/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2008

 * 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 <vector>

#include <lemon/error.h>

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

  /// \author Balazs Dezso

  template <typename _ItemIntMap>

  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

    /// \author Balazs Dezso

    class UnderFlowPriorityError : public RuntimeError {

    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<RadixItem> data;

    std::vector<RadixBox> 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<RadixHeap<ItemIntMap>&>(*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<RadixHeap<ItemIntMap>&>(*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