diff --git a/lemon/radix_heap.h b/lemon/radix_heap.h new file mode 100644 --- /dev/null +++ b/lemon/radix_heap.h @@ -0,0 +1,433 @@ +/* -*- 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_RADIX_HEAP_H +#define LEMON_RADIX_HEAP_H + +///\ingroup auxdat +///\file +///\brief Radix Heap implementation. + +#include +#include + +namespace lemon { + + + /// \ingroup auxdata + /// + /// \brief A Radix Heap implementation. + /// + /// This class implements the \e radix \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. This heap type can store only items with \e int priority. + /// In a heap one can change the priority of an item, add or erase an + /// item, but the priority cannot be decreased under the last removed + /// item's priority. + /// + /// \param _ItemIntMap A read and writable Item int map, used internally + /// to handle the cross references. + /// + /// \see BinHeap + /// \see Dijkstra + template + class RadixHeap { + + public: + typedef typename _ItemIntMap::Key Item; + typedef int Prio; + typedef _ItemIntMap ItemIntMap; + + /// \brief Exception thrown by RadixHeap. + /// + /// This Exception is thrown when a smaller priority + /// is inserted into the \e RadixHeap then the last time erased. + /// \see RadixHeap + + class UnderFlowPriorityError : public Exception { + public: + virtual const char* what() const throw() { + return "lemon::RadixHeap::UnderFlowPriorityError"; + } + }; + + /// \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 ItemIntMap \e should be initialized in such way that it maps + /// PRE_HEAP (-1) to any element to be put in the heap... + enum State { + IN_HEAP = 0, + PRE_HEAP = -1, + POST_HEAP = -2 + }; + + private: + + struct RadixItem { + int prev, next, box; + Item item; + int prio; + RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} + }; + + struct RadixBox { + int first; + int min, size; + RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} + }; + + std::vector data; + std::vector boxes; + + ItemIntMap &iim; + + + public: + /// \brief The constructor. + /// + /// The constructor. + /// + /// \param _iim It 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. + /// + /// \param minimal The initial minimal value of the heap. + /// \param capacity It determines the initial capacity of the heap. + RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0) + : iim(_iim) { + boxes.push_back(RadixBox(minimal, 1)); + boxes.push_back(RadixBox(minimal + 1, 1)); + while (lower(boxes.size() - 1, capacity + minimal - 1)) { + extend(); + } + } + + /// 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(int minimal = 0, int capacity = 0) { + data.clear(); boxes.clear(); + boxes.push_back(RadixBox(minimal, 1)); + boxes.push_back(RadixBox(minimal + 1, 1)); + while (lower(boxes.size() - 1, capacity + minimal - 1)) { + extend(); + } + } + + private: + + bool upper(int box, Prio pr) { + return pr < boxes[box].min; + } + + bool lower(int box, Prio pr) { + return pr >= boxes[box].min + boxes[box].size; + } + + /// \brief Remove item from the box list. + void remove(int index) { + if (data[index].prev >= 0) { + data[data[index].prev].next = data[index].next; + } else { + boxes[data[index].box].first = data[index].next; + } + if (data[index].next >= 0) { + data[data[index].next].prev = data[index].prev; + } + } + + /// \brief Insert item into the box list. + void insert(int box, int index) { + if (boxes[box].first == -1) { + boxes[box].first = index; + data[index].next = data[index].prev = -1; + } else { + data[index].next = boxes[box].first; + data[boxes[box].first].prev = index; + data[index].prev = -1; + boxes[box].first = index; + } + data[index].box = box; + } + + /// \brief Add a new box to the box list. + void extend() { + int min = boxes.back().min + boxes.back().size; + int bs = 2 * boxes.back().size; + boxes.push_back(RadixBox(min, bs)); + } + + /// \brief Move an item up into the proper box. + void bubble_up(int index) { + if (!lower(data[index].box, data[index].prio)) return; + remove(index); + int box = findUp(data[index].box, data[index].prio); + insert(box, index); + } + + /// \brief Find up the proper box for the item with the given prio. + int findUp(int start, int pr) { + while (lower(start, pr)) { + if (++start == int(boxes.size())) { + extend(); + } + } + return start; + } + + /// \brief Move an item down into the proper box. + void bubble_down(int index) { + if (!upper(data[index].box, data[index].prio)) return; + remove(index); + int box = findDown(data[index].box, data[index].prio); + insert(box, index); + } + + /// \brief Find up the proper box for the item with the given prio. + int findDown(int start, int pr) { + while (upper(start, pr)) { + if (--start < 0) throw UnderFlowPriorityError(); + } + return start; + } + + /// \brief Find the first not empty box. + int findFirst() { + int first = 0; + while (boxes[first].first == -1) ++first; + return first; + } + + /// \brief Gives back the minimal prio of the box. + int minValue(int box) { + int min = data[boxes[box].first].prio; + for (int k = boxes[box].first; k != -1; k = data[k].next) { + if (data[k].prio < min) min = data[k].prio; + } + return min; + } + + /// \brief Rearrange the items of the heap and makes the + /// first box not empty. + void moveDown() { + int box = findFirst(); + if (box == 0) return; + int min = minValue(box); + for (int i = 0; i <= box; ++i) { + boxes[i].min = min; + min += boxes[i].size; + } + int curr = boxes[box].first, next; + while (curr != -1) { + next = data[curr].next; + bubble_down(curr); + curr = next; + } + } + + void relocate_last(int index) { + if (index != int(data.size()) - 1) { + data[index] = data.back(); + if (data[index].prev != -1) { + data[data[index].prev].next = index; + } else { + boxes[data[index].box].first = index; + } + if (data[index].next != -1) { + data[data[index].next].prev = index; + } + iim[data[index].item] = index; + } + data.pop_back(); + } + + public: + + /// \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 n = data.size(); + iim.set(i, n); + data.push_back(RadixItem(i, p)); + while (lower(boxes.size() - 1, p)) { + extend(); + } + int box = findDown(boxes.size() - 1, p); + insert(box, n); + } + + /// \brief Returns the item with minimum priority. + /// + /// This method returns the item with minimum priority. + /// \pre The heap must be nonempty. + Item top() const { + const_cast&>(*this).moveDown(); + return data[boxes[0].first].item; + } + + /// \brief Returns the minimum priority. + /// + /// It returns the minimum priority. + /// \pre The heap must be nonempty. + Prio prio() const { + const_cast&>(*this).moveDown(); + return data[boxes[0].first].prio; + } + + /// \brief Deletes the item with minimum priority. + /// + /// This method deletes the item with minimum priority. + /// \pre The heap must be non-empty. + void pop() { + moveDown(); + int index = boxes[0].first; + iim[data[index].item] = POST_HEAP; + remove(index); + relocate_last(index); + } + + /// \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 index = iim[i]; + iim[i] = POST_HEAP; + remove(index); + relocate_last(index); + } + + /// \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].prio; + } + + /// \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. + /// It may throw an \e UnderFlowPriorityException. + /// \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( p >= data[idx].prio ) { + data[idx].prio = p; + bubble_up(idx); + } else { + data[idx].prio = p; + bubble_down(idx); + } + } + + + /// \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, and + /// \c should be greater or equal to the last removed item's priority. + /// \param i The item. + /// \param p The priority. + void decrease(const Item &i, const Prio &p) { + int idx = iim[i]; + data[idx].prio = p; + bubble_down(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 + /// \param i The item. + /// \param p The priority. + void increase(const Item &i, const Prio &p) { + int idx = iim[i]; + data[idx].prio = p; + bubble_up(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 s = iim[i]; + if( s >= 0 ) s = 0; + return State(s); + } + + /// \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; + } + } + + }; // class RadixHeap + +} // namespace lemon + +#endif // LEMON_RADIX_HEAP_H