/* -*- 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 UnderFlowPriorityError : public Exception {

    public:

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

        return "lemon::RadixHeap::UnderFlowPriorityError";

      }

    };

    /// \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 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);

    }

    // 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 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);

    }

    // 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 UnderFlowPriorityError();

      }

      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;

        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.

    ///

    /// 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);

      relocate_last(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);

      relocate_last(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;

        bubble_up(idx);

      } else {

        data[idx].prio = p;

        bubble_down(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;

      bubble_down(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;

      bubble_up(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