deba@681: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@681: *
deba@681: * This file is a part of LEMON, a generic C++ optimization library.
deba@681: *
deba@681: * Copyright (C) 2003-2009
deba@681: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@681: * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@681: *
deba@681: * Permission to use, modify and distribute this software is granted
deba@681: * provided that this copyright notice appears in all copies. For
deba@681: * precise terms see the accompanying LICENSE file.
deba@681: *
deba@681: * This software is provided "AS IS" with no warranty of any kind,
deba@681: * express or implied, and with no claim as to its suitability for any
deba@681: * purpose.
deba@681: *
deba@681: */
deba@681:
deba@681: #ifndef LEMON_RADIX_HEAP_H
deba@681: #define LEMON_RADIX_HEAP_H
deba@681:
kpeter@710: ///\ingroup heaps
deba@681: ///\file
kpeter@709: ///\brief Radix heap implementation.
deba@681:
deba@681: #include <vector>
deba@681: #include <lemon/error.h>
deba@681:
deba@681: namespace lemon {
deba@681:
deba@681:
kpeter@710: /// \ingroup heaps
deba@681: ///
kpeter@709: /// \brief Radix heap data structure.
deba@681: ///
kpeter@709: /// This class implements the \e radix \e heap data structure.
kpeter@709: /// It practically conforms to the \ref concepts::Heap "heap concept",
kpeter@709: /// but it has some limitations due its special implementation.
kpeter@709: /// The type of the priorities must be \c int and the priority of an
kpeter@709: /// item cannot be decreased under the priority of the last removed item.
deba@681: ///
kpeter@709: /// \tparam IM A read-writable item map with \c int values, used
kpeter@709: /// internally to handle the cross references.
deba@683: template <typename IM>
deba@681: class RadixHeap {
deba@681:
deba@681: public:
kpeter@709:
kpeter@709: /// Type of the item-int map.
kpeter@709: typedef IM ItemIntMap;
kpeter@709: /// Type of the priorities.
deba@681: typedef int Prio;
kpeter@709: /// Type of the items stored in the heap.
kpeter@709: typedef typename ItemIntMap::Key Item;
deba@681:
deba@681: /// \brief Exception thrown by RadixHeap.
deba@681: ///
kpeter@709: /// This exception is thrown when an item is inserted into a
kpeter@709: /// RadixHeap with a priority smaller than the last erased one.
deba@681: /// \see RadixHeap
kpeter@711: class PriorityUnderflowError : public Exception {
deba@681: public:
deba@681: virtual const char* what() const throw() {
kpeter@711: return "lemon::RadixHeap::PriorityUnderflowError";
deba@681: }
deba@681: };
deba@681:
kpeter@709: /// \brief Type to represent the states of the items.
deba@681: ///
kpeter@709: /// Each item has a state associated to it. It can be "in heap",
kpeter@709: /// "pre-heap" or "post-heap". The latter two are indifferent from the
deba@681: /// heap's point of view, but may be useful to the user.
deba@681: ///
kpeter@709: /// The item-int map must be initialized in such way that it assigns
kpeter@709: /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
deba@681: enum State {
kpeter@709: IN_HEAP = 0, ///< = 0.
kpeter@709: PRE_HEAP = -1, ///< = -1.
kpeter@709: POST_HEAP = -2 ///< = -2.
deba@681: };
deba@681:
deba@681: private:
deba@681:
deba@681: struct RadixItem {
deba@681: int prev, next, box;
deba@681: Item item;
deba@681: int prio;
deba@681: RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
deba@681: };
deba@681:
deba@681: struct RadixBox {
deba@681: int first;
deba@681: int min, size;
deba@681: RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
deba@681: };
deba@681:
kpeter@711: std::vector<RadixItem> _data;
kpeter@711: std::vector<RadixBox> _boxes;
deba@681:
deba@683: ItemIntMap &_iim;
deba@681:
kpeter@709: public:
deba@681:
kpeter@709: /// \brief Constructor.
deba@681: ///
kpeter@709: /// Constructor.
kpeter@709: /// \param map A map that assigns \c int values to the items.
kpeter@709: /// It is used internally to handle the cross references.
kpeter@709: /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@709: /// \param minimum The initial minimum value of the heap.
kpeter@709: /// \param capacity The initial capacity of the heap.
kpeter@709: RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0)
kpeter@709: : _iim(map)
kpeter@709: {
kpeter@711: _boxes.push_back(RadixBox(minimum, 1));
kpeter@711: _boxes.push_back(RadixBox(minimum + 1, 1));
kpeter@711: while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
deba@681: extend();
deba@681: }
deba@681: }
deba@681:
kpeter@709: /// \brief The number of items stored in the heap.
deba@681: ///
kpeter@709: /// This function returns the number of items stored in the heap.
kpeter@711: int size() const { return _data.size(); }
kpeter@709:
kpeter@709: /// \brief Check if the heap is empty.
deba@681: ///
kpeter@709: /// This function returns \c true if the heap is empty.
kpeter@711: bool empty() const { return _data.empty(); }
deba@681:
kpeter@709: /// \brief Make the heap empty.
deba@681: ///
kpeter@709: /// This functon makes the heap empty.
kpeter@709: /// It does not change the cross reference map. If you want to reuse
kpeter@709: /// a heap that is not surely empty, you should first clear it and
kpeter@709: /// then you should set the cross reference map to \c PRE_HEAP
kpeter@709: /// for each item.
kpeter@709: /// \param minimum The minimum value of the heap.
kpeter@709: /// \param capacity The capacity of the heap.
kpeter@709: void clear(int minimum = 0, int capacity = 0) {
kpeter@711: _data.clear(); _boxes.clear();
kpeter@711: _boxes.push_back(RadixBox(minimum, 1));
kpeter@711: _boxes.push_back(RadixBox(minimum + 1, 1));
kpeter@711: while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
deba@681: extend();
deba@681: }
deba@681: }
deba@681:
deba@681: private:
deba@681:
deba@681: bool upper(int box, Prio pr) {
kpeter@711: return pr < _boxes[box].min;
deba@681: }
deba@681:
deba@681: bool lower(int box, Prio pr) {
kpeter@711: return pr >= _boxes[box].min + _boxes[box].size;
deba@681: }
deba@681:
kpeter@709: // Remove item from the box list
deba@681: void remove(int index) {
kpeter@711: if (_data[index].prev >= 0) {
kpeter@711: _data[_data[index].prev].next = _data[index].next;
deba@681: } else {
kpeter@711: _boxes[_data[index].box].first = _data[index].next;
deba@681: }
kpeter@711: if (_data[index].next >= 0) {
kpeter@711: _data[_data[index].next].prev = _data[index].prev;
deba@681: }
deba@681: }
deba@681:
kpeter@709: // Insert item into the box list
deba@681: void insert(int box, int index) {
kpeter@711: if (_boxes[box].first == -1) {
kpeter@711: _boxes[box].first = index;
kpeter@711: _data[index].next = _data[index].prev = -1;
deba@681: } else {
kpeter@711: _data[index].next = _boxes[box].first;
kpeter@711: _data[_boxes[box].first].prev = index;
kpeter@711: _data[index].prev = -1;
kpeter@711: _boxes[box].first = index;
deba@681: }
kpeter@711: _data[index].box = box;
deba@681: }
deba@681:
kpeter@709: // Add a new box to the box list
deba@681: void extend() {
kpeter@711: int min = _boxes.back().min + _boxes.back().size;
kpeter@711: int bs = 2 * _boxes.back().size;
kpeter@711: _boxes.push_back(RadixBox(min, bs));
deba@681: }
deba@681:
kpeter@709: // Move an item up into the proper box.
kpeter@711: void bubbleUp(int index) {
kpeter@711: if (!lower(_data[index].box, _data[index].prio)) return;
deba@681: remove(index);
kpeter@711: int box = findUp(_data[index].box, _data[index].prio);
deba@681: insert(box, index);
deba@681: }
deba@681:
kpeter@709: // Find up the proper box for the item with the given priority
deba@681: int findUp(int start, int pr) {
deba@681: while (lower(start, pr)) {
kpeter@711: if (++start == int(_boxes.size())) {
deba@681: extend();
deba@681: }
deba@681: }
deba@681: return start;
deba@681: }
deba@681:
kpeter@709: // Move an item down into the proper box
kpeter@711: void bubbleDown(int index) {
kpeter@711: if (!upper(_data[index].box, _data[index].prio)) return;
deba@681: remove(index);
kpeter@711: int box = findDown(_data[index].box, _data[index].prio);
deba@681: insert(box, index);
deba@681: }
deba@681:
kpeter@709: // Find down the proper box for the item with the given priority
deba@681: int findDown(int start, int pr) {
deba@681: while (upper(start, pr)) {
kpeter@711: if (--start < 0) throw PriorityUnderflowError();
deba@681: }
deba@681: return start;
deba@681: }
deba@681:
kpeter@709: // Find the first non-empty box
deba@681: int findFirst() {
deba@681: int first = 0;
kpeter@711: while (_boxes[first].first == -1) ++first;
deba@681: return first;
deba@681: }
deba@681:
kpeter@709: // Gives back the minimum priority of the given box
deba@681: int minValue(int box) {
kpeter@711: int min = _data[_boxes[box].first].prio;
kpeter@711: for (int k = _boxes[box].first; k != -1; k = _data[k].next) {
kpeter@711: if (_data[k].prio < min) min = _data[k].prio;
deba@681: }
deba@681: return min;
deba@681: }
deba@681:
kpeter@709: // Rearrange the items of the heap and make the first box non-empty
deba@681: void moveDown() {
deba@681: int box = findFirst();
deba@681: if (box == 0) return;
deba@681: int min = minValue(box);
deba@681: for (int i = 0; i <= box; ++i) {
kpeter@711: _boxes[i].min = min;
kpeter@711: min += _boxes[i].size;
deba@681: }
kpeter@711: int curr = _boxes[box].first, next;
deba@681: while (curr != -1) {
kpeter@711: next = _data[curr].next;
kpeter@711: bubbleDown(curr);
deba@681: curr = next;
deba@681: }
deba@681: }
deba@681:
kpeter@711: void relocateLast(int index) {
kpeter@711: if (index != int(_data.size()) - 1) {
kpeter@711: _data[index] = _data.back();
kpeter@711: if (_data[index].prev != -1) {
kpeter@711: _data[_data[index].prev].next = index;
deba@681: } else {
kpeter@711: _boxes[_data[index].box].first = index;
deba@681: }
kpeter@711: if (_data[index].next != -1) {
kpeter@711: _data[_data[index].next].prev = index;
deba@681: }
kpeter@711: _iim[_data[index].item] = index;
deba@681: }
kpeter@711: _data.pop_back();
deba@681: }
deba@681:
deba@681: public:
deba@681:
deba@681: /// \brief Insert an item into the heap with the given priority.
deba@681: ///
kpeter@709: /// This function inserts the given item into the heap with the
kpeter@709: /// given priority.
deba@681: /// \param i The item to insert.
deba@681: /// \param p The priority of the item.
kpeter@709: /// \pre \e i must not be stored in the heap.
kpeter@709: /// \warning This method may throw an \c UnderFlowPriorityException.
deba@681: void push(const Item &i, const Prio &p) {
kpeter@711: int n = _data.size();
deba@683: _iim.set(i, n);
kpeter@711: _data.push_back(RadixItem(i, p));
kpeter@711: while (lower(_boxes.size() - 1, p)) {
deba@681: extend();
deba@681: }
kpeter@711: int box = findDown(_boxes.size() - 1, p);
deba@681: insert(box, n);
deba@681: }
deba@681:
kpeter@709: /// \brief Return the item having minimum priority.
deba@681: ///
kpeter@709: /// This function returns the item having minimum priority.
kpeter@709: /// \pre The heap must be non-empty.
deba@681: Item top() const {
deba@681: const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
kpeter@711: return _data[_boxes[0].first].item;
deba@681: }
deba@681:
kpeter@709: /// \brief The minimum priority.
deba@681: ///
kpeter@709: /// This function returns the minimum priority.
kpeter@709: /// \pre The heap must be non-empty.
deba@681: Prio prio() const {
deba@681: const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
kpeter@711: return _data[_boxes[0].first].prio;
deba@681: }
deba@681:
kpeter@709: /// \brief Remove the item having minimum priority.
deba@681: ///
kpeter@709: /// This function removes the item having minimum priority.
deba@681: /// \pre The heap must be non-empty.
deba@681: void pop() {
deba@681: moveDown();
kpeter@711: int index = _boxes[0].first;
kpeter@711: _iim[_data[index].item] = POST_HEAP;
deba@681: remove(index);
kpeter@711: relocateLast(index);
deba@681: }
deba@681:
kpeter@709: /// \brief Remove the given item from the heap.
deba@681: ///
kpeter@709: /// This function removes the given item from the heap if it is
kpeter@709: /// already stored.
kpeter@709: /// \param i The item to delete.
kpeter@709: /// \pre \e i must be in the heap.
deba@681: void erase(const Item &i) {
deba@683: int index = _iim[i];
deba@683: _iim[i] = POST_HEAP;
deba@681: remove(index);
kpeter@711: relocateLast(index);
deba@681: }
deba@681:
kpeter@709: /// \brief The priority of the given item.
deba@681: ///
kpeter@709: /// This function returns the priority of the given item.
deba@681: /// \param i The item.
kpeter@709: /// \pre \e i must be in the heap.
deba@681: Prio operator[](const Item &i) const {
deba@683: int idx = _iim[i];
kpeter@711: return _data[idx].prio;
deba@681: }
deba@681:
kpeter@709: /// \brief Set the priority of an item or insert it, if it is
kpeter@709: /// not stored in the heap.
deba@681: ///
kpeter@709: /// This method sets the priority of the given item if it is
kpeter@709: /// already stored in the heap. Otherwise it inserts the given
kpeter@709: /// item into the heap with the given priority.
deba@681: /// \param i The item.
deba@681: /// \param p The priority.
kpeter@709: /// \pre \e i must be in the heap.
kpeter@709: /// \warning This method may throw an \c UnderFlowPriorityException.
deba@681: void set(const Item &i, const Prio &p) {
deba@683: int idx = _iim[i];
deba@681: if( idx < 0 ) {
deba@681: push(i, p);
deba@681: }
kpeter@711: else if( p >= _data[idx].prio ) {
kpeter@711: _data[idx].prio = p;
kpeter@711: bubbleUp(idx);
deba@681: } else {
kpeter@711: _data[idx].prio = p;
kpeter@711: bubbleDown(idx);
deba@681: }
deba@681: }
deba@681:
kpeter@709: /// \brief Decrease the priority of an item to the given value.
deba@681: ///
kpeter@709: /// This function decreases the priority of an item to the given value.
deba@681: /// \param i The item.
deba@681: /// \param p The priority.
kpeter@709: /// \pre \e i must be stored in the heap with priority at least \e p.
kpeter@709: /// \warning This method may throw an \c UnderFlowPriorityException.
deba@681: void decrease(const Item &i, const Prio &p) {
deba@683: int idx = _iim[i];
kpeter@711: _data[idx].prio = p;
kpeter@711: bubbleDown(idx);
deba@681: }
deba@681:
kpeter@709: /// \brief Increase the priority of an item to the given value.
deba@681: ///
kpeter@709: /// This function increases the priority of an item to the given value.
deba@681: /// \param i The item.
deba@681: /// \param p The priority.
kpeter@709: /// \pre \e i must be stored in the heap with priority at most \e p.
deba@681: void increase(const Item &i, const Prio &p) {
deba@683: int idx = _iim[i];
kpeter@711: _data[idx].prio = p;
kpeter@711: bubbleUp(idx);
deba@681: }
deba@681:
kpeter@709: /// \brief Return the state of an item.
deba@681: ///
kpeter@709: /// This method returns \c PRE_HEAP if the given item has never
kpeter@709: /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@709: /// and \c POST_HEAP otherwise.
kpeter@709: /// In the latter case it is possible that the item will get back
kpeter@709: /// to the heap again.
deba@681: /// \param i The item.
deba@681: State state(const Item &i) const {
deba@683: int s = _iim[i];
deba@681: if( s >= 0 ) s = 0;
deba@681: return State(s);
deba@681: }
deba@681:
kpeter@709: /// \brief Set the state of an item in the heap.
deba@681: ///
kpeter@709: /// This function sets the state of the given item in the heap.
kpeter@709: /// It can be used to manually clear the heap when it is important
kpeter@709: /// to achive better time complexity.
deba@681: /// \param i The item.
deba@681: /// \param st The state. It should not be \c IN_HEAP.
deba@681: void state(const Item& i, State st) {
deba@681: switch (st) {
deba@681: case POST_HEAP:
deba@681: case PRE_HEAP:
deba@681: if (state(i) == IN_HEAP) {
deba@681: erase(i);
deba@681: }
deba@683: _iim[i] = st;
deba@681: break;
deba@681: case IN_HEAP:
deba@681: break;
deba@681: }
deba@681: }
deba@681:
deba@681: }; // class RadixHeap
deba@681:
deba@681: } // namespace lemon
deba@681:
deba@681: #endif // LEMON_RADIX_HEAP_H