diff --git a/lemon/bucket_heap.h b/lemon/bucket_heap.h new file mode 100644 --- /dev/null +++ b/lemon/bucket_heap.h @@ -0,0 +1,567 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_BUCKET_HEAP_H +#define LEMON_BUCKET_HEAP_H + +///\ingroup auxdat +///\file +///\brief Bucket Heap implementation. + +#include +#include +#include + +namespace lemon { + + namespace _bucket_heap_bits { + + template + struct DirectionTraits { + static bool less(int left, int right) { + return left < right; + } + static void increase(int& value) { + ++value; + } + }; + + template <> + struct DirectionTraits { + static bool less(int left, int right) { + return left > right; + } + static void increase(int& value) { + --value; + } + }; + + } + + /// \ingroup auxdat + /// + /// \brief A Bucket Heap implementation. + /// + /// This class implements the \e bucket \e heap data structure. A \e heap + /// is a data structure for storing items with specified values called \e + /// priorities in such a way that finding the item with minimum priority is + /// efficient. The bucket heap is very simple implementation, it can store + /// only integer priorities and it stores for each priority in the + /// \f$ [0..C) \f$ range a list of items. So it should be used only when + /// the priorities are small. It is not intended to use as dijkstra heap. + /// + /// \param IM A read and write Item int map, used internally + /// to handle the cross references. + /// \param MIN If the given parameter is false then instead of the + /// minimum value the maximum can be retrivied with the top() and + /// prio() member functions. + template + class BucketHeap { + + public: + /// \e + typedef typename IM::Key Item; + /// \e + typedef int Prio; + /// \e + typedef std::pair Pair; + /// \e + typedef IM ItemIntMap; + + private: + + typedef _bucket_heap_bits::DirectionTraits Direction; + + public: + + /// \brief Type to represent the items states. + /// + /// Each Item element have a state associated to it. It may be "in heap", + /// "pre heap" or "post heap". The latter two are indifferent from the + /// heap's point of view, but may be useful to the user. + /// + /// The item-int map must be initialized in such way that it assigns + /// \c PRE_HEAP (-1) to any element to be put in the heap. + enum State { + IN_HEAP = 0, ///< = 0. + PRE_HEAP = -1, ///< = -1. + POST_HEAP = -2 ///< = -2. + }; + + public: + /// \brief The constructor. + /// + /// The constructor. + /// \param map should be given to the constructor, since it is used + /// internally to handle the cross references. The value of the map + /// should be PRE_HEAP (-1) for each element. + explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {} + + /// The number of items stored in the heap. + /// + /// \brief Returns the number of items stored in the heap. + int size() const { return _data.size(); } + + /// \brief Checks if the heap stores no items. + /// + /// Returns \c true if and only if the heap stores no items. + bool empty() const { return _data.empty(); } + + /// \brief Make empty this heap. + /// + /// Make empty this heap. It does not change the cross reference + /// map. If you want to reuse a heap what is not surely empty you + /// should first clear the heap and after that you should set the + /// cross reference map for each item to \c PRE_HEAP. + void clear() { + _data.clear(); _first.clear(); _minimum = 0; + } + + private: + + void relocate_last(int idx) { + if (idx + 1 < int(_data.size())) { + _data[idx] = _data.back(); + if (_data[idx].prev != -1) { + _data[_data[idx].prev].next = idx; + } else { + _first[_data[idx].value] = idx; + } + if (_data[idx].next != -1) { + _data[_data[idx].next].prev = idx; + } + _iim[_data[idx].item] = idx; + } + _data.pop_back(); + } + + void unlace(int idx) { + if (_data[idx].prev != -1) { + _data[_data[idx].prev].next = _data[idx].next; + } else { + _first[_data[idx].value] = _data[idx].next; + } + if (_data[idx].next != -1) { + _data[_data[idx].next].prev = _data[idx].prev; + } + } + + void lace(int idx) { + if (int(_first.size()) <= _data[idx].value) { + _first.resize(_data[idx].value + 1, -1); + } + _data[idx].next = _first[_data[idx].value]; + if (_data[idx].next != -1) { + _data[_data[idx].next].prev = idx; + } + _first[_data[idx].value] = idx; + _data[idx].prev = -1; + } + + public: + /// \brief Insert a pair of item and priority into the heap. + /// + /// Adds \c p.first to the heap with priority \c p.second. + /// \param p The pair to insert. + void push(const Pair& p) { + push(p.first, p.second); + } + + /// \brief Insert an item into the heap with the given priority. + /// + /// Adds \c i to the heap with priority \c p. + /// \param i The item to insert. + /// \param p The priority of the item. + void push(const Item &i, const Prio &p) { + int idx = _data.size(); + _iim[i] = idx; + _data.push_back(BucketItem(i, p)); + lace(idx); + if (Direction::less(p, _minimum)) { + _minimum = p; + } + } + + /// \brief Returns the item with minimum priority. + /// + /// This method returns the item with minimum priority. + /// \pre The heap must be nonempty. + Item top() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _data[_first[_minimum]].item; + } + + /// \brief Returns the minimum priority. + /// + /// It returns the minimum priority. + /// \pre The heap must be nonempty. + Prio prio() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _minimum; + } + + /// \brief Deletes the item with minimum priority. + /// + /// This method deletes the item with minimum priority from the heap. + /// \pre The heap must be non-empty. + void pop() { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + int idx = _first[_minimum]; + _iim[_data[idx].item] = -2; + unlace(idx); + relocate_last(idx); + } + + /// \brief Deletes \c i from the heap. + /// + /// This method deletes item \c i from the heap, if \c i was + /// already stored in the heap. + /// \param i The item to erase. + void erase(const Item &i) { + int idx = _iim[i]; + _iim[_data[idx].item] = -2; + unlace(idx); + relocate_last(idx); + } + + + /// \brief Returns the priority of \c i. + /// + /// This function returns the priority of item \c i. + /// \pre \c i must be in the heap. + /// \param i The item. + Prio operator[](const Item &i) const { + int idx = _iim[i]; + return _data[idx].value; + } + + /// \brief \c i gets to the heap with priority \c p independently + /// if \c i was already there. + /// + /// This method calls \ref push(\c i, \c p) if \c i is not stored + /// in the heap and sets the priority of \c i to \c p otherwise. + /// \param i The item. + /// \param p The priority. + void set(const Item &i, const Prio &p) { + int idx = _iim[i]; + if (idx < 0) { + push(i, p); + } else if (Direction::less(p, _data[idx].value)) { + decrease(i, p); + } else { + increase(i, p); + } + } + + /// \brief Decreases the priority of \c i to \c p. + /// + /// This method decreases the priority of item \c i to \c p. + /// \pre \c i must be stored in the heap with priority at least \c + /// p relative to \c Compare. + /// \param i The item. + /// \param p The priority. + void decrease(const Item &i, const Prio &p) { + int idx = _iim[i]; + unlace(idx); + _data[idx].value = p; + if (Direction::less(p, _minimum)) { + _minimum = p; + } + lace(idx); + } + + /// \brief Increases the priority of \c i to \c p. + /// + /// This method sets the priority of item \c i to \c p. + /// \pre \c i must be stored in the heap with priority at most \c + /// p relative to \c Compare. + /// \param i The item. + /// \param p The priority. + void increase(const Item &i, const Prio &p) { + int idx = _iim[i]; + unlace(idx); + _data[idx].value = p; + lace(idx); + } + + /// \brief Returns if \c item is in, has already been in, or has + /// never been in the heap. + /// + /// This method returns PRE_HEAP if \c item has never been in the + /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP + /// otherwise. In the latter case it is possible that \c item will + /// get back to the heap again. + /// \param i The item. + State state(const Item &i) const { + int idx = _iim[i]; + if (idx >= 0) idx = 0; + return State(idx); + } + + /// \brief Sets the state of the \c item in the heap. + /// + /// Sets the state of the \c item in the heap. It can be used to + /// manually clear the heap when it is important to achive the + /// better time complexity. + /// \param i The item. + /// \param st The state. It should not be \c IN_HEAP. + void state(const Item& i, State st) { + switch (st) { + case POST_HEAP: + case PRE_HEAP: + if (state(i) == IN_HEAP) { + erase(i); + } + _iim[i] = st; + break; + case IN_HEAP: + break; + } + } + + private: + + struct BucketItem { + BucketItem(const Item& _item, int _value) + : item(_item), value(_value) {} + + Item item; + int value; + + int prev, next; + }; + + ItemIntMap& _iim; + std::vector _first; + std::vector _data; + mutable int _minimum; + + }; // class BucketHeap + + /// \ingroup auxdat + /// + /// \brief A Simplified Bucket Heap implementation. + /// + /// This class implements a simplified \e bucket \e heap data + /// structure. It does not provide some functionality but it faster + /// and simplier data structure than the BucketHeap. The main + /// difference is that the BucketHeap stores for every key a double + /// linked list while this class stores just simple lists. In the + /// other way it does not support erasing each elements just the + /// minimal and it does not supports key increasing, decreasing. + /// + /// \param IM A read and write Item int map, used internally + /// to handle the cross references. + /// \param MIN If the given parameter is false then instead of the + /// minimum value the maximum can be retrivied with the top() and + /// prio() member functions. + /// + /// \sa BucketHeap + template + class SimpleBucketHeap { + + public: + typedef typename IM::Key Item; + typedef int Prio; + typedef std::pair Pair; + typedef IM ItemIntMap; + + private: + + typedef _bucket_heap_bits::DirectionTraits Direction; + + public: + + /// \brief Type to represent the items states. + /// + /// Each Item element have a state associated to it. It may be "in heap", + /// "pre heap" or "post heap". The latter two are indifferent from the + /// heap's point of view, but may be useful to the user. + /// + /// The item-int map must be initialized in such way that it assigns + /// \c PRE_HEAP (-1) to any element to be put in the heap. + enum State { + IN_HEAP = 0, ///< = 0. + PRE_HEAP = -1, ///< = -1. + POST_HEAP = -2 ///< = -2. + }; + + public: + + /// \brief The constructor. + /// + /// The constructor. + /// \param map should be given to the constructor, since it is used + /// internally to handle the cross references. The value of the map + /// should be PRE_HEAP (-1) for each element. + explicit SimpleBucketHeap(ItemIntMap &map) + : _iim(map), _free(-1), _num(0), _minimum(0) {} + + /// \brief Returns the number of items stored in the heap. + /// + /// The number of items stored in the heap. + int size() const { return _num; } + + /// \brief Checks if the heap stores no items. + /// + /// Returns \c true if and only if the heap stores no items. + bool empty() const { return _num == 0; } + + /// \brief Make empty this heap. + /// + /// Make empty this heap. It does not change the cross reference + /// map. If you want to reuse a heap what is not surely empty you + /// should first clear the heap and after that you should set the + /// cross reference map for each item to \c PRE_HEAP. + void clear() { + _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0; + } + + /// \brief Insert a pair of item and priority into the heap. + /// + /// Adds \c p.first to the heap with priority \c p.second. + /// \param p The pair to insert. + void push(const Pair& p) { + push(p.first, p.second); + } + + /// \brief Insert an item into the heap with the given priority. + /// + /// Adds \c i to the heap with priority \c p. + /// \param i The item to insert. + /// \param p The priority of the item. + void push(const Item &i, const Prio &p) { + int idx; + if (_free == -1) { + idx = _data.size(); + _data.push_back(BucketItem(i)); + } else { + idx = _free; + _free = _data[idx].next; + _data[idx].item = i; + } + _iim[i] = idx; + if (p >= int(_first.size())) _first.resize(p + 1, -1); + _data[idx].next = _first[p]; + _first[p] = idx; + if (Direction::less(p, _minimum)) { + _minimum = p; + } + ++_num; + } + + /// \brief Returns the item with minimum priority. + /// + /// This method returns the item with minimum priority. + /// \pre The heap must be nonempty. + Item top() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _data[_first[_minimum]].item; + } + + /// \brief Returns the minimum priority. + /// + /// It returns the minimum priority. + /// \pre The heap must be nonempty. + Prio prio() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _minimum; + } + + /// \brief Deletes the item with minimum priority. + /// + /// This method deletes the item with minimum priority from the heap. + /// \pre The heap must be non-empty. + void pop() { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + int idx = _first[_minimum]; + _iim[_data[idx].item] = -2; + _first[_minimum] = _data[idx].next; + _data[idx].next = _free; + _free = idx; + --_num; + } + + /// \brief Returns the priority of \c i. + /// + /// This function returns the priority of item \c i. + /// \warning This operator is not a constant time function + /// because it scans the whole data structure to find the proper + /// value. + /// \pre \c i must be in the heap. + /// \param i The item. + Prio operator[](const Item &i) const { + for (int k = 0; k < _first.size(); ++k) { + int idx = _first[k]; + while (idx != -1) { + if (_data[idx].item == i) { + return k; + } + idx = _data[idx].next; + } + } + return -1; + } + + /// \brief Returns if \c item is in, has already been in, or has + /// never been in the heap. + /// + /// This method returns PRE_HEAP if \c item has never been in the + /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP + /// otherwise. In the latter case it is possible that \c item will + /// get back to the heap again. + /// \param i The item. + State state(const Item &i) const { + int idx = _iim[i]; + if (idx >= 0) idx = 0; + return State(idx); + } + + private: + + struct BucketItem { + BucketItem(const Item& _item) + : item(_item) {} + + Item item; + int next; + }; + + ItemIntMap& _iim; + std::vector _first; + std::vector _data; + int _free, _num; + mutable int _minimum; + + }; // class SimpleBucketHeap + +} + +#endif