap and it calls \ref decrease(\c item, \c value) or - /// \ref increase(\c item, \c value) otherwise. - void set (const Item& item, const Prio& value) { - int i=_iim[item]; - if ( i >= 0 && _data[i].in ) { - if ( _comp(value, _data[i].prio) ) decrease(item, value); - if ( _comp(_data[i].prio, value) ) increase(item, value); - } else push(item, value); - } - - /// \brief Adds \c item to the heap with priority \c value. - /// - /// Adds \c item to the heap with priority \c value. - /// \pre \c item must not be stored in the heap. - void push (const Item& item, const Prio& value) { + /// This function inserts the given item into the heap with the + /// given priority. + /// \param item The item to insert. + /// \param prio The priority of the item. + /// \pre \e item must not be stored in the heap. + void push (const Item& item, const Prio& prio) { int i=_iim[item]; if ( i < 0 ) { int s=_data.size(); @@ -168,40 +158,30 @@ _data[i].right_neighbor=_data[_minimum].right_neighbor; _data[_minimum].right_neighbor=i; _data[i].left_neighbor=_minimum; - if ( _comp( value, _data[_minimum].prio) ) _minimum=i; + if ( _comp( prio, _data[_minimum].prio) ) _minimum=i; } else { _data[i].right_neighbor=_data[i].left_neighbor=i; _minimum=i; } - _data[i].prio=value; + _data[i].prio=prio; ++_num; } - /// \brief Returns the item with minimum priority relative to \c Compare. + /// \brief Return the item having minimum priority. /// - /// This method returns the item with minimum priority relative to \c - /// Compare. - /// \pre The heap must be nonempty. + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. Item top() const { return _data[_minimum].name; } - /// \brief Returns the minimum priority relative to \c Compare. + /// \brief The minimum priority. /// - /// It returns the minimum priority relative to \c Compare. - /// \pre The heap must be nonempty. - const Prio& prio() const { return _data[_minimum].prio; } + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { return _data[_minimum].prio; } - /// \brief Returns the priority of \c item. + /// \brief Remove the item having minimum priority. /// - /// It returns the priority of \c item. - /// \pre \c item must be in the heap. - const Prio& operator[](const Item& item) const { - return _data[_iim[item]].prio; - } - - /// \brief Deletes the item with minimum priority relative to \c Compare. - /// - /// This method deletes the item with minimum priority relative to \c - /// Compare from the heap. + /// This function removes the item having minimum priority. /// \pre The heap must be non-empty. void pop() { /*The first case is that there are only one root.*/ @@ -234,10 +214,12 @@ --_num; } - /// \brief Deletes \c item from the heap. + /// \brief Remove the given item from the heap. /// - /// This method deletes \c item from the heap, if \c item was already - /// stored in the heap. It is quite inefficient in Fibonacci heaps. + /// This function removes the given item from the heap if it is + /// already stored. + /// \param item The item to delete. + /// \pre \e item must be in the heap. void erase (const Item& item) { int i=_iim[item]; @@ -252,43 +234,68 @@ } } - /// \brief Decreases the priority of \c item to \c value. + /// \brief The priority of the given item. /// - /// This method decreases the priority of \c item to \c value. - /// \pre \c item must be stored in the heap with priority at least \c - /// value relative to \c Compare. - void decrease (Item item, const Prio& value) { + /// This function returns the priority of the given item. + /// \param item The item. + /// \pre \e item must be in the heap. + Prio operator[](const Item& item) const { + return _data[_iim[item]].prio; + } + + /// \brief Set the priority of an item or insert it, if it is + /// not stored in the heap. + /// + /// This method sets the priority of the given item if it is + /// already stored in the heap. Otherwise it inserts the given + /// item into the heap with the given priority. + /// \param item The item. + /// \param prio The priority. + void set (const Item& item, const Prio& prio) { int i=_iim[item]; - _data[i].prio=value; + if ( i >= 0 && _data[i].in ) { + if ( _comp(prio, _data[i].prio) ) decrease(item, prio); + if ( _comp(_data[i].prio, prio) ) increase(item, prio); + } else push(item, prio); + } + + /// \brief Decrease the priority of an item to the given value. + /// + /// This function decreases the priority of an item to the given value. + /// \param item The item. + /// \param prio The priority. + /// \pre \e item must be stored in the heap with priority at least \e prio. + void decrease (const Item& item, const Prio& prio) { + int i=_iim[item]; + _data[i].prio=prio; int p=_data[i].parent; - if ( p!=-1 && _comp(value, _data[p].prio) ) { + if ( p!=-1 && _comp(prio, _data[p].prio) ) { cut(i,p); cascade(p); } - if ( _comp(value, _data[_minimum].prio) ) _minimum=i; + if ( _comp(prio, _data[_minimum].prio) ) _minimum=i; } - /// \brief Increases the priority of \c item to \c value. + /// \brief Increase the priority of an item to the given value. /// - /// This method sets the priority of \c item to \c value. Though - /// there is no precondition on the priority of \c item, this - /// method should be used only if it is indeed necessary to increase - /// (relative to \c Compare) the priority of \c item, because this - /// method is inefficient. - void increase (Item item, const Prio& value) { + /// This function increases the priority of an item to the given value. + /// \param item The item. + /// \param prio The priority. + /// \pre \e item must be stored in the heap with priority at most \e prio. + void increase (const Item& item, const Prio& prio) { erase(item); - push(item, value); + push(item, prio); } - - /// \brief Returns if \c item is in, has already been in, or has never - /// been in the heap. + /// \brief Return the state of an item. /// - /// This method returns PRE_HEAP if \c item has never been in the - /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP - /// otherwise. In the latter case it is possible that \c item will - /// get back to the heap again. + /// This method returns \c PRE_HEAP if the given item has never + /// been in the heap, \c IN_HEAP if it is in the heap at the moment, + /// and \c POST_HEAP otherwise. + /// In the latter case it is possible that the item will get back + /// to the heap again. + /// \param item The item. State state(const Item &item) const { int i=_iim[item]; if( i>=0 ) { @@ -298,11 +305,11 @@ return State(i); } - /// \brief Sets the state of the \c item in the heap. + /// \brief Set the state of an item in the heap. /// - /// Sets the state of the \c item in the heap. It can be used to - /// manually clear the heap when it is important to achive the - /// better time _complexity. + /// This function sets the state of the given item in the heap. + /// It can be used to manually clear the heap when it is important + /// to achive better time complexity. /// \param i The item. /// \param st The state. It should not be \c IN_HEAP. void state(const Item& i, State st) {