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_KARY_HEAP_H |
---|
20 | #define LEMON_KARY_HEAP_H |
---|
21 | |
---|
22 | ///\ingroup heaps |
---|
23 | ///\file |
---|
24 | ///\brief Fourary heap implementation. |
---|
25 | |
---|
26 | #include <vector> |
---|
27 | #include <utility> |
---|
28 | #include <functional> |
---|
29 | |
---|
30 | namespace lemon { |
---|
31 | |
---|
32 | /// \ingroup heaps |
---|
33 | /// |
---|
34 | ///\brief K-ary heap data structure. |
---|
35 | /// |
---|
36 | /// This class implements the \e K-ary \e heap data structure. |
---|
37 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
---|
38 | /// |
---|
39 | /// The \ref KaryHeap "K-ary heap" is a generalization of the |
---|
40 | /// \ref BinHeap "binary heap" structure, its nodes have at most |
---|
41 | /// \c K children, instead of two. |
---|
42 | /// \ref BinHeap and \ref FouraryHeap are specialized implementations |
---|
43 | /// of this structure for <tt>K=2</tt> and <tt>K=4</tt>, respectively. |
---|
44 | /// |
---|
45 | /// \tparam PR Type of the priorities of the items. |
---|
46 | /// \tparam IM A read-writable item map with \c int values, used |
---|
47 | /// internally to handle the cross references. |
---|
48 | /// \tparam K The degree of the heap, each node have at most \e K |
---|
49 | /// children. The default is 16. Powers of two are suggested to use |
---|
50 | /// so that the multiplications and divisions needed to traverse the |
---|
51 | /// nodes of the heap could be performed faster. |
---|
52 | /// \tparam CMP A functor class for comparing the priorities. |
---|
53 | /// The default is \c std::less<PR>. |
---|
54 | /// |
---|
55 | ///\sa BinHeap |
---|
56 | ///\sa FouraryHeap |
---|
57 | #ifdef DOXYGEN |
---|
58 | template <typename PR, typename IM, int K, typename CMP> |
---|
59 | #else |
---|
60 | template <typename PR, typename IM, int K = 16, |
---|
61 | typename CMP = std::less<PR> > |
---|
62 | #endif |
---|
63 | class KaryHeap { |
---|
64 | public: |
---|
65 | /// Type of the item-int map. |
---|
66 | typedef IM ItemIntMap; |
---|
67 | /// Type of the priorities. |
---|
68 | typedef PR Prio; |
---|
69 | /// Type of the items stored in the heap. |
---|
70 | typedef typename ItemIntMap::Key Item; |
---|
71 | /// Type of the item-priority pairs. |
---|
72 | typedef std::pair<Item,Prio> Pair; |
---|
73 | /// Functor type for comparing the priorities. |
---|
74 | typedef CMP Compare; |
---|
75 | |
---|
76 | /// \brief Type to represent the states of the items. |
---|
77 | /// |
---|
78 | /// Each item has a state associated to it. It can be "in heap", |
---|
79 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
---|
80 | /// heap's point of view, but may be useful to the user. |
---|
81 | /// |
---|
82 | /// The item-int map must be initialized in such way that it assigns |
---|
83 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
---|
84 | enum State { |
---|
85 | IN_HEAP = 0, ///< = 0. |
---|
86 | PRE_HEAP = -1, ///< = -1. |
---|
87 | POST_HEAP = -2 ///< = -2. |
---|
88 | }; |
---|
89 | |
---|
90 | private: |
---|
91 | std::vector<Pair> _data; |
---|
92 | Compare _comp; |
---|
93 | ItemIntMap &_iim; |
---|
94 | |
---|
95 | public: |
---|
96 | /// \brief Constructor. |
---|
97 | /// |
---|
98 | /// Constructor. |
---|
99 | /// \param map A map that assigns \c int values to the items. |
---|
100 | /// It is used internally to handle the cross references. |
---|
101 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
---|
102 | explicit KaryHeap(ItemIntMap &map) : _iim(map) {} |
---|
103 | |
---|
104 | /// \brief Constructor. |
---|
105 | /// |
---|
106 | /// Constructor. |
---|
107 | /// \param map A map that assigns \c int values to the items. |
---|
108 | /// It is used internally to handle the cross references. |
---|
109 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
---|
110 | /// \param comp The function object used for comparing the priorities. |
---|
111 | KaryHeap(ItemIntMap &map, const Compare &comp) |
---|
112 | : _iim(map), _comp(comp) {} |
---|
113 | |
---|
114 | /// \brief The number of items stored in the heap. |
---|
115 | /// |
---|
116 | /// This function returns the number of items stored in the heap. |
---|
117 | int size() const { return _data.size(); } |
---|
118 | |
---|
119 | /// \brief Check if the heap is empty. |
---|
120 | /// |
---|
121 | /// This function returns \c true if the heap is empty. |
---|
122 | bool empty() const { return _data.empty(); } |
---|
123 | |
---|
124 | /// \brief Make the heap empty. |
---|
125 | /// |
---|
126 | /// This functon makes the heap empty. |
---|
127 | /// It does not change the cross reference map. If you want to reuse |
---|
128 | /// a heap that is not surely empty, you should first clear it and |
---|
129 | /// then you should set the cross reference map to \c PRE_HEAP |
---|
130 | /// for each item. |
---|
131 | void clear() { _data.clear(); } |
---|
132 | |
---|
133 | private: |
---|
134 | int parent(int i) { return (i-1)/K; } |
---|
135 | int firstChild(int i) { return K*i+1; } |
---|
136 | |
---|
137 | bool less(const Pair &p1, const Pair &p2) const { |
---|
138 | return _comp(p1.second, p2.second); |
---|
139 | } |
---|
140 | |
---|
141 | void bubbleUp(int hole, Pair p) { |
---|
142 | int par = parent(hole); |
---|
143 | while( hole>0 && less(p,_data[par]) ) { |
---|
144 | move(_data[par],hole); |
---|
145 | hole = par; |
---|
146 | par = parent(hole); |
---|
147 | } |
---|
148 | move(p, hole); |
---|
149 | } |
---|
150 | |
---|
151 | void bubbleDown(int hole, Pair p, int length) { |
---|
152 | if( length>1 ) { |
---|
153 | int child = firstChild(hole); |
---|
154 | while( child+K<=length ) { |
---|
155 | int min=child; |
---|
156 | for (int i=1; i<K; ++i) { |
---|
157 | if( less(_data[child+i], _data[min]) ) |
---|
158 | min=child+i; |
---|
159 | } |
---|
160 | if( !less(_data[min], p) ) |
---|
161 | goto ok; |
---|
162 | move(_data[min], hole); |
---|
163 | hole = min; |
---|
164 | child = firstChild(hole); |
---|
165 | } |
---|
166 | if ( child<length ) { |
---|
167 | int min = child; |
---|
168 | while (++child < length) { |
---|
169 | if( less(_data[child], _data[min]) ) |
---|
170 | min=child; |
---|
171 | } |
---|
172 | if( less(_data[min], p) ) { |
---|
173 | move(_data[min], hole); |
---|
174 | hole = min; |
---|
175 | } |
---|
176 | } |
---|
177 | } |
---|
178 | ok: |
---|
179 | move(p, hole); |
---|
180 | } |
---|
181 | |
---|
182 | void move(const Pair &p, int i) { |
---|
183 | _data[i] = p; |
---|
184 | _iim.set(p.first, i); |
---|
185 | } |
---|
186 | |
---|
187 | public: |
---|
188 | /// \brief Insert a pair of item and priority into the heap. |
---|
189 | /// |
---|
190 | /// This function inserts \c p.first to the heap with priority |
---|
191 | /// \c p.second. |
---|
192 | /// \param p The pair to insert. |
---|
193 | /// \pre \c p.first must not be stored in the heap. |
---|
194 | void push(const Pair &p) { |
---|
195 | int n = _data.size(); |
---|
196 | _data.resize(n+1); |
---|
197 | bubbleUp(n, p); |
---|
198 | } |
---|
199 | |
---|
200 | /// \brief Insert an item into the heap with the given priority. |
---|
201 | /// |
---|
202 | /// This function inserts the given item into the heap with the |
---|
203 | /// given priority. |
---|
204 | /// \param i The item to insert. |
---|
205 | /// \param p The priority of the item. |
---|
206 | /// \pre \e i must not be stored in the heap. |
---|
207 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
---|
208 | |
---|
209 | /// \brief Return the item having minimum priority. |
---|
210 | /// |
---|
211 | /// This function returns the item having minimum priority. |
---|
212 | /// \pre The heap must be non-empty. |
---|
213 | Item top() const { return _data[0].first; } |
---|
214 | |
---|
215 | /// \brief The minimum priority. |
---|
216 | /// |
---|
217 | /// This function returns the minimum priority. |
---|
218 | /// \pre The heap must be non-empty. |
---|
219 | Prio prio() const { return _data[0].second; } |
---|
220 | |
---|
221 | /// \brief Remove the item having minimum priority. |
---|
222 | /// |
---|
223 | /// This function removes the item having minimum priority. |
---|
224 | /// \pre The heap must be non-empty. |
---|
225 | void pop() { |
---|
226 | int n = _data.size()-1; |
---|
227 | _iim.set(_data[0].first, POST_HEAP); |
---|
228 | if (n>0) bubbleDown(0, _data[n], n); |
---|
229 | _data.pop_back(); |
---|
230 | } |
---|
231 | |
---|
232 | /// \brief Remove the given item from the heap. |
---|
233 | /// |
---|
234 | /// This function removes the given item from the heap if it is |
---|
235 | /// already stored. |
---|
236 | /// \param i The item to delete. |
---|
237 | /// \pre \e i must be in the heap. |
---|
238 | void erase(const Item &i) { |
---|
239 | int h = _iim[i]; |
---|
240 | int n = _data.size()-1; |
---|
241 | _iim.set(_data[h].first, POST_HEAP); |
---|
242 | if( h<n ) { |
---|
243 | if( less(_data[parent(h)], _data[n]) ) |
---|
244 | bubbleDown(h, _data[n], n); |
---|
245 | else |
---|
246 | bubbleUp(h, _data[n]); |
---|
247 | } |
---|
248 | _data.pop_back(); |
---|
249 | } |
---|
250 | |
---|
251 | /// \brief The priority of the given item. |
---|
252 | /// |
---|
253 | /// This function returns the priority of the given item. |
---|
254 | /// \param i The item. |
---|
255 | /// \pre \e i must be in the heap. |
---|
256 | Prio operator[](const Item &i) const { |
---|
257 | int idx = _iim[i]; |
---|
258 | return _data[idx].second; |
---|
259 | } |
---|
260 | |
---|
261 | /// \brief Set the priority of an item or insert it, if it is |
---|
262 | /// not stored in the heap. |
---|
263 | /// |
---|
264 | /// This method sets the priority of the given item if it is |
---|
265 | /// already stored in the heap. Otherwise it inserts the given |
---|
266 | /// item into the heap with the given priority. |
---|
267 | /// \param i The item. |
---|
268 | /// \param p The priority. |
---|
269 | void set(const Item &i, const Prio &p) { |
---|
270 | int idx = _iim[i]; |
---|
271 | if( idx<0 ) |
---|
272 | push(i,p); |
---|
273 | else if( _comp(p, _data[idx].second) ) |
---|
274 | bubbleUp(idx, Pair(i,p)); |
---|
275 | else |
---|
276 | bubbleDown(idx, Pair(i,p), _data.size()); |
---|
277 | } |
---|
278 | |
---|
279 | /// \brief Decrease the priority of an item to the given value. |
---|
280 | /// |
---|
281 | /// This function decreases the priority of an item to the given value. |
---|
282 | /// \param i The item. |
---|
283 | /// \param p The priority. |
---|
284 | /// \pre \e i must be stored in the heap with priority at least \e p. |
---|
285 | void decrease(const Item &i, const Prio &p) { |
---|
286 | int idx = _iim[i]; |
---|
287 | bubbleUp(idx, Pair(i,p)); |
---|
288 | } |
---|
289 | |
---|
290 | /// \brief Increase the priority of an item to the given value. |
---|
291 | /// |
---|
292 | /// This function increases the priority of an item to the given value. |
---|
293 | /// \param i The item. |
---|
294 | /// \param p The priority. |
---|
295 | /// \pre \e i must be stored in the heap with priority at most \e p. |
---|
296 | void increase(const Item &i, const Prio &p) { |
---|
297 | int idx = _iim[i]; |
---|
298 | bubbleDown(idx, Pair(i,p), _data.size()); |
---|
299 | } |
---|
300 | |
---|
301 | /// \brief Return the state of an item. |
---|
302 | /// |
---|
303 | /// This method returns \c PRE_HEAP if the given item has never |
---|
304 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
---|
305 | /// and \c POST_HEAP otherwise. |
---|
306 | /// In the latter case it is possible that the item will get back |
---|
307 | /// to the heap again. |
---|
308 | /// \param i The item. |
---|
309 | State state(const Item &i) const { |
---|
310 | int s = _iim[i]; |
---|
311 | if (s>=0) s=0; |
---|
312 | return State(s); |
---|
313 | } |
---|
314 | |
---|
315 | /// \brief Set the state of an item in the heap. |
---|
316 | /// |
---|
317 | /// This function sets the state of the given item in the heap. |
---|
318 | /// It can be used to manually clear the heap when it is important |
---|
319 | /// to achive better time complexity. |
---|
320 | /// \param i The item. |
---|
321 | /// \param st The state. It should not be \c IN_HEAP. |
---|
322 | void state(const Item& i, State st) { |
---|
323 | switch (st) { |
---|
324 | case POST_HEAP: |
---|
325 | case PRE_HEAP: |
---|
326 | if (state(i) == IN_HEAP) erase(i); |
---|
327 | _iim[i] = st; |
---|
328 | break; |
---|
329 | case IN_HEAP: |
---|
330 | break; |
---|
331 | } |
---|
332 | } |
---|
333 | |
---|
334 | /// \brief Replace an item in the heap. |
---|
335 | /// |
---|
336 | /// This function replaces item \c i with item \c j. |
---|
337 | /// Item \c i must be in the heap, while \c j must be out of the heap. |
---|
338 | /// After calling this method, item \c i will be out of the |
---|
339 | /// heap and \c j will be in the heap with the same prioriority |
---|
340 | /// as item \c i had before. |
---|
341 | void replace(const Item& i, const Item& j) { |
---|
342 | int idx=_iim[i]; |
---|
343 | _iim.set(i, _iim[j]); |
---|
344 | _iim.set(j, idx); |
---|
345 | _data[idx].first=j; |
---|
346 | } |
---|
347 | |
---|
348 | }; // class KaryHeap |
---|
349 | |
---|
350 | } // namespace lemon |
---|
351 | |
---|
352 | #endif // LEMON_KARY_HEAP_H |
---|