1.1 --- a/lemon/fib_heap.h Thu Jun 11 23:13:24 2009 +0200
1.2 +++ b/lemon/fib_heap.h Wed Jul 08 17:21:30 2009 +0200
1.3 @@ -21,9 +21,10 @@
1.4
1.5 ///\file
1.6 ///\ingroup auxdat
1.7 -///\brief Fibonacci Heap implementation.
1.8 +///\brief Fibonacci heap implementation.
1.9
1.10 #include <vector>
1.11 +#include <utility>
1.12 #include <functional>
1.13 #include <lemon/math.h>
1.14
1.15 @@ -31,42 +32,37 @@
1.16
1.17 /// \ingroup auxdat
1.18 ///
1.19 - ///\brief Fibonacci Heap.
1.20 + /// \brief Fibonacci heap data structure.
1.21 ///
1.22 - ///This class implements the \e Fibonacci \e heap data structure. A \e heap
1.23 - ///is a data structure for storing items with specified values called \e
1.24 - ///priorities in such a way that finding the item with minimum priority is
1.25 - ///efficient. \c CMP specifies the ordering of the priorities. In a heap
1.26 - ///one can change the priority of an item, add or erase an item, etc.
1.27 + /// This class implements the \e Fibonacci \e heap data structure.
1.28 + /// It fully conforms to the \ref concepts::Heap "heap concept".
1.29 ///
1.30 - ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
1.31 - ///heap. In case of many calls to these operations, it is better to use a
1.32 - ///\ref BinHeap "binary heap".
1.33 + /// The methods \ref increase() and \ref erase() are not efficient in a
1.34 + /// Fibonacci heap. In case of many calls of these operations, it is
1.35 + /// better to use other heap structure, e.g. \ref BinHeap "binary heap".
1.36 ///
1.37 - ///\param PRIO Type of the priority of the items.
1.38 - ///\param IM A read and writable Item int map, used internally
1.39 - ///to handle the cross references.
1.40 - ///\param CMP A class for the ordering of the priorities. The
1.41 - ///default is \c std::less<PRIO>.
1.42 - ///
1.43 - ///\sa BinHeap
1.44 - ///\sa Dijkstra
1.45 + /// \tparam PR Type of the priorities of the items.
1.46 + /// \tparam IM A read-writable item map with \c int values, used
1.47 + /// internally to handle the cross references.
1.48 + /// \tparam CMP A functor class for comparing the priorities.
1.49 + /// The default is \c std::less<PR>.
1.50 #ifdef DOXYGEN
1.51 - template <typename PRIO, typename IM, typename CMP>
1.52 + template <typename PR, typename IM, typename CMP>
1.53 #else
1.54 - template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
1.55 + template <typename PR, typename IM, typename CMP = std::less<PR> >
1.56 #endif
1.57 class FibHeap {
1.58 public:
1.59 - ///\e
1.60 +
1.61 + /// Type of the item-int map.
1.62 typedef IM ItemIntMap;
1.63 - ///\e
1.64 - typedef PRIO Prio;
1.65 - ///\e
1.66 + /// Type of the priorities.
1.67 + typedef PR Prio;
1.68 + /// Type of the items stored in the heap.
1.69 typedef typename ItemIntMap::Key Item;
1.70 - ///\e
1.71 + /// Type of the item-priority pairs.
1.72 typedef std::pair<Item,Prio> Pair;
1.73 - ///\e
1.74 + /// Functor type for comparing the priorities.
1.75 typedef CMP Compare;
1.76
1.77 private:
1.78 @@ -80,10 +76,10 @@
1.79
1.80 public:
1.81
1.82 - /// \brief Type to represent the items states.
1.83 + /// \brief Type to represent the states of the items.
1.84 ///
1.85 - /// Each Item element have a state associated to it. It may be "in heap",
1.86 - /// "pre heap" or "post heap". The latter two are indifferent from the
1.87 + /// Each item has a state associated to it. It can be "in heap",
1.88 + /// "pre-heap" or "post-heap". The latter two are indifferent from the
1.89 /// heap's point of view, but may be useful to the user.
1.90 ///
1.91 /// The item-int map must be initialized in such way that it assigns
1.92 @@ -94,60 +90,54 @@
1.93 POST_HEAP = -2 ///< = -2.
1.94 };
1.95
1.96 - /// \brief The constructor
1.97 + /// \brief Constructor.
1.98 ///
1.99 - /// \c map should be given to the constructor, since it is
1.100 - /// used internally to handle the cross references.
1.101 + /// Constructor.
1.102 + /// \param map A map that assigns \c int values to the items.
1.103 + /// It is used internally to handle the cross references.
1.104 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.105 explicit FibHeap(ItemIntMap &map)
1.106 : _minimum(0), _iim(map), _num() {}
1.107
1.108 - /// \brief The constructor
1.109 + /// \brief Constructor.
1.110 ///
1.111 - /// \c map should be given to the constructor, since it is used
1.112 - /// internally to handle the cross references. \c comp is an
1.113 - /// object for ordering of the priorities.
1.114 + /// Constructor.
1.115 + /// \param map A map that assigns \c int values to the items.
1.116 + /// It is used internally to handle the cross references.
1.117 + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
1.118 + /// \param comp The function object used for comparing the priorities.
1.119 FibHeap(ItemIntMap &map, const Compare &comp)
1.120 : _minimum(0), _iim(map), _comp(comp), _num() {}
1.121
1.122 /// \brief The number of items stored in the heap.
1.123 ///
1.124 - /// Returns the number of items stored in the heap.
1.125 + /// This function returns the number of items stored in the heap.
1.126 int size() const { return _num; }
1.127
1.128 - /// \brief Checks if the heap stores no items.
1.129 + /// \brief Check if the heap is empty.
1.130 ///
1.131 - /// Returns \c true if and only if the heap stores no items.
1.132 + /// This function returns \c true if the heap is empty.
1.133 bool empty() const { return _num==0; }
1.134
1.135 - /// \brief Make empty this heap.
1.136 + /// \brief Make the heap empty.
1.137 ///
1.138 - /// Make empty this heap. It does not change the cross reference
1.139 - /// map. If you want to reuse a heap what is not surely empty you
1.140 - /// should first clear the heap and after that you should set the
1.141 - /// cross reference map for each item to \c PRE_HEAP.
1.142 + /// This functon makes the heap empty.
1.143 + /// It does not change the cross reference map. If you want to reuse
1.144 + /// a heap that is not surely empty, you should first clear it and
1.145 + /// then you should set the cross reference map to \c PRE_HEAP
1.146 + /// for each item.
1.147 void clear() {
1.148 _data.clear(); _minimum = 0; _num = 0;
1.149 }
1.150
1.151 - /// \brief \c item gets to the heap with priority \c value independently
1.152 - /// if \c item was already there.
1.153 + /// \brief Insert an item into the heap with the given priority.
1.154 ///
1.155 - /// This method calls \ref push(\c item, \c value) if \c item is not
1.156 - /// stored in the heap and it calls \ref decrease(\c item, \c value) or
1.157 - /// \ref increase(\c item, \c value) otherwise.
1.158 - void set (const Item& item, const Prio& value) {
1.159 - int i=_iim[item];
1.160 - if ( i >= 0 && _data[i].in ) {
1.161 - if ( _comp(value, _data[i].prio) ) decrease(item, value);
1.162 - if ( _comp(_data[i].prio, value) ) increase(item, value);
1.163 - } else push(item, value);
1.164 - }
1.165 -
1.166 - /// \brief Adds \c item to the heap with priority \c value.
1.167 - ///
1.168 - /// Adds \c item to the heap with priority \c value.
1.169 - /// \pre \c item must not be stored in the heap.
1.170 - void push (const Item& item, const Prio& value) {
1.171 + /// This function inserts the given item into the heap with the
1.172 + /// given priority.
1.173 + /// \param item The item to insert.
1.174 + /// \param prio The priority of the item.
1.175 + /// \pre \e item must not be stored in the heap.
1.176 + void push (const Item& item, const Prio& prio) {
1.177 int i=_iim[item];
1.178 if ( i < 0 ) {
1.179 int s=_data.size();
1.180 @@ -168,40 +158,30 @@
1.181 _data[i].right_neighbor=_data[_minimum].right_neighbor;
1.182 _data[_minimum].right_neighbor=i;
1.183 _data[i].left_neighbor=_minimum;
1.184 - if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
1.185 + if ( _comp( prio, _data[_minimum].prio) ) _minimum=i;
1.186 } else {
1.187 _data[i].right_neighbor=_data[i].left_neighbor=i;
1.188 _minimum=i;
1.189 }
1.190 - _data[i].prio=value;
1.191 + _data[i].prio=prio;
1.192 ++_num;
1.193 }
1.194
1.195 - /// \brief Returns the item with minimum priority relative to \c Compare.
1.196 + /// \brief Return the item having minimum priority.
1.197 ///
1.198 - /// This method returns the item with minimum priority relative to \c
1.199 - /// Compare.
1.200 - /// \pre The heap must be nonempty.
1.201 + /// This function returns the item having minimum priority.
1.202 + /// \pre The heap must be non-empty.
1.203 Item top() const { return _data[_minimum].name; }
1.204
1.205 - /// \brief Returns the minimum priority relative to \c Compare.
1.206 + /// \brief The minimum priority.
1.207 ///
1.208 - /// It returns the minimum priority relative to \c Compare.
1.209 - /// \pre The heap must be nonempty.
1.210 - const Prio& prio() const { return _data[_minimum].prio; }
1.211 + /// This function returns the minimum priority.
1.212 + /// \pre The heap must be non-empty.
1.213 + Prio prio() const { return _data[_minimum].prio; }
1.214
1.215 - /// \brief Returns the priority of \c item.
1.216 + /// \brief Remove the item having minimum priority.
1.217 ///
1.218 - /// It returns the priority of \c item.
1.219 - /// \pre \c item must be in the heap.
1.220 - const Prio& operator[](const Item& item) const {
1.221 - return _data[_iim[item]].prio;
1.222 - }
1.223 -
1.224 - /// \brief Deletes the item with minimum priority relative to \c Compare.
1.225 - ///
1.226 - /// This method deletes the item with minimum priority relative to \c
1.227 - /// Compare from the heap.
1.228 + /// This function removes the item having minimum priority.
1.229 /// \pre The heap must be non-empty.
1.230 void pop() {
1.231 /*The first case is that there are only one root.*/
1.232 @@ -234,10 +214,12 @@
1.233 --_num;
1.234 }
1.235
1.236 - /// \brief Deletes \c item from the heap.
1.237 + /// \brief Remove the given item from the heap.
1.238 ///
1.239 - /// This method deletes \c item from the heap, if \c item was already
1.240 - /// stored in the heap. It is quite inefficient in Fibonacci heaps.
1.241 + /// This function removes the given item from the heap if it is
1.242 + /// already stored.
1.243 + /// \param item The item to delete.
1.244 + /// \pre \e item must be in the heap.
1.245 void erase (const Item& item) {
1.246 int i=_iim[item];
1.247
1.248 @@ -252,43 +234,68 @@
1.249 }
1.250 }
1.251
1.252 - /// \brief Decreases the priority of \c item to \c value.
1.253 + /// \brief The priority of the given item.
1.254 ///
1.255 - /// This method decreases the priority of \c item to \c value.
1.256 - /// \pre \c item must be stored in the heap with priority at least \c
1.257 - /// value relative to \c Compare.
1.258 - void decrease (Item item, const Prio& value) {
1.259 + /// This function returns the priority of the given item.
1.260 + /// \param item The item.
1.261 + /// \pre \e item must be in the heap.
1.262 + Prio operator[](const Item& item) const {
1.263 + return _data[_iim[item]].prio;
1.264 + }
1.265 +
1.266 + /// \brief Set the priority of an item or insert it, if it is
1.267 + /// not stored in the heap.
1.268 + ///
1.269 + /// This method sets the priority of the given item if it is
1.270 + /// already stored in the heap. Otherwise it inserts the given
1.271 + /// item into the heap with the given priority.
1.272 + /// \param item The item.
1.273 + /// \param prio The priority.
1.274 + void set (const Item& item, const Prio& prio) {
1.275 int i=_iim[item];
1.276 - _data[i].prio=value;
1.277 + if ( i >= 0 && _data[i].in ) {
1.278 + if ( _comp(prio, _data[i].prio) ) decrease(item, prio);
1.279 + if ( _comp(_data[i].prio, prio) ) increase(item, prio);
1.280 + } else push(item, prio);
1.281 + }
1.282 +
1.283 + /// \brief Decrease the priority of an item to the given value.
1.284 + ///
1.285 + /// This function decreases the priority of an item to the given value.
1.286 + /// \param item The item.
1.287 + /// \param prio The priority.
1.288 + /// \pre \e item must be stored in the heap with priority at least \e prio.
1.289 + void decrease (const Item& item, const Prio& prio) {
1.290 + int i=_iim[item];
1.291 + _data[i].prio=prio;
1.292 int p=_data[i].parent;
1.293
1.294 - if ( p!=-1 && _comp(value, _data[p].prio) ) {
1.295 + if ( p!=-1 && _comp(prio, _data[p].prio) ) {
1.296 cut(i,p);
1.297 cascade(p);
1.298 }
1.299 - if ( _comp(value, _data[_minimum].prio) ) _minimum=i;
1.300 + if ( _comp(prio, _data[_minimum].prio) ) _minimum=i;
1.301 }
1.302
1.303 - /// \brief Increases the priority of \c item to \c value.
1.304 + /// \brief Increase the priority of an item to the given value.
1.305 ///
1.306 - /// This method sets the priority of \c item to \c value. Though
1.307 - /// there is no precondition on the priority of \c item, this
1.308 - /// method should be used only if it is indeed necessary to increase
1.309 - /// (relative to \c Compare) the priority of \c item, because this
1.310 - /// method is inefficient.
1.311 - void increase (Item item, const Prio& value) {
1.312 + /// This function increases the priority of an item to the given value.
1.313 + /// \param item The item.
1.314 + /// \param prio The priority.
1.315 + /// \pre \e item must be stored in the heap with priority at most \e prio.
1.316 + void increase (const Item& item, const Prio& prio) {
1.317 erase(item);
1.318 - push(item, value);
1.319 + push(item, prio);
1.320 }
1.321
1.322 -
1.323 - /// \brief Returns if \c item is in, has already been in, or has never
1.324 - /// been in the heap.
1.325 + /// \brief Return the state of an item.
1.326 ///
1.327 - /// This method returns PRE_HEAP if \c item has never been in the
1.328 - /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
1.329 - /// otherwise. In the latter case it is possible that \c item will
1.330 - /// get back to the heap again.
1.331 + /// This method returns \c PRE_HEAP if the given item has never
1.332 + /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
1.333 + /// and \c POST_HEAP otherwise.
1.334 + /// In the latter case it is possible that the item will get back
1.335 + /// to the heap again.
1.336 + /// \param item The item.
1.337 State state(const Item &item) const {
1.338 int i=_iim[item];
1.339 if( i>=0 ) {
1.340 @@ -298,11 +305,11 @@
1.341 return State(i);
1.342 }
1.343
1.344 - /// \brief Sets the state of the \c item in the heap.
1.345 + /// \brief Set the state of an item in the heap.
1.346 ///
1.347 - /// Sets the state of the \c item in the heap. It can be used to
1.348 - /// manually clear the heap when it is important to achive the
1.349 - /// better time _complexity.
1.350 + /// This function sets the state of the given item in the heap.
1.351 + /// It can be used to manually clear the heap when it is important
1.352 + /// to achive better time complexity.
1.353 /// \param i The item.
1.354 /// \param st The state. It should not be \c IN_HEAP.
1.355 void state(const Item& i, State st) {