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diff --git a/lemon/lemon/bucket_heap.h b/lemon/lemon/bucket_heap.h new file mode 100644 index 0000000..92dbc08 --- /dev/null +++ b/lemon/lemon/bucket_heap.h @@ -0,0 +1,594 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2010 + * 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 heaps +///\file +///\brief Bucket heap implementation. + +#include <vector> +#include <utility> +#include <functional> + +namespace lemon { + + namespace _bucket_heap_bits { + + template <bool MIN> + struct DirectionTraits { + static bool less(int left, int right) { + return left < right; + } + static void increase(int& value) { + ++value; + } + }; + + template <> + struct DirectionTraits<false> { + static bool less(int left, int right) { + return left > right; + } + static void increase(int& value) { + --value; + } + }; + + } + + /// \ingroup heaps + /// + /// \brief Bucket heap data structure. + /// + /// This class implements the \e bucket \e heap data structure. + /// It practically conforms to the \ref concepts::Heap "heap concept", + /// but it has some limitations. + /// + /// The bucket heap is a very simple structure. It can store only + /// \c int priorities and it maintains a list of items for each priority + /// in the range <tt>[0..C)</tt>. So it should only be used when the + /// priorities are small. It is not intended to use as a Dijkstra heap. + /// + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap. + /// The default is \e min-heap. If this parameter is set to \c false, + /// then the comparison is reversed, so the top(), prio() and pop() + /// functions deal with the item having maximum priority instead of the + /// minimum. + /// + /// \sa SimpleBucketHeap + template <typename IM, bool MIN = true> + class BucketHeap { + + public: + + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef int Prio; + /// Type of the items stored in the heap. + typedef typename ItemIntMap::Key Item; + /// Type of the item-priority pairs. + typedef std::pair<Item,Prio> Pair; + + private: + + typedef _bucket_heap_bits::DirectionTraits<MIN> Direction; + + public: + + /// \brief Type to represent the states of the items. + /// + /// Each item has a state associated to it. It can 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 (<tt>-1</tt>) 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 Constructor. + /// + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. + explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {} + + /// \brief The number of items stored in the heap. + /// + /// This function returns the number of items stored in the heap. + int size() const { return _data.size(); } + + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _data.empty(); } + + /// \brief Make the heap empty. + /// + /// This functon makes the heap empty. + /// It does not change the cross reference map. If you want to reuse + /// a heap that is not surely empty, you should first clear it and + /// then you should set the cross reference map to \c PRE_HEAP + /// for each item. + void clear() { + _data.clear(); _first.clear(); _minimum = 0; + } + + private: + + void relocateLast(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. + /// + /// This function inserts \c p.first to the heap with priority + /// \c p.second. + /// \param p The pair to insert. + /// \pre \c p.first must not be stored in the heap. + void push(const Pair& p) { + push(p.first, p.second); + } + + /// \brief Insert an item into the heap with the given priority. + /// + /// This function inserts the given item into the heap with the + /// given priority. + /// \param i The item to insert. + /// \param p The priority of the item. + /// \pre \e i must not be stored in the heap. + 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 Return the item having minimum priority. + /// + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _data[_first[_minimum]].item; + } + + /// \brief The minimum priority. + /// + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _minimum; + } + + /// \brief Remove the item having minimum priority. + /// + /// This function removes the item having minimum priority. + /// \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); + relocateLast(idx); + } + + /// \brief Remove the given item from the heap. + /// + /// This function removes the given item from the heap if it is + /// already stored. + /// \param i The item to delete. + /// \pre \e i must be in the heap. + void erase(const Item &i) { + int idx = _iim[i]; + _iim[_data[idx].item] = -2; + unlace(idx); + relocateLast(idx); + } + + /// \brief The priority of the given item. + /// + /// This function returns the priority of the given item. + /// \param i The item. + /// \pre \e i must be in the heap. + Prio operator[](const Item &i) const { + int idx = _iim[i]; + return _data[idx].value; + } + + /// \brief Set the priority of an item or insert it, if it is + /// not stored in the heap. + /// + /// This method sets the priority of the given item if it is + /// already stored in the heap. Otherwise it inserts the given + /// item into the heap with the given priority. + /// \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 Decrease the priority of an item to the given value. + /// + /// This function decreases the priority of an item to the given value. + /// \param i The item. + /// \param p The priority. + /// \pre \e i must be stored in the heap with priority at least \e p. + 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 Increase the priority of an item to the given value. + /// + /// This function increases the priority of an item to the given value. + /// \param i The item. + /// \param p The priority. + /// \pre \e i must be stored in the heap with priority at most \e p. + void increase(const Item &i, const Prio &p) { + int idx = _iim[i]; + unlace(idx); + _data[idx].value = p; + lace(idx); + } + + /// \brief Return the state of an item. + /// + /// This method returns \c PRE_HEAP if the given item has never + /// been in the heap, \c IN_HEAP if it is in the heap at the moment, + /// and \c POST_HEAP otherwise. + /// In the latter case it is possible that the 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 Set the state of an item in the heap. + /// + /// This function sets the state of the given item in the heap. + /// It can be used to manually clear the heap when it is important + /// to achive 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<int> _first; + std::vector<BucketItem> _data; + mutable int _minimum; + + }; // class BucketHeap + + /// \ingroup heaps + /// + /// \brief Simplified bucket heap data structure. + /// + /// This class implements a simplified \e bucket \e heap data + /// structure. It does not provide some functionality, but it is + /// faster and simpler than BucketHeap. The main difference is + /// that BucketHeap stores a doubly-linked list for each key while + /// this class stores only simply-linked lists. It supports erasing + /// only for the item having minimum priority and it does not support + /// key increasing and decreasing. + /// + /// Note that this implementation does not conform to the + /// \ref concepts::Heap "heap concept" due to the lack of some + /// functionality. + /// + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap. + /// The default is \e min-heap. If this parameter is set to \c false, + /// then the comparison is reversed, so the top(), prio() and pop() + /// functions deal with the item having maximum priority instead of the + /// minimum. + /// + /// \sa BucketHeap + template <typename IM, bool MIN = true > + class SimpleBucketHeap { + + public: + + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef int Prio; + /// Type of the items stored in the heap. + typedef typename ItemIntMap::Key Item; + /// Type of the item-priority pairs. + typedef std::pair<Item,Prio> Pair; + + private: + + typedef _bucket_heap_bits::DirectionTraits<MIN> Direction; + + public: + + /// \brief Type to represent the states of the items. + /// + /// Each item has a state associated to it. It can 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 (<tt>-1</tt>) 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 Constructor. + /// + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. + explicit SimpleBucketHeap(ItemIntMap &map) + : _iim(map), _free(-1), _num(0), _minimum(0) {} + + /// \brief The number of items stored in the heap. + /// + /// This function returns the number of items stored in the heap. + int size() const { return _num; } + + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _num == 0; } + + /// \brief Make the heap empty. + /// + /// This functon makes the heap empty. + /// It does not change the cross reference map. If you want to reuse + /// a heap that is not surely empty, you should first clear it and + /// then you should set the cross reference map to \c PRE_HEAP + /// for each item. + void clear() { + _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0; + } + + /// \brief Insert a pair of item and priority into the heap. + /// + /// This function inserts \c p.first to the heap with priority + /// \c p.second. + /// \param p The pair to insert. + /// \pre \c p.first must not be stored in the heap. + void push(const Pair& p) { + push(p.first, p.second); + } + + /// \brief Insert an item into the heap with the given priority. + /// + /// This function inserts the given item into the heap with the + /// given priority. + /// \param i The item to insert. + /// \param p The priority of the item. + /// \pre \e i must not be stored in the heap. + 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 Return the item having minimum priority. + /// + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _data[_first[_minimum]].item; + } + + /// \brief The minimum priority. + /// + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { + while (_first[_minimum] == -1) { + Direction::increase(_minimum); + } + return _minimum; + } + + /// \brief Remove the item having minimum priority. + /// + /// This function removes the item having minimum priority. + /// \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 The priority of the given item. + /// + /// This function returns the priority of the given item. + /// \param i The item. + /// \pre \e i must be in the heap. + /// \warning This operator is not a constant time function because + /// it scans the whole data structure to find the proper value. + Prio operator[](const Item &i) const { + for (int k = 0; k < int(_first.size()); ++k) { + int idx = _first[k]; + while (idx != -1) { + if (_data[idx].item == i) { + return k; + } + idx = _data[idx].next; + } + } + return -1; + } + + /// \brief Return the state of an item. + /// + /// This method returns \c PRE_HEAP if the given item has never + /// been in the heap, \c IN_HEAP if it is in the heap at the moment, + /// and \c POST_HEAP otherwise. + /// In the latter case it is possible that the 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<int> _first; + std::vector<BucketItem> _data; + int _free, _num; + mutable int _minimum; + + }; // class SimpleBucketHeap + +} + +#endif |