1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2006 |
---|
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_BIN_HEAP_H |
---|
20 | #define LEMON_BIN_HEAP_H |
---|
21 | |
---|
22 | ///\ingroup auxdat |
---|
23 | ///\file |
---|
24 | ///\brief Binary Heap implementation. |
---|
25 | |
---|
26 | #include <vector> |
---|
27 | #include <utility> |
---|
28 | #include <functional> |
---|
29 | |
---|
30 | namespace lemon { |
---|
31 | |
---|
32 | /// \ingroup auxdat |
---|
33 | |
---|
34 | /// A Binary Heap implementation. |
---|
35 | |
---|
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. |
---|
41 | /// |
---|
42 | ///\param Item Type of the items to be stored. |
---|
43 | ///\param Prio Type of the priority of the items. |
---|
44 | ///\param ItemIntMap A read and writable Item int map, used internally |
---|
45 | ///to handle the cross references. |
---|
46 | ///\param Compare A class for the ordering of the priorities. The |
---|
47 | ///default is \c std::less<Prio>. |
---|
48 | /// |
---|
49 | ///\sa FibHeap |
---|
50 | ///\sa Dijkstra |
---|
51 | template <typename Item, typename Prio, typename ItemIntMap, |
---|
52 | typename Compare = std::less<Prio> > |
---|
53 | class BinHeap { |
---|
54 | |
---|
55 | public: |
---|
56 | typedef Item ItemType; |
---|
57 | // FIXME: stl-ben nem ezt hivjak value_type -nak, hanem a kovetkezot... |
---|
58 | typedef Prio PrioType; |
---|
59 | typedef std::pair<ItemType,PrioType> PairType; |
---|
60 | typedef ItemIntMap ItemIntMapType; |
---|
61 | typedef Compare PrioCompare; |
---|
62 | |
---|
63 | /// \brief Type to represent the items states. |
---|
64 | /// |
---|
65 | /// Each Item element have a state associated to it. It may be "in heap", |
---|
66 | /// "pre heap" or "post heap". The latter two are indifferent from the |
---|
67 | /// heap's point of view, but may be useful to the user. |
---|
68 | /// |
---|
69 | /// The ItemIntMap \e should be initialized in such way that it maps |
---|
70 | /// PRE_HEAP (-1) to any element to be put in the heap... |
---|
71 | enum state_enum { |
---|
72 | IN_HEAP = 0, |
---|
73 | PRE_HEAP = -1, |
---|
74 | POST_HEAP = -2 |
---|
75 | }; |
---|
76 | |
---|
77 | private: |
---|
78 | std::vector<PairType> data; |
---|
79 | Compare comp; |
---|
80 | ItemIntMap &iim; |
---|
81 | |
---|
82 | public: |
---|
83 | /// \brief The constructor. |
---|
84 | /// |
---|
85 | /// The constructor. |
---|
86 | /// \param _iim should be given to the constructor, since it is used |
---|
87 | /// internally to handle the cross references. The value of the map |
---|
88 | /// should be PRE_HEAP (-1) for each element. |
---|
89 | explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {} |
---|
90 | |
---|
91 | /// \brief The constructor. |
---|
92 | /// |
---|
93 | /// The constructor. |
---|
94 | /// \param _iim should be given to the constructor, since it is used |
---|
95 | /// internally to handle the cross references. The value of the map |
---|
96 | /// should be PRE_HEAP (-1) for each element. |
---|
97 | /// |
---|
98 | /// \param _comp The comparator function object. |
---|
99 | BinHeap(ItemIntMap &_iim, const Compare &_comp) |
---|
100 | : iim(_iim), comp(_comp) {} |
---|
101 | |
---|
102 | |
---|
103 | /// The number of items stored in the heap. |
---|
104 | /// |
---|
105 | /// \brief Returns the number of items stored in the heap. |
---|
106 | int size() const { return data.size(); } |
---|
107 | |
---|
108 | /// \brief Checks if the heap stores no items. |
---|
109 | /// |
---|
110 | /// Returns \c true if and only if the heap stores no items. |
---|
111 | bool empty() const { return data.empty(); } |
---|
112 | |
---|
113 | /// \brief Make empty this heap. |
---|
114 | /// |
---|
115 | /// Make empty this heap. It does not change the cross reference map. |
---|
116 | /// If you want to reuse what is not surely empty you should first clear |
---|
117 | /// the heap and after that you should set the cross reference map for |
---|
118 | /// each item to \c PRE_HEAP. |
---|
119 | void clear() { |
---|
120 | data.clear(); |
---|
121 | } |
---|
122 | |
---|
123 | private: |
---|
124 | static int parent(int i) { return (i-1)/2; } |
---|
125 | static int second_child(int i) { return 2*i+2; } |
---|
126 | bool less(const PairType &p1, const PairType &p2) const { |
---|
127 | return comp(p1.second, p2.second); |
---|
128 | } |
---|
129 | |
---|
130 | int bubble_up(int hole, PairType p); |
---|
131 | int bubble_down(int hole, PairType p, int length); |
---|
132 | |
---|
133 | void move(const PairType &p, int i) { |
---|
134 | data[i] = p; |
---|
135 | iim.set(p.first, i); |
---|
136 | } |
---|
137 | |
---|
138 | void rmidx(int h) { |
---|
139 | int n = data.size()-1; |
---|
140 | if( h>=0 && h<=n ) { |
---|
141 | iim.set(data[h].first, POST_HEAP); |
---|
142 | if ( h<n ) { |
---|
143 | bubble_down(h, data[n], n); |
---|
144 | } |
---|
145 | data.pop_back(); |
---|
146 | } |
---|
147 | } |
---|
148 | |
---|
149 | public: |
---|
150 | /// \brief Insert a pair of item and priority into the heap. |
---|
151 | /// |
---|
152 | /// Adds \c p.first to the heap with priority \c p.second. |
---|
153 | /// \param p The pair to insert. |
---|
154 | void push(const PairType &p) { |
---|
155 | int n = data.size(); |
---|
156 | data.resize(n+1); |
---|
157 | bubble_up(n, p); |
---|
158 | } |
---|
159 | |
---|
160 | /// \brief Insert an item into the heap with the given heap. |
---|
161 | /// |
---|
162 | /// Adds \c i to the heap with priority \c p. |
---|
163 | /// \param i The item to insert. |
---|
164 | /// \param p The priority of the item. |
---|
165 | void push(const Item &i, const Prio &p) { push(PairType(i,p)); } |
---|
166 | |
---|
167 | /// \brief Returns the item with minimum priority relative to \c Compare. |
---|
168 | /// |
---|
169 | /// This method returns the item with minimum priority relative to \c |
---|
170 | /// Compare. |
---|
171 | /// \pre The heap must be nonempty. |
---|
172 | Item top() const { |
---|
173 | return data[0].first; |
---|
174 | } |
---|
175 | |
---|
176 | /// \brief Returns the minimum priority relative to \c Compare. |
---|
177 | /// |
---|
178 | /// It returns the minimum priority relative to \c Compare. |
---|
179 | /// \pre The heap must be nonempty. |
---|
180 | Prio prio() const { |
---|
181 | return data[0].second; |
---|
182 | } |
---|
183 | |
---|
184 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
---|
185 | /// |
---|
186 | /// This method deletes the item with minimum priority relative to \c |
---|
187 | /// Compare from the heap. |
---|
188 | /// \pre The heap must be non-empty. |
---|
189 | void pop() { |
---|
190 | rmidx(0); |
---|
191 | } |
---|
192 | |
---|
193 | /// \brief Deletes \c i from the heap. |
---|
194 | /// |
---|
195 | /// This method deletes item \c i from the heap, if \c i was |
---|
196 | /// already stored in the heap. |
---|
197 | /// \param i The item to erase. |
---|
198 | void erase(const Item &i) { |
---|
199 | rmidx(iim[i]); |
---|
200 | } |
---|
201 | |
---|
202 | |
---|
203 | /// \brief Returns the priority of \c i. |
---|
204 | /// |
---|
205 | /// This function returns the priority of item \c i. |
---|
206 | /// \pre \c i must be in the heap. |
---|
207 | /// \param i The item. |
---|
208 | Prio operator[](const Item &i) const { |
---|
209 | int idx = iim[i]; |
---|
210 | return data[idx].second; |
---|
211 | } |
---|
212 | |
---|
213 | /// \brief \c i gets to the heap with priority \c p independently |
---|
214 | /// if \c i was already there. |
---|
215 | /// |
---|
216 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
---|
217 | /// in the heap and sets the priority of \c i to \c p otherwise. |
---|
218 | /// \param i The item. |
---|
219 | /// \param p The priority. |
---|
220 | void set(const Item &i, const Prio &p) { |
---|
221 | int idx = iim[i]; |
---|
222 | if( idx < 0 ) { |
---|
223 | push(i,p); |
---|
224 | } |
---|
225 | else if( comp(p, data[idx].second) ) { |
---|
226 | bubble_up(idx, PairType(i,p)); |
---|
227 | } |
---|
228 | else { |
---|
229 | bubble_down(idx, PairType(i,p), data.size()); |
---|
230 | } |
---|
231 | } |
---|
232 | |
---|
233 | /// \brief Decreases the priority of \c i to \c p. |
---|
234 | |
---|
235 | /// This method decreases the priority of item \c i to \c p. |
---|
236 | /// \pre \c i must be stored in the heap with priority at least \c |
---|
237 | /// p relative to \c Compare. |
---|
238 | /// \param i The item. |
---|
239 | /// \param p The priority. |
---|
240 | void decrease(const Item &i, const Prio &p) { |
---|
241 | int idx = iim[i]; |
---|
242 | bubble_up(idx, PairType(i,p)); |
---|
243 | } |
---|
244 | |
---|
245 | /// \brief Increases the priority of \c i to \c p. |
---|
246 | /// |
---|
247 | /// This method sets the priority of item \c i to \c p. |
---|
248 | /// \pre \c i must be stored in the heap with priority at most \c |
---|
249 | /// p relative to \c Compare. |
---|
250 | /// \param i The item. |
---|
251 | /// \param p The priority. |
---|
252 | void increase(const Item &i, const Prio &p) { |
---|
253 | int idx = iim[i]; |
---|
254 | bubble_down(idx, PairType(i,p), data.size()); |
---|
255 | } |
---|
256 | |
---|
257 | /// \brief Returns if \c item is in, has already been in, or has |
---|
258 | /// never been in the heap. |
---|
259 | /// |
---|
260 | /// This method returns PRE_HEAP if \c item has never been in the |
---|
261 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
---|
262 | /// otherwise. In the latter case it is possible that \c item will |
---|
263 | /// get back to the heap again. |
---|
264 | /// \param i The item. |
---|
265 | state_enum state(const Item &i) const { |
---|
266 | int s = iim[i]; |
---|
267 | if( s>=0 ) |
---|
268 | s=0; |
---|
269 | return state_enum(s); |
---|
270 | } |
---|
271 | |
---|
272 | /// \brief Sets the state of the \c item in the heap. |
---|
273 | /// |
---|
274 | /// Sets the state of the \c item in the heap. It can be used to |
---|
275 | /// manually clear the heap when it is important to achive the |
---|
276 | /// better time complexity. |
---|
277 | /// \param i The item. |
---|
278 | /// \param st The state. It should not be \c IN_HEAP. |
---|
279 | void state(const Item& i, state_enum st) { |
---|
280 | switch (st) { |
---|
281 | case POST_HEAP: |
---|
282 | case PRE_HEAP: |
---|
283 | if (state(i) == IN_HEAP) { |
---|
284 | erase(i); |
---|
285 | } |
---|
286 | iim[i] = st; |
---|
287 | break; |
---|
288 | case IN_HEAP: |
---|
289 | break; |
---|
290 | } |
---|
291 | } |
---|
292 | |
---|
293 | }; // class BinHeap |
---|
294 | |
---|
295 | |
---|
296 | template <typename K, typename V, typename M, typename C> |
---|
297 | int BinHeap<K,V,M,C>::bubble_up(int hole, PairType p) { |
---|
298 | int par = parent(hole); |
---|
299 | while( hole>0 && less(p,data[par]) ) { |
---|
300 | move(data[par],hole); |
---|
301 | hole = par; |
---|
302 | par = parent(hole); |
---|
303 | } |
---|
304 | move(p, hole); |
---|
305 | return hole; |
---|
306 | } |
---|
307 | |
---|
308 | template <typename K, typename V, typename M, typename C> |
---|
309 | int BinHeap<K,V,M,C>::bubble_down(int hole, PairType p, int length) { |
---|
310 | int child = second_child(hole); |
---|
311 | while(child < length) { |
---|
312 | if( less(data[child-1], data[child]) ) { |
---|
313 | --child; |
---|
314 | } |
---|
315 | if( !less(data[child], p) ) |
---|
316 | goto ok; |
---|
317 | move(data[child], hole); |
---|
318 | hole = child; |
---|
319 | child = second_child(hole); |
---|
320 | } |
---|
321 | child--; |
---|
322 | if( child<length && less(data[child], p) ) { |
---|
323 | move(data[child], hole); |
---|
324 | hole=child; |
---|
325 | } |
---|
326 | ok: |
---|
327 | move(p, hole); |
---|
328 | return hole; |
---|
329 | } |
---|
330 | |
---|
331 | |
---|
332 | } // namespace lemon |
---|
333 | |
---|
334 | #endif // LEMON_BIN_HEAP_H |
---|