/* -*- 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 heaps

 ///\file

 ///\brief Radix heap implementation.

 #include <vector>

 #include <lemon/error.h>

 namespace lemon {

   /// \ingroup heaps

   ///

   /// \brief Radix heap data structure.

   ///

   /// This class implements the \e radix \e heap data structure.

   /// It practically conforms to the \ref concepts::Heap "heap concept",

   /// but it has some limitations due its special implementation.

   /// The type of the priorities must be \c int and the priority of an

   /// item cannot be decreased under the priority of the last removed item.

   ///

   /// \tparam IM A read-writable item map with \c int values, used

   /// internally to handle the cross references.

   template <typename IM>

   class RadixHeap {

   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;

     /// \brief Exception thrown by RadixHeap.

     ///

     /// This exception is thrown when an item is inserted into a

     /// RadixHeap with a priority smaller than the last erased one.

     /// \see RadixHeap

     class PriorityUnderflowError : public Exception {

     public:

       virtual const char* what() const throw() {

         return "lemon::RadixHeap::PriorityUnderflowError";

       }

     };

     /// \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.

     };

   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<RadixItem> _data;

     std::vector<RadixBox> _boxes;

     ItemIntMap &_iim;

   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.

     /// \param minimum The initial minimum value of the heap.

     /// \param capacity The initial capacity of the heap.

     RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0)

       : _iim(map)

     {

       _boxes.push_back(RadixBox(minimum, 1));

       _boxes.push_back(RadixBox(minimum + 1, 1));

       while (lower(_boxes.size() - 1, capacity + minimum - 1)) {

         extend();

       }

     }

     /// \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.

     /// \param minimum The minimum value of the heap.

     /// \param capacity The capacity of the heap.

     void clear(int minimum = 0, int capacity = 0) {

       _data.clear(); _boxes.clear();

       _boxes.push_back(RadixBox(minimum, 1));

       _boxes.push_back(RadixBox(minimum + 1, 1));

       while (lower(_boxes.size() - 1, capacity + minimum - 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;

     }

     // 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;

       }

     }

     // 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;

     }

     // 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));

     }

     // Move an item up into the proper box.

     void bubbleUp(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);

     }

     // Find up the proper box for the item with the given priority

     int findUp(int start, int pr) {

       while (lower(start, pr)) {

         if (++start == int(_boxes.size())) {

           extend();

         }

       }

       return start;

     }

     // Move an item down into the proper box

     void bubbleDown(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);

     }

     // Find down the proper box for the item with the given priority

     int findDown(int start, int pr) {

       while (upper(start, pr)) {

         if (--start < 0) throw PriorityUnderflowError();

       }

       return start;

     }

     // Find the first non-empty box

     int findFirst() {

       int first = 0;

       while (_boxes[first].first == -1) ++first;

       return first;

     }

     // Gives back the minimum priority of the given 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;

     }

     // Rearrange the items of the heap and make the first box non-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;

         bubbleDown(curr);

         curr = next;

       }

     }

     void relocateLast(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.

     ///

     /// 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.

     /// \warning This method may throw an \c UnderFlowPriorityException.

     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 Return the item having minimum priority.

     ///

     /// This function returns the item having minimum priority.

     /// \pre The heap must be non-empty.

     Item top() const {

       const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();

       return _data[_boxes[0].first].item;

     }

     /// \brief The minimum priority.

     ///

     /// This function returns the minimum priority.

     /// \pre The heap must be non-empty.

     Prio prio() const {

       const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();

       return _data[_boxes[0].first].prio;

      }

     /// \brief Remove the item having minimum priority.

     ///

     /// This function removes the item having 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);

       relocateLast(index);

     }

     /// \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 index = _iim[i];

       _iim[i] = POST_HEAP;

       remove(index);

       relocateLast(index);

    }

     /// \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].prio;

     }

     /// \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.

     /// \pre \e i must be in the heap.

     /// \warning This method may throw an \c UnderFlowPriorityException.

     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;

         bubbleUp(idx);

       } else {

         _data[idx].prio = p;

         bubbleDown(idx);

       }

     }

     /// \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.

     /// \warning This method may throw an \c UnderFlowPriorityException.

     void decrease(const Item &i, const Prio &p) {

       int idx = _iim[i];

       _data[idx].prio = p;

       bubbleDown(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];

       _data[idx].prio = p;

       bubbleUp(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 s = _iim[i];

       if( s >= 0 ) s = 0;

       return State(s);

     }

     /// \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;

       }

     }

   }; // class RadixHeap

 } // namespace lemon

 #endif // LEMON_RADIX_HEAP_H