Empty graph is (strongly) connected.
2 * lemon/linear_heap.h - Part of LEMON, a generic C++ optimization library
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
17 #ifndef LEMON_LINEAR_HEAP_H
18 #define LEMON_LINEAR_HEAP_H
22 ///\brief Binary Heap implementation.
30 /// \addtogroup auxdat
33 /// \brief A Linear Heap implementation.
35 /// This class implements the \e linear \e heap data structure. A \e heap
36 /// is a data structure for storing items with specified values called \e
37 /// priorities in such a way that finding the item with minimum priority is
38 /// efficient. The linear heap is very simple implementation, it can store
39 /// only integer priorities and it stores for each priority in the [0..C]
40 /// range a list of items. So it should be used only when the priorities
41 /// are small. It is not intended to use as dijkstra heap.
43 /// \param _Item Type of the items to be stored.
44 /// \param _ItemIntMap A read and writable Item int map, used internally
45 /// to handle the cross references.
46 /// \param minimize If the given parameter is true then the heap gives back
47 /// the lowest priority.
48 template <typename _Item, typename _ItemIntMap, bool minimize = true >
54 typedef std::pair<Item, Prio> Pair;
55 typedef _ItemIntMap ItemIntMap;
57 /// \brief Type to represent the items states.
59 /// Each Item element have a state associated to it. It may be "in heap",
60 /// "pre heap" or "post heap". The latter two are indifferent from the
61 /// heap's point of view, but may be useful to the user.
63 /// The ItemIntMap \e should be initialized in such way that it maps
64 /// PRE_HEAP (-1) to any element to be put in the heap...
72 /// \brief The constructor.
75 /// \param _index should be given to the constructor, since it is used
76 /// internally to handle the cross references. The value of the map
77 /// should be PRE_HEAP (-1) for each element.
78 explicit LinearHeap(ItemIntMap &_index) : index(_index), minimal(0) {}
80 /// The number of items stored in the heap.
82 /// \brief Returns the number of items stored in the heap.
83 int size() const { return data.size(); }
85 /// \brief Checks if the heap stores no items.
87 /// Returns \c true if and only if the heap stores no items.
88 bool empty() const { return data.empty(); }
90 /// \brief Make empty this heap.
92 /// Make empty this heap.
94 for (int i = 0; i < (int)data.size(); ++i) {
95 index[data[i].item] = -2;
97 data.clear(); first.clear(); minimal = 0;
102 void relocate_last(int idx) {
103 if (idx + 1 < (int)data.size()) {
104 data[idx] = data.back();
105 if (data[idx].prev != -1) {
106 data[data[idx].prev].next = idx;
108 first[data[idx].value] = idx;
110 if (data[idx].next != -1) {
111 data[data[idx].next].prev = idx;
113 index[data[idx].item] = idx;
118 void unlace(int idx) {
119 if (data[idx].prev != -1) {
120 data[data[idx].prev].next = data[idx].next;
122 first[data[idx].value] = data[idx].next;
124 if (data[idx].next != -1) {
125 data[data[idx].next].prev = data[idx].prev;
130 if ((int)first.size() <= data[idx].value) {
131 first.resize(data[idx].value + 1, -1);
133 data[idx].next = first[data[idx].value];
134 if (data[idx].next != -1) {
135 data[data[idx].next].prev = idx;
137 first[data[idx].value] = idx;
142 /// \brief Insert a pair of item and priority into the heap.
144 /// Adds \c p.first to the heap with priority \c p.second.
145 /// \param p The pair to insert.
146 void push(const Pair& p) {
147 push(p.first, p.second);
150 /// \brief Insert an item into the heap with the given priority.
152 /// Adds \c i to the heap with priority \c p.
153 /// \param i The item to insert.
154 /// \param p The priority of the item.
155 void push(const Item &i, const Prio &p) {
156 int idx = data.size();
158 data.push_back(LinearItem(i, p));
165 /// \brief Returns the item with minimum priority.
167 /// This method returns the item with minimum priority.
168 /// \pre The heap must be nonempty.
170 while (first[minimal] == -1) {
173 return data[first[minimal]].item;
176 /// \brief Returns the minimum priority.
178 /// It returns the minimum priority.
179 /// \pre The heap must be nonempty.
181 while (first[minimal] == -1) {
187 /// \brief Deletes the item with minimum priority.
189 /// This method deletes the item with minimum priority from the heap.
190 /// \pre The heap must be non-empty.
192 while (first[minimal] == -1) {
195 int idx = first[minimal];
196 index[data[idx].item] = -2;
201 /// \brief Deletes \c i from the heap.
203 /// This method deletes item \c i from the heap, if \c i was
204 /// already stored in the heap.
205 /// \param i The item to erase.
206 void erase(const Item &i) {
208 index[data[idx].item] = -2;
214 /// \brief Returns the priority of \c i.
216 /// This function returns the priority of item \c i.
217 /// \pre \c i must be in the heap.
218 /// \param i The item.
219 Prio operator[](const Item &i) const {
221 return data[idx].value;
224 /// \brief \c i gets to the heap with priority \c p independently
225 /// if \c i was already there.
227 /// This method calls \ref push(\c i, \c p) if \c i is not stored
228 /// in the heap and sets the priority of \c i to \c p otherwise.
229 /// \param i The item.
230 /// \param p The priority.
231 void set(const Item &i, const Prio &p) {
235 } else if (p > data[idx].value) {
242 /// \brief Decreases the priority of \c i to \c p.
244 /// This method decreases the priority of item \c i to \c p.
245 /// \pre \c i must be stored in the heap with priority at least \c
246 /// p relative to \c Compare.
247 /// \param i The item.
248 /// \param p The priority.
249 void decrease(const Item &i, const Prio &p) {
259 /// \brief Increases the priority of \c i to \c p.
261 /// This method sets the priority of item \c i to \c p.
262 /// \pre \c i must be stored in the heap with priority at most \c
263 /// p relative to \c Compare.
264 /// \param i The item.
265 /// \param p The priority.
266 void increase(const Item &i, const Prio &p) {
273 /// \brief Returns if \c item is in, has already been in, or has
274 /// never been in the heap.
276 /// This method returns PRE_HEAP if \c item has never been in the
277 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
278 /// otherwise. In the latter case it is possible that \c item will
279 /// get back to the heap again.
280 /// \param i The item.
281 state_enum state(const Item &i) const {
283 if (idx >= 0) idx = 0;
284 return state_enum(idx);
290 LinearItem(const Item& _item, int _value)
291 : item(_item), value(_value) {}
300 std::vector<int> first;
301 std::vector<LinearItem> data;
304 }; // class LinearHeap
307 template <typename _Item, typename _ItemIntMap>
308 class LinearHeap<_Item, _ItemIntMap, false> {
313 typedef std::pair<Item, Prio> Pair;
314 typedef _ItemIntMap ItemIntMap;
324 explicit LinearHeap(ItemIntMap &_index) : index(_index), maximal(-1) {}
326 int size() const { return data.size(); }
327 bool empty() const { return data.empty(); }
330 for (int i = 0; i < (int)data.size(); ++i) {
331 index[data[i].item] = -2;
333 data.clear(); first.clear(); maximal = -1;
338 void relocate_last(int idx) {
339 if (idx + 1 != (int)data.size()) {
340 data[idx] = data.back();
341 if (data[idx].prev != -1) {
342 data[data[idx].prev].next = idx;
344 first[data[idx].value] = idx;
346 if (data[idx].next != -1) {
347 data[data[idx].next].prev = idx;
349 index[data[idx].item] = idx;
354 void unlace(int idx) {
355 if (data[idx].prev != -1) {
356 data[data[idx].prev].next = data[idx].next;
358 first[data[idx].value] = data[idx].next;
360 if (data[idx].next != -1) {
361 data[data[idx].next].prev = data[idx].prev;
366 if ((int)first.size() <= data[idx].value) {
367 first.resize(data[idx].value + 1, -1);
369 data[idx].next = first[data[idx].value];
370 if (data[idx].next != -1) {
371 data[data[idx].next].prev = idx;
373 first[data[idx].value] = idx;
379 void push(const Pair& p) {
380 push(p.first, p.second);
383 void push(const Item &i, const Prio &p) {
384 int idx = data.size();
386 data.push_back(LinearItem(i, p));
388 if (data[idx].value > maximal) {
389 maximal = data[idx].value;
394 while (first[maximal] == -1) {
397 return data[first[maximal]].item;
401 while (first[maximal] == -1) {
408 while (first[maximal] == -1) {
411 int idx = first[maximal];
412 index[data[idx].item] = -2;
417 void erase(const Item &i) {
419 index[data[idx].item] = -2;
424 Prio operator[](const Item &i) const {
426 return data[idx].value;
429 void set(const Item &i, const Prio &p) {
433 } else if (p > data[idx].value) {
440 void decrease(const Item &i, const Prio &p) {
450 void increase(const Item &i, const Prio &p) {
457 state_enum state(const Item &i) const {
459 if (idx >= 0) idx = 0;
460 return state_enum(idx);
466 LinearItem(const Item& _item, int _value)
467 : item(_item), value(_value) {}
476 std::vector<int> first;
477 std::vector<LinearItem> data;
480 }; // class LinearHeap