1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2009 |
---|
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 | ///\brief A Binary Heap implementation. |
---|
35 | /// |
---|
36 | ///This class implements the \e binary \e heap data structure. |
---|
37 | /// |
---|
38 | ///A \e heap is a data structure for storing items with specified values |
---|
39 | ///called \e priorities in such a way that finding the item with minimum |
---|
40 | ///priority is efficient. \c CMP specifies the ordering of the priorities. |
---|
41 | ///In a heap one can change the priority of an item, add or erase an |
---|
42 | ///item, etc. |
---|
43 | /// |
---|
44 | ///\tparam PR Type of the priority of the items. |
---|
45 | ///\tparam IM A read and writable item map with int values, used internally |
---|
46 | ///to handle the cross references. |
---|
47 | ///\tparam CMP A functor class for the ordering of the priorities. |
---|
48 | ///The default is \c std::less<PR>. |
---|
49 | /// |
---|
50 | ///\sa FibHeap |
---|
51 | ///\sa Dijkstra |
---|
52 | template <typename PR, typename IM, typename CMP = std::less<PR> > |
---|
53 | class BinHeap { |
---|
54 | |
---|
55 | public: |
---|
56 | ///\e |
---|
57 | typedef IM ItemIntMap; |
---|
58 | ///\e |
---|
59 | typedef PR Prio; |
---|
60 | ///\e |
---|
61 | typedef typename ItemIntMap::Key Item; |
---|
62 | ///\e |
---|
63 | typedef std::pair<Item,Prio> Pair; |
---|
64 | ///\e |
---|
65 | typedef CMP Compare; |
---|
66 | |
---|
67 | /// \brief Type to represent the items states. |
---|
68 | /// |
---|
69 | /// Each Item element have a state associated to it. It may be "in heap", |
---|
70 | /// "pre heap" or "post heap". The latter two are indifferent from the |
---|
71 | /// heap's point of view, but may be useful to the user. |
---|
72 | /// |
---|
73 | /// The item-int map must be initialized in such way that it assigns |
---|
74 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
---|
75 | enum State { |
---|
76 | IN_HEAP = 0, ///< = 0. |
---|
77 | PRE_HEAP = -1, ///< = -1. |
---|
78 | POST_HEAP = -2 ///< = -2. |
---|
79 | }; |
---|
80 | |
---|
81 | private: |
---|
82 | std::vector<Pair> _data; |
---|
83 | Compare _comp; |
---|
84 | ItemIntMap &_iim; |
---|
85 | |
---|
86 | public: |
---|
87 | /// \brief The constructor. |
---|
88 | /// |
---|
89 | /// The constructor. |
---|
90 | /// \param map should be given to the constructor, since it is used |
---|
91 | /// internally to handle the cross references. The value of the map |
---|
92 | /// must be \c PRE_HEAP (<tt>-1</tt>) for every item. |
---|
93 | explicit BinHeap(ItemIntMap &map) : _iim(map) {} |
---|
94 | |
---|
95 | /// \brief The constructor. |
---|
96 | /// |
---|
97 | /// The constructor. |
---|
98 | /// \param map should be given to the constructor, since it is used |
---|
99 | /// internally to handle the cross references. The value of the map |
---|
100 | /// should be PRE_HEAP (-1) for each element. |
---|
101 | /// |
---|
102 | /// \param comp The comparator function object. |
---|
103 | BinHeap(ItemIntMap &map, const Compare &comp) |
---|
104 | : _iim(map), _comp(comp) {} |
---|
105 | |
---|
106 | |
---|
107 | /// The number of items stored in the heap. |
---|
108 | /// |
---|
109 | /// \brief Returns the number of items stored in the heap. |
---|
110 | int size() const { return _data.size(); } |
---|
111 | |
---|
112 | /// \brief Checks if the heap stores no items. |
---|
113 | /// |
---|
114 | /// Returns \c true if and only if the heap stores no items. |
---|
115 | bool empty() const { return _data.empty(); } |
---|
116 | |
---|
117 | /// \brief Make empty this heap. |
---|
118 | /// |
---|
119 | /// Make empty this heap. It does not change the cross reference map. |
---|
120 | /// If you want to reuse what is not surely empty you should first clear |
---|
121 | /// the heap and after that you should set the cross reference map for |
---|
122 | /// each item to \c PRE_HEAP. |
---|
123 | void clear() { |
---|
124 | _data.clear(); |
---|
125 | } |
---|
126 | |
---|
127 | private: |
---|
128 | static int parent(int i) { return (i-1)/2; } |
---|
129 | |
---|
130 | static int second_child(int i) { return 2*i+2; } |
---|
131 | bool less(const Pair &p1, const Pair &p2) const { |
---|
132 | return _comp(p1.second, p2.second); |
---|
133 | } |
---|
134 | |
---|
135 | int bubble_up(int hole, Pair p) { |
---|
136 | int par = parent(hole); |
---|
137 | while( hole>0 && less(p,_data[par]) ) { |
---|
138 | move(_data[par],hole); |
---|
139 | hole = par; |
---|
140 | par = parent(hole); |
---|
141 | } |
---|
142 | move(p, hole); |
---|
143 | return hole; |
---|
144 | } |
---|
145 | |
---|
146 | int bubble_down(int hole, Pair p, int length) { |
---|
147 | int child = second_child(hole); |
---|
148 | while(child < length) { |
---|
149 | if( less(_data[child-1], _data[child]) ) { |
---|
150 | --child; |
---|
151 | } |
---|
152 | if( !less(_data[child], p) ) |
---|
153 | goto ok; |
---|
154 | move(_data[child], hole); |
---|
155 | hole = child; |
---|
156 | child = second_child(hole); |
---|
157 | } |
---|
158 | child--; |
---|
159 | if( child<length && less(_data[child], p) ) { |
---|
160 | move(_data[child], hole); |
---|
161 | hole=child; |
---|
162 | } |
---|
163 | ok: |
---|
164 | move(p, hole); |
---|
165 | return hole; |
---|
166 | } |
---|
167 | |
---|
168 | void move(const Pair &p, int i) { |
---|
169 | _data[i] = p; |
---|
170 | _iim.set(p.first, i); |
---|
171 | } |
---|
172 | |
---|
173 | public: |
---|
174 | /// \brief Insert a pair of item and priority into the heap. |
---|
175 | /// |
---|
176 | /// Adds \c p.first to the heap with priority \c p.second. |
---|
177 | /// \param p The pair to insert. |
---|
178 | void push(const Pair &p) { |
---|
179 | int n = _data.size(); |
---|
180 | _data.resize(n+1); |
---|
181 | bubble_up(n, p); |
---|
182 | } |
---|
183 | |
---|
184 | /// \brief Insert an item into the heap with the given heap. |
---|
185 | /// |
---|
186 | /// Adds \c i to the heap with priority \c p. |
---|
187 | /// \param i The item to insert. |
---|
188 | /// \param p The priority of the item. |
---|
189 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
---|
190 | |
---|
191 | /// \brief Returns the item with minimum priority relative to \c Compare. |
---|
192 | /// |
---|
193 | /// This method returns the item with minimum priority relative to \c |
---|
194 | /// Compare. |
---|
195 | /// \pre The heap must be nonempty. |
---|
196 | Item top() const { |
---|
197 | return _data[0].first; |
---|
198 | } |
---|
199 | |
---|
200 | /// \brief Returns the minimum priority relative to \c Compare. |
---|
201 | /// |
---|
202 | /// It returns the minimum priority relative to \c Compare. |
---|
203 | /// \pre The heap must be nonempty. |
---|
204 | Prio prio() const { |
---|
205 | return _data[0].second; |
---|
206 | } |
---|
207 | |
---|
208 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
---|
209 | /// |
---|
210 | /// This method deletes the item with minimum priority relative to \c |
---|
211 | /// Compare from the heap. |
---|
212 | /// \pre The heap must be non-empty. |
---|
213 | void pop() { |
---|
214 | int n = _data.size()-1; |
---|
215 | _iim.set(_data[0].first, POST_HEAP); |
---|
216 | if (n > 0) { |
---|
217 | bubble_down(0, _data[n], n); |
---|
218 | } |
---|
219 | _data.pop_back(); |
---|
220 | } |
---|
221 | |
---|
222 | /// \brief Deletes \c i from the heap. |
---|
223 | /// |
---|
224 | /// This method deletes item \c i from the heap. |
---|
225 | /// \param i The item to erase. |
---|
226 | /// \pre The item should be in the heap. |
---|
227 | void erase(const Item &i) { |
---|
228 | int h = _iim[i]; |
---|
229 | int n = _data.size()-1; |
---|
230 | _iim.set(_data[h].first, POST_HEAP); |
---|
231 | if( h < n ) { |
---|
232 | if ( bubble_up(h, _data[n]) == h) { |
---|
233 | bubble_down(h, _data[n], n); |
---|
234 | } |
---|
235 | } |
---|
236 | _data.pop_back(); |
---|
237 | } |
---|
238 | |
---|
239 | |
---|
240 | /// \brief Returns the priority of \c i. |
---|
241 | /// |
---|
242 | /// This function returns the priority of item \c i. |
---|
243 | /// \param i The item. |
---|
244 | /// \pre \c i must be in the heap. |
---|
245 | Prio operator[](const Item &i) const { |
---|
246 | int idx = _iim[i]; |
---|
247 | return _data[idx].second; |
---|
248 | } |
---|
249 | |
---|
250 | /// \brief \c i gets to the heap with priority \c p independently |
---|
251 | /// if \c i was already there. |
---|
252 | /// |
---|
253 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
---|
254 | /// in the heap and sets the priority of \c i to \c p otherwise. |
---|
255 | /// \param i The item. |
---|
256 | /// \param p The priority. |
---|
257 | void set(const Item &i, const Prio &p) { |
---|
258 | int idx = _iim[i]; |
---|
259 | if( idx < 0 ) { |
---|
260 | push(i,p); |
---|
261 | } |
---|
262 | else if( _comp(p, _data[idx].second) ) { |
---|
263 | bubble_up(idx, Pair(i,p)); |
---|
264 | } |
---|
265 | else { |
---|
266 | bubble_down(idx, Pair(i,p), _data.size()); |
---|
267 | } |
---|
268 | } |
---|
269 | |
---|
270 | /// \brief Decreases the priority of \c i to \c p. |
---|
271 | /// |
---|
272 | /// This method decreases the priority of item \c i to \c p. |
---|
273 | /// \param i The item. |
---|
274 | /// \param p The priority. |
---|
275 | /// \pre \c i must be stored in the heap with priority at least \c |
---|
276 | /// p relative to \c Compare. |
---|
277 | void decrease(const Item &i, const Prio &p) { |
---|
278 | int idx = _iim[i]; |
---|
279 | bubble_up(idx, Pair(i,p)); |
---|
280 | } |
---|
281 | |
---|
282 | /// \brief Increases the priority of \c i to \c p. |
---|
283 | /// |
---|
284 | /// This method sets the priority of item \c i to \c p. |
---|
285 | /// \param i The item. |
---|
286 | /// \param p The priority. |
---|
287 | /// \pre \c i must be stored in the heap with priority at most \c |
---|
288 | /// p relative to \c Compare. |
---|
289 | void increase(const Item &i, const Prio &p) { |
---|
290 | int idx = _iim[i]; |
---|
291 | bubble_down(idx, Pair(i,p), _data.size()); |
---|
292 | } |
---|
293 | |
---|
294 | /// \brief Returns if \c item is in, has already been in, or has |
---|
295 | /// never been in the heap. |
---|
296 | /// |
---|
297 | /// This method returns PRE_HEAP if \c item has never been in the |
---|
298 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
---|
299 | /// otherwise. In the latter case it is possible that \c item will |
---|
300 | /// get back to the heap again. |
---|
301 | /// \param i The item. |
---|
302 | State state(const Item &i) const { |
---|
303 | int s = _iim[i]; |
---|
304 | if( s>=0 ) |
---|
305 | s=0; |
---|
306 | return State(s); |
---|
307 | } |
---|
308 | |
---|
309 | /// \brief Sets the state of the \c item in the heap. |
---|
310 | /// |
---|
311 | /// Sets the state of the \c item in the heap. It can be used to |
---|
312 | /// manually clear the heap when it is important to achive the |
---|
313 | /// better time complexity. |
---|
314 | /// \param i The item. |
---|
315 | /// \param st The state. It should not be \c IN_HEAP. |
---|
316 | void state(const Item& i, State st) { |
---|
317 | switch (st) { |
---|
318 | case POST_HEAP: |
---|
319 | case PRE_HEAP: |
---|
320 | if (state(i) == IN_HEAP) { |
---|
321 | erase(i); |
---|
322 | } |
---|
323 | _iim[i] = st; |
---|
324 | break; |
---|
325 | case IN_HEAP: |
---|
326 | break; |
---|
327 | } |
---|
328 | } |
---|
329 | |
---|
330 | /// \brief Replaces an item in the heap. |
---|
331 | /// |
---|
332 | /// The \c i item is replaced with \c j item. The \c i item should |
---|
333 | /// be in the heap, while the \c j should be out of the heap. The |
---|
334 | /// \c i item will out of the heap and \c j will be in the heap |
---|
335 | /// with the same prioriority as prevoiusly the \c i item. |
---|
336 | void replace(const Item& i, const Item& j) { |
---|
337 | int idx = _iim[i]; |
---|
338 | _iim.set(i, _iim[j]); |
---|
339 | _iim.set(j, idx); |
---|
340 | _data[idx].first = j; |
---|
341 | } |
---|
342 | |
---|
343 | }; // class BinHeap |
---|
344 | |
---|
345 | } // namespace lemon |
---|
346 | |
---|
347 | #endif // LEMON_BIN_HEAP_H |
---|