deba@728: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@728:  *
deba@728:  * This file is a part of LEMON, a generic C++ optimization library.
deba@728:  *
deba@728:  * Copyright (C) 2003-2009
deba@728:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@728:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@728:  *
deba@728:  * Permission to use, modify and distribute this software is granted
deba@728:  * provided that this copyright notice appears in all copies. For
deba@728:  * precise terms see the accompanying LICENSE file.
deba@728:  *
deba@728:  * This software is provided "AS IS" with no warranty of any kind,
deba@728:  * express or implied, and with no claim as to its suitability for any
deba@728:  * purpose.
deba@728:  *
deba@728:  */
deba@728: 
deba@728: #ifndef LEMON_RADIX_HEAP_H
deba@728: #define LEMON_RADIX_HEAP_H
deba@728: 
kpeter@757: ///\ingroup heaps
deba@728: ///\file
kpeter@756: ///\brief Radix heap implementation.
deba@728: 
deba@728: #include <vector>
deba@728: #include <lemon/error.h>
deba@728: 
deba@728: namespace lemon {
deba@728: 
deba@728: 
kpeter@757:   /// \ingroup heaps
deba@728:   ///
kpeter@756:   /// \brief Radix heap data structure.
deba@728:   ///
kpeter@756:   /// This class implements the \e radix \e heap data structure.
kpeter@756:   /// It practically conforms to the \ref concepts::Heap "heap concept",
kpeter@756:   /// but it has some limitations due its special implementation.
kpeter@756:   /// The type of the priorities must be \c int and the priority of an
kpeter@756:   /// item cannot be decreased under the priority of the last removed item.
deba@728:   ///
kpeter@756:   /// \tparam IM A read-writable item map with \c int values, used
kpeter@756:   /// internally to handle the cross references.
deba@730:   template <typename IM>
deba@728:   class RadixHeap {
deba@728: 
deba@728:   public:
kpeter@756: 
kpeter@756:     /// Type of the item-int map.
kpeter@756:     typedef IM ItemIntMap;
kpeter@756:     /// Type of the priorities.
deba@728:     typedef int Prio;
kpeter@756:     /// Type of the items stored in the heap.
kpeter@756:     typedef typename ItemIntMap::Key Item;
deba@728: 
deba@728:     /// \brief Exception thrown by RadixHeap.
deba@728:     ///
kpeter@756:     /// This exception is thrown when an item is inserted into a
kpeter@756:     /// RadixHeap with a priority smaller than the last erased one.
deba@728:     /// \see RadixHeap
kpeter@758:     class PriorityUnderflowError : public Exception {
deba@728:     public:
deba@728:       virtual const char* what() const throw() {
kpeter@758:         return "lemon::RadixHeap::PriorityUnderflowError";
deba@728:       }
deba@728:     };
deba@728: 
kpeter@756:     /// \brief Type to represent the states of the items.
deba@728:     ///
kpeter@756:     /// Each item has a state associated to it. It can be "in heap",
kpeter@756:     /// "pre-heap" or "post-heap". The latter two are indifferent from the
deba@728:     /// heap's point of view, but may be useful to the user.
deba@728:     ///
kpeter@756:     /// The item-int map must be initialized in such way that it assigns
kpeter@756:     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
deba@728:     enum State {
kpeter@756:       IN_HEAP = 0,    ///< = 0.
kpeter@756:       PRE_HEAP = -1,  ///< = -1.
kpeter@756:       POST_HEAP = -2  ///< = -2.
deba@728:     };
deba@728: 
deba@728:   private:
deba@728: 
deba@728:     struct RadixItem {
deba@728:       int prev, next, box;
deba@728:       Item item;
deba@728:       int prio;
deba@728:       RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
deba@728:     };
deba@728: 
deba@728:     struct RadixBox {
deba@728:       int first;
deba@728:       int min, size;
deba@728:       RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
deba@728:     };
deba@728: 
kpeter@758:     std::vector<RadixItem> _data;
kpeter@758:     std::vector<RadixBox> _boxes;
deba@728: 
deba@730:     ItemIntMap &_iim;
deba@728: 
kpeter@756:   public:
deba@728: 
kpeter@756:     /// \brief Constructor.
deba@728:     ///
kpeter@756:     /// Constructor.
kpeter@756:     /// \param map A map that assigns \c int values to the items.
kpeter@756:     /// It is used internally to handle the cross references.
kpeter@756:     /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@756:     /// \param minimum The initial minimum value of the heap.
kpeter@756:     /// \param capacity The initial capacity of the heap.
kpeter@756:     RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0)
kpeter@756:       : _iim(map)
kpeter@756:     {
kpeter@758:       _boxes.push_back(RadixBox(minimum, 1));
kpeter@758:       _boxes.push_back(RadixBox(minimum + 1, 1));
kpeter@758:       while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
deba@728:         extend();
deba@728:       }
deba@728:     }
deba@728: 
kpeter@756:     /// \brief The number of items stored in the heap.
deba@728:     ///
kpeter@756:     /// This function returns the number of items stored in the heap.
kpeter@758:     int size() const { return _data.size(); }
kpeter@756: 
kpeter@756:     /// \brief Check if the heap is empty.
deba@728:     ///
kpeter@756:     /// This function returns \c true if the heap is empty.
kpeter@758:     bool empty() const { return _data.empty(); }
deba@728: 
kpeter@756:     /// \brief Make the heap empty.
deba@728:     ///
kpeter@756:     /// This functon makes the heap empty.
kpeter@756:     /// It does not change the cross reference map. If you want to reuse
kpeter@756:     /// a heap that is not surely empty, you should first clear it and
kpeter@756:     /// then you should set the cross reference map to \c PRE_HEAP
kpeter@756:     /// for each item.
kpeter@756:     /// \param minimum The minimum value of the heap.
kpeter@756:     /// \param capacity The capacity of the heap.
kpeter@756:     void clear(int minimum = 0, int capacity = 0) {
kpeter@758:       _data.clear(); _boxes.clear();
kpeter@758:       _boxes.push_back(RadixBox(minimum, 1));
kpeter@758:       _boxes.push_back(RadixBox(minimum + 1, 1));
kpeter@758:       while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
deba@728:         extend();
deba@728:       }
deba@728:     }
deba@728: 
deba@728:   private:
deba@728: 
deba@728:     bool upper(int box, Prio pr) {
kpeter@758:       return pr < _boxes[box].min;
deba@728:     }
deba@728: 
deba@728:     bool lower(int box, Prio pr) {
kpeter@758:       return pr >= _boxes[box].min + _boxes[box].size;
deba@728:     }
deba@728: 
kpeter@756:     // Remove item from the box list
deba@728:     void remove(int index) {
kpeter@758:       if (_data[index].prev >= 0) {
kpeter@758:         _data[_data[index].prev].next = _data[index].next;
deba@728:       } else {
kpeter@758:         _boxes[_data[index].box].first = _data[index].next;
deba@728:       }
kpeter@758:       if (_data[index].next >= 0) {
kpeter@758:         _data[_data[index].next].prev = _data[index].prev;
deba@728:       }
deba@728:     }
deba@728: 
kpeter@756:     // Insert item into the box list
deba@728:     void insert(int box, int index) {
kpeter@758:       if (_boxes[box].first == -1) {
kpeter@758:         _boxes[box].first = index;
kpeter@758:         _data[index].next = _data[index].prev = -1;
deba@728:       } else {
kpeter@758:         _data[index].next = _boxes[box].first;
kpeter@758:         _data[_boxes[box].first].prev = index;
kpeter@758:         _data[index].prev = -1;
kpeter@758:         _boxes[box].first = index;
deba@728:       }
kpeter@758:       _data[index].box = box;
deba@728:     }
deba@728: 
kpeter@756:     // Add a new box to the box list
deba@728:     void extend() {
kpeter@758:       int min = _boxes.back().min + _boxes.back().size;
kpeter@758:       int bs = 2 * _boxes.back().size;
kpeter@758:       _boxes.push_back(RadixBox(min, bs));
deba@728:     }
deba@728: 
kpeter@756:     // Move an item up into the proper box.
kpeter@758:     void bubbleUp(int index) {
kpeter@758:       if (!lower(_data[index].box, _data[index].prio)) return;
deba@728:       remove(index);
kpeter@758:       int box = findUp(_data[index].box, _data[index].prio);
deba@728:       insert(box, index);
deba@728:     }
deba@728: 
kpeter@756:     // Find up the proper box for the item with the given priority
deba@728:     int findUp(int start, int pr) {
deba@728:       while (lower(start, pr)) {
kpeter@758:         if (++start == int(_boxes.size())) {
deba@728:           extend();
deba@728:         }
deba@728:       }
deba@728:       return start;
deba@728:     }
deba@728: 
kpeter@756:     // Move an item down into the proper box
kpeter@758:     void bubbleDown(int index) {
kpeter@758:       if (!upper(_data[index].box, _data[index].prio)) return;
deba@728:       remove(index);
kpeter@758:       int box = findDown(_data[index].box, _data[index].prio);
deba@728:       insert(box, index);
deba@728:     }
deba@728: 
kpeter@756:     // Find down the proper box for the item with the given priority
deba@728:     int findDown(int start, int pr) {
deba@728:       while (upper(start, pr)) {
kpeter@758:         if (--start < 0) throw PriorityUnderflowError();
deba@728:       }
deba@728:       return start;
deba@728:     }
deba@728: 
kpeter@756:     // Find the first non-empty box
deba@728:     int findFirst() {
deba@728:       int first = 0;
kpeter@758:       while (_boxes[first].first == -1) ++first;
deba@728:       return first;
deba@728:     }
deba@728: 
kpeter@756:     // Gives back the minimum priority of the given box
deba@728:     int minValue(int box) {
kpeter@758:       int min = _data[_boxes[box].first].prio;
kpeter@758:       for (int k = _boxes[box].first; k != -1; k = _data[k].next) {
kpeter@758:         if (_data[k].prio < min) min = _data[k].prio;
deba@728:       }
deba@728:       return min;
deba@728:     }
deba@728: 
kpeter@756:     // Rearrange the items of the heap and make the first box non-empty
deba@728:     void moveDown() {
deba@728:       int box = findFirst();
deba@728:       if (box == 0) return;
deba@728:       int min = minValue(box);
deba@728:       for (int i = 0; i <= box; ++i) {
kpeter@758:         _boxes[i].min = min;
kpeter@758:         min += _boxes[i].size;
deba@728:       }
kpeter@758:       int curr = _boxes[box].first, next;
deba@728:       while (curr != -1) {
kpeter@758:         next = _data[curr].next;
kpeter@758:         bubbleDown(curr);
deba@728:         curr = next;
deba@728:       }
deba@728:     }
deba@728: 
kpeter@758:     void relocateLast(int index) {
kpeter@758:       if (index != int(_data.size()) - 1) {
kpeter@758:         _data[index] = _data.back();
kpeter@758:         if (_data[index].prev != -1) {
kpeter@758:           _data[_data[index].prev].next = index;
deba@728:         } else {
kpeter@758:           _boxes[_data[index].box].first = index;
deba@728:         }
kpeter@758:         if (_data[index].next != -1) {
kpeter@758:           _data[_data[index].next].prev = index;
deba@728:         }
kpeter@758:         _iim[_data[index].item] = index;
deba@728:       }
kpeter@758:       _data.pop_back();
deba@728:     }
deba@728: 
deba@728:   public:
deba@728: 
deba@728:     /// \brief Insert an item into the heap with the given priority.
deba@728:     ///
kpeter@756:     /// This function inserts the given item into the heap with the
kpeter@756:     /// given priority.
deba@728:     /// \param i The item to insert.
deba@728:     /// \param p The priority of the item.
kpeter@756:     /// \pre \e i must not be stored in the heap.
kpeter@756:     /// \warning This method may throw an \c UnderFlowPriorityException.
deba@728:     void push(const Item &i, const Prio &p) {
kpeter@758:       int n = _data.size();
deba@730:       _iim.set(i, n);
kpeter@758:       _data.push_back(RadixItem(i, p));
kpeter@758:       while (lower(_boxes.size() - 1, p)) {
deba@728:         extend();
deba@728:       }
kpeter@758:       int box = findDown(_boxes.size() - 1, p);
deba@728:       insert(box, n);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Return the item having minimum priority.
deba@728:     ///
kpeter@756:     /// This function returns the item having minimum priority.
kpeter@756:     /// \pre The heap must be non-empty.
deba@728:     Item top() const {
deba@728:       const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
kpeter@758:       return _data[_boxes[0].first].item;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief The minimum priority.
deba@728:     ///
kpeter@756:     /// This function returns the minimum priority.
kpeter@756:     /// \pre The heap must be non-empty.
deba@728:     Prio prio() const {
deba@728:       const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
kpeter@758:       return _data[_boxes[0].first].prio;
deba@728:      }
deba@728: 
kpeter@756:     /// \brief Remove the item having minimum priority.
deba@728:     ///
kpeter@756:     /// This function removes the item having minimum priority.
deba@728:     /// \pre The heap must be non-empty.
deba@728:     void pop() {
deba@728:       moveDown();
kpeter@758:       int index = _boxes[0].first;
kpeter@758:       _iim[_data[index].item] = POST_HEAP;
deba@728:       remove(index);
kpeter@758:       relocateLast(index);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Remove the given item from the heap.
deba@728:     ///
kpeter@756:     /// This function removes the given item from the heap if it is
kpeter@756:     /// already stored.
kpeter@756:     /// \param i The item to delete.
kpeter@756:     /// \pre \e i must be in the heap.
deba@728:     void erase(const Item &i) {
deba@730:       int index = _iim[i];
deba@730:       _iim[i] = POST_HEAP;
deba@728:       remove(index);
kpeter@758:       relocateLast(index);
deba@728:    }
deba@728: 
kpeter@756:     /// \brief The priority of the given item.
deba@728:     ///
kpeter@756:     /// This function returns the priority of the given item.
deba@728:     /// \param i The item.
kpeter@756:     /// \pre \e i must be in the heap.
deba@728:     Prio operator[](const Item &i) const {
deba@730:       int idx = _iim[i];
kpeter@758:       return _data[idx].prio;
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Set the priority of an item or insert it, if it is
kpeter@756:     /// not stored in the heap.
deba@728:     ///
kpeter@756:     /// This method sets the priority of the given item if it is
kpeter@756:     /// already stored in the heap. Otherwise it inserts the given
kpeter@756:     /// item into the heap with the given priority.
deba@728:     /// \param i The item.
deba@728:     /// \param p The priority.
kpeter@756:     /// \pre \e i must be in the heap.
kpeter@756:     /// \warning This method may throw an \c UnderFlowPriorityException.
deba@728:     void set(const Item &i, const Prio &p) {
deba@730:       int idx = _iim[i];
deba@728:       if( idx < 0 ) {
deba@728:         push(i, p);
deba@728:       }
kpeter@758:       else if( p >= _data[idx].prio ) {
kpeter@758:         _data[idx].prio = p;
kpeter@758:         bubbleUp(idx);
deba@728:       } else {
kpeter@758:         _data[idx].prio = p;
kpeter@758:         bubbleDown(idx);
deba@728:       }
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Decrease the priority of an item to the given value.
deba@728:     ///
kpeter@756:     /// This function decreases the priority of an item to the given value.
deba@728:     /// \param i The item.
deba@728:     /// \param p The priority.
kpeter@756:     /// \pre \e i must be stored in the heap with priority at least \e p.
kpeter@756:     /// \warning This method may throw an \c UnderFlowPriorityException.
deba@728:     void decrease(const Item &i, const Prio &p) {
deba@730:       int idx = _iim[i];
kpeter@758:       _data[idx].prio = p;
kpeter@758:       bubbleDown(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Increase the priority of an item to the given value.
deba@728:     ///
kpeter@756:     /// This function increases the priority of an item to the given value.
deba@728:     /// \param i The item.
deba@728:     /// \param p The priority.
kpeter@756:     /// \pre \e i must be stored in the heap with priority at most \e p.
deba@728:     void increase(const Item &i, const Prio &p) {
deba@730:       int idx = _iim[i];
kpeter@758:       _data[idx].prio = p;
kpeter@758:       bubbleUp(idx);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Return the state of an item.
deba@728:     ///
kpeter@756:     /// This method returns \c PRE_HEAP if the given item has never
kpeter@756:     /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@756:     /// and \c POST_HEAP otherwise.
kpeter@756:     /// In the latter case it is possible that the item will get back
kpeter@756:     /// to the heap again.
deba@728:     /// \param i The item.
deba@728:     State state(const Item &i) const {
deba@730:       int s = _iim[i];
deba@728:       if( s >= 0 ) s = 0;
deba@728:       return State(s);
deba@728:     }
deba@728: 
kpeter@756:     /// \brief Set the state of an item in the heap.
deba@728:     ///
kpeter@756:     /// This function sets the state of the given item in the heap.
kpeter@756:     /// It can be used to manually clear the heap when it is important
kpeter@756:     /// to achive better time complexity.
deba@728:     /// \param i The item.
deba@728:     /// \param st The state. It should not be \c IN_HEAP.
deba@728:     void state(const Item& i, State st) {
deba@728:       switch (st) {
deba@728:       case POST_HEAP:
deba@728:       case PRE_HEAP:
deba@728:         if (state(i) == IN_HEAP) {
deba@728:           erase(i);
deba@728:         }
deba@730:         _iim[i] = st;
deba@728:         break;
deba@728:       case IN_HEAP:
deba@728:         break;
deba@728:       }
deba@728:     }
deba@728: 
deba@728:   }; // class RadixHeap
deba@728: 
deba@728: } // namespace lemon
deba@728: 
deba@728: #endif // LEMON_RADIX_HEAP_H