/* -*- 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