/* -*- C++ -*-

  * src/lemon/bin_heap.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Combinatorial Optimization Research Group, 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_BIN_HEAP_H

 #define LEMON_BIN_HEAP_H

 ///\ingroup auxdat

 ///\file

 ///\brief Binary Heap implementation.

 #include <vector>

 #include <utility>

 #include <functional>

 namespace lemon {

   /// \addtogroup auxdat

   /// @{

   /// A Binary Heap implementation.

   ///This class implements the \e binary \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. \c Compare specifies the ordering of the priorities. In a heap

   ///one can change the priority of an item, add or erase an item, etc.

   ///

   ///\param Item Type of the items to be stored.  

   ///\param Prio Type of the priority of the items.

   ///\param ItemIntMap A read and writable Item int map, used internally

   ///to handle the cross references.

   ///\param Compare A class for the ordering of the priorities. The

   ///default is \c std::less<Prio>.

   ///

   ///\sa FibHeap

   ///\sa Dijkstra

   template <typename Item, typename Prio, typename ItemIntMap,

 	    typename Compare = std::less<Prio> >

   class BinHeap {

   public:

     typedef Item                             ItemType;

     // FIXME: stl-ben nem ezt hivjak value_type -nak, hanem a kovetkezot...

     typedef Prio                             PrioType;

     typedef std::pair<ItemType,PrioType>     PairType;

     typedef ItemIntMap                       ItemIntMapType;

     typedef Compare                          PrioCompare;

     /**

      * Each Item element have a state associated to it. It may be "in heap",

      * "pre heap" or "post heap". The later two are indifferent from the

      * heap's point of view, but may be useful to the user.

      *

      * The ItemIntMap _should_ be initialized in such way, that it maps

      * PRE_HEAP (-1) to any element to be put in the heap...

      */

     ///\todo it is used nowhere

     ///

     enum state_enum {

       IN_HEAP = 0,

       PRE_HEAP = -1,

       POST_HEAP = -2

     };

   private:

     std::vector<PairType> data;

     Compare comp;

     // FIXME: jo ez igy???

     ItemIntMap &iim;

   public:

     ///The constructor

     /**

        \c _iim should be given to the constructor, since it is used

        internally to handle the cross references.

     */

     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}

     ///The constructor

     /**

        \c _iim should be given to the constructor, since it is used

        internally to handle the cross references. \c _comp is an

        object for ordering of the priorities.

     */

     BinHeap(ItemIntMap &_iim, const Compare &_comp) 

       : iim(_iim), comp(_comp) {}

     ///The number of items stored in the heap.

     /**

        Returns the number of items stored in the heap.

     */

     int size() const { return data.size(); }

     ///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(); }

   private:

     static int parent(int i) { return (i-1)/2; }

     static int second_child(int i) { return 2*i+2; }

     bool less(const PairType &p1, const PairType &p2) const {

       return comp(p1.second, p2.second);

     }

     int bubble_up(int hole, PairType p);

     int bubble_down(int hole, PairType p, int length);

     void move(const PairType &p, int i) {

       data[i] = p;

       iim.set(p.first, i);

     }

     void rmidx(int h) {

       int n = data.size()-1;

       if( h>=0 && h<=n ) {

 	iim.set(data[h].first, POST_HEAP);

 	if ( h<n ) {

 	  bubble_down(h, data[n], n);

 	}

 	data.pop_back();

       }

     }

   public:

     ///Adds \c p.first to the heap with priority \c p.second.

     /**

        Adds \c p.first to the heap with priority \c p.second.

        \c p.first must not be stored in the heap. 

     */

     void push(const PairType &p) {

       int n = data.size();

       data.resize(n+1);

       bubble_up(n, p);

     }

     ///Adds \c i to the heap with priority \c p. 

     /**

        Adds \c i to the heap with priority \c p. 

        \pre \c i must not be stored in the heap. 

     */

     void push(const Item &i, const Prio &p) { push(PairType(i,p)); }

     ///Returns the item with minimum priority relative to \c Compare.

     /**

        This method returns the item with minimum priority relative to \c

        Compare.  

        \pre The heap must be nonempty.  

     */

     Item top() const {

       return data[0].first;

     }

     ///Returns the minimum priority relative to \c Compare.

     /**

        It returns the minimum priority relative to \c Compare.

        \pre The heap must be nonempty.

     */

     Prio prio() const {

       return data[0].second;

     }

     ///Deletes the item with minimum priority relative to \c Compare.

     /**

     This method deletes the item with minimum priority relative to \c

     Compare from the heap.  

     \pre The heap must be non-empty.  

     */

     void pop() {

       rmidx(0);

     }

     ///Deletes \c i from the heap.

     /**

        This method deletes item \c i from the heap, if \c i was

        already stored in the heap. 

     */

     void erase(const Item &i) {

       rmidx(iim[i]);

     }

     ///Returns the priority of \c i.

     /**

        This function returns the priority of item \c i.  

        \pre \c i must be in the heap.

     */

     Prio operator[](const Item &i) const {

       int idx = iim[i];

       return data[idx].second;

     }

     ///\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.

     */

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

       int idx = iim[i];

       if( idx < 0 ) {

 	push(i,p);

       }

       else if( comp(p, data[idx].second) ) {

 	bubble_up(idx, PairType(i,p));

       }

       else {

 	bubble_down(idx, PairType(i,p), data.size());

       }

     }

     ///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 relative to \c Compare.

     */

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

       int idx = iim[i];

       bubble_up(idx, PairType(i,p));

     }

     ///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 relative to \c Compare.

     */

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

       int idx = iim[i];

       bubble_down(idx, PairType(i,p), data.size());

     }

     ///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.

     */

     state_enum state(const Item &i) const {

       int s = iim[i];

       if( s>=0 )

 	s=0;

       return state_enum(s);

     }

   }; // class BinHeap

   template <typename K, typename V, typename M, typename C>

   int BinHeap<K,V,M,C>::bubble_up(int hole, PairType p) {

     int par = parent(hole);

     while( hole>0 && less(p,data[par]) ) {

       move(data[par],hole);

       hole = par;

       par = parent(hole);

     }

     move(p, hole);

     return hole;

   }

   template <typename K, typename V, typename M, typename C>

   int BinHeap<K,V,M,C>::bubble_down(int hole, PairType p, int length) {

     int child = second_child(hole);

     while(child < length) {

       if( less(data[child-1], data[child]) ) {

 	--child;

       }

       if( !less(data[child], p) )

 	goto ok;

       move(data[child], hole);

       hole = child;

       child = second_child(hole);

     }

     child--;

     if( child<length && less(data[child], p) ) {

       move(data[child], hole);

       hole=child;

     }

   ok:

     move(p, hole);

     return hole;

   }

   ///@}

 } // namespace lemon

 #endif // LEMON_BIN_HEAP_H