Better handling of inexact computation.
We do not use tolerance for excess, just for edges
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2006
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
19 #ifndef LEMON_BIN_HEAP_H
20 #define LEMON_BIN_HEAP_H
24 ///\brief Binary Heap implementation.
34 /// A Binary Heap implementation.
36 ///This class implements the \e binary \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.
42 ///\param Prio Type of the priority of the items.
43 ///\param ItemIntMap A read and writable Item int map, used internally
44 ///to handle the cross references.
45 ///\param Compare A class for the ordering of the priorities. The
46 ///default is \c std::less<Prio>.
50 template <typename Prio, typename ItemIntMap,
51 typename Compare = std::less<Prio> >
55 typedef typename ItemIntMap::Key ItemType;
56 typedef Prio PrioType;
57 typedef std::pair<ItemType,PrioType> PairType;
58 typedef ItemIntMap ItemIntMapType;
59 typedef Compare PrioCompare;
61 /// \brief Type to represent the items states.
63 /// Each Item element have a state associated to it. It may be "in heap",
64 /// "pre heap" or "post heap". The latter two are indifferent from the
65 /// heap's point of view, but may be useful to the user.
67 /// The ItemIntMap \e should be initialized in such way that it maps
68 /// PRE_HEAP (-1) to any element to be put in the heap...
76 std::vector<PairType> data;
81 /// \brief The constructor.
84 /// \param _iim should be given to the constructor, since it is used
85 /// internally to handle the cross references. The value of the map
86 /// should be PRE_HEAP (-1) for each element.
87 explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
89 /// \brief The constructor.
92 /// \param _iim should be given to the constructor, since it is used
93 /// internally to handle the cross references. The value of the map
94 /// should be PRE_HEAP (-1) for each element.
96 /// \param _comp The comparator function object.
97 BinHeap(ItemIntMap &_iim, const Compare &_comp)
98 : iim(_iim), comp(_comp) {}
101 /// The number of items stored in the heap.
103 /// \brief Returns the number of items stored in the heap.
104 int size() const { return data.size(); }
106 /// \brief Checks if the heap stores no items.
108 /// Returns \c true if and only if the heap stores no items.
109 bool empty() const { return data.empty(); }
111 /// \brief Make empty this heap.
113 /// Make empty this heap. It does not change the cross reference map.
114 /// If you want to reuse what is not surely empty you should first clear
115 /// the heap and after that you should set the cross reference map for
116 /// each item to \c PRE_HEAP.
122 static int parent(int i) { return (i-1)/2; }
123 static int second_child(int i) { return 2*i+2; }
124 bool less(const PairType &p1, const PairType &p2) const {
125 return comp(p1.second, p2.second);
128 int bubble_up(int hole, PairType p);
129 int bubble_down(int hole, PairType p, int length);
131 void move(const PairType &p, int i) {
137 int n = data.size()-1;
139 iim.set(data[h].first, POST_HEAP);
141 bubble_down(h, data[n], n);
148 /// \brief Insert a pair of item and priority into the heap.
150 /// Adds \c p.first to the heap with priority \c p.second.
151 /// \param p The pair to insert.
152 void push(const PairType &p) {
158 /// \brief Insert an item into the heap with the given heap.
160 /// Adds \c i to the heap with priority \c p.
161 /// \param i The item to insert.
162 /// \param p The priority of the item.
163 void push(const ItemType &i, const Prio &p) { push(PairType(i,p)); }
165 /// \brief Returns the item with minimum priority relative to \c Compare.
167 /// This method returns the item with minimum priority relative to \c
169 /// \pre The heap must be nonempty.
170 ItemType top() const {
171 return data[0].first;
174 /// \brief Returns the minimum priority relative to \c Compare.
176 /// It returns the minimum priority relative to \c Compare.
177 /// \pre The heap must be nonempty.
179 return data[0].second;
182 /// \brief Deletes the item with minimum priority relative to \c Compare.
184 /// This method deletes the item with minimum priority relative to \c
185 /// Compare from the heap.
186 /// \pre The heap must be non-empty.
191 /// \brief Deletes \c i from the heap.
193 /// This method deletes item \c i from the heap, if \c i was
194 /// already stored in the heap.
195 /// \param i The item to erase.
196 void erase(const ItemType &i) {
201 /// \brief Returns the priority of \c i.
203 /// This function returns the priority of item \c i.
204 /// \pre \c i must be in the heap.
205 /// \param i The item.
206 Prio operator[](const ItemType &i) const {
208 return data[idx].second;
211 /// \brief \c i gets to the heap with priority \c p independently
212 /// if \c i was already there.
214 /// This method calls \ref push(\c i, \c p) if \c i is not stored
215 /// in the heap and sets the priority of \c i to \c p otherwise.
216 /// \param i The item.
217 /// \param p The priority.
218 void set(const ItemType &i, const Prio &p) {
223 else if( comp(p, data[idx].second) ) {
224 bubble_up(idx, PairType(i,p));
227 bubble_down(idx, PairType(i,p), data.size());
231 /// \brief Decreases the priority of \c i to \c p.
233 /// This method decreases the priority of item \c i to \c p.
234 /// \pre \c i must be stored in the heap with priority at least \c
235 /// p relative to \c Compare.
236 /// \param i The item.
237 /// \param p The priority.
238 void decrease(const ItemType &i, const Prio &p) {
240 bubble_up(idx, PairType(i,p));
243 /// \brief Increases the priority of \c i to \c p.
245 /// This method sets the priority of item \c i to \c p.
246 /// \pre \c i must be stored in the heap with priority at most \c
247 /// p relative to \c Compare.
248 /// \param i The item.
249 /// \param p The priority.
250 void increase(const ItemType &i, const Prio &p) {
252 bubble_down(idx, PairType(i,p), data.size());
255 /// \brief Returns if \c item is in, has already been in, or has
256 /// never been in the heap.
258 /// This method returns PRE_HEAP if \c item has never been in the
259 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
260 /// otherwise. In the latter case it is possible that \c item will
261 /// get back to the heap again.
262 /// \param i The item.
263 state_enum state(const ItemType &i) const {
267 return state_enum(s);
270 /// \brief Sets the state of the \c item in the heap.
272 /// Sets the state of the \c item in the heap. It can be used to
273 /// manually clear the heap when it is important to achive the
274 /// better time complexity.
275 /// \param i The item.
276 /// \param st The state. It should not be \c IN_HEAP.
277 void state(const ItemType& i, state_enum st) {
281 if (state(i) == IN_HEAP) {
294 template <typename V, typename M, typename C>
295 int BinHeap<V,M,C>::bubble_up(int hole, PairType p) {
296 int par = parent(hole);
297 while( hole>0 && less(p,data[par]) ) {
298 move(data[par],hole);
306 template <typename V, typename M, typename C>
307 int BinHeap<V,M,C>::bubble_down(int hole, PairType p, int length) {
308 int child = second_child(hole);
309 while(child < length) {
310 if( less(data[child-1], data[child]) ) {
313 if( !less(data[child], p) )
315 move(data[child], hole);
317 child = second_child(hole);
320 if( child<length && less(data[child], p) ) {
321 move(data[child], hole);
332 #endif // LEMON_BIN_HEAP_H