/* -*- 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_KARY_HEAP_H

 #define LEMON_KARY_HEAP_H

 ///\ingroup heaps

 ///\file

 ///\brief Fourary heap implementation.

 #include <vector>

 #include <utility>

 #include <functional>

 namespace lemon {

   /// \ingroup heaps

   ///

   ///\brief K-ary heap data structure.

   ///

   /// This class implements the \e K-ary \e heap data structure.

   /// It fully conforms to the \ref concepts::Heap "heap concept".

   ///

   /// The \ref KaryHeap "K-ary heap" is a generalization of the

   /// \ref BinHeap "binary heap" structure, its nodes have at most

   /// \c K children, instead of two.

   /// \ref BinHeap and \ref FouraryHeap are specialized implementations

   /// of this structure for <tt>K=2</tt> and <tt>K=4</tt>, respectively.

   ///

   /// \tparam PR Type of the priorities of the items.

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

   /// internally to handle the cross references.

   /// \tparam K The degree of the heap, each node have at most \e K

   /// children. The default is 16. Powers of two are suggested to use

   /// so that the multiplications and divisions needed to traverse the

   /// nodes of the heap could be performed faster.

   /// \tparam CMP A functor class for comparing the priorities.

   /// The default is \c std::less<PR>.

   ///

   ///\sa BinHeap

   ///\sa FouraryHeap

 #ifdef DOXYGEN

   template <typename PR, typename IM, int K, typename CMP>

 #else

   template <typename PR, typename IM, int K = 16,

             typename CMP = std::less<PR> >

 #endif

   class KaryHeap {

   public:

     /// Type of the item-int map.

     typedef IM ItemIntMap;

     /// Type of the priorities.

     typedef PR Prio;

     /// Type of the items stored in the heap.

     typedef typename ItemIntMap::Key Item;

     /// Type of the item-priority pairs.

     typedef std::pair<Item,Prio> Pair;

     /// Functor type for comparing the priorities.

     typedef CMP Compare;

     /// \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:

     std::vector<Pair> _data;

     Compare _comp;

     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.

     explicit KaryHeap(ItemIntMap &map) : _iim(map) {}

     /// \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 comp The function object used for comparing the priorities.

     KaryHeap(ItemIntMap &map, const Compare &comp)

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

     /// \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.

     void clear() { _data.clear(); }

   private:

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

     int firstChild(int i) { return K*i+1; }

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

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

     }

     void bubbleUp(int hole, Pair p) {

       int par = parent(hole);

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

         move(_data[par],hole);

         hole = par;

         par = parent(hole);

       }

       move(p, hole);

     }

     void bubbleDown(int hole, Pair p, int length) {

       if( length>1 ) {

         int child = firstChild(hole);

         while( child+K<=length ) {

           int min=child;

           for (int i=1; i<K; ++i) {

             if( less(_data[child+i], _data[min]) )

               min=child+i;

           }

           if( !less(_data[min], p) )

             goto ok;

           move(_data[min], hole);

           hole = min;

           child = firstChild(hole);

         }

         if ( child<length ) {

           int min = child;

           while (++child < length) {

             if( less(_data[child], _data[min]) )

               min=child;

           }

           if( less(_data[min], p) ) {

             move(_data[min], hole);

             hole = min;

           }

         }

       }

     ok:

       move(p, hole);

     }

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

       _data[i] = p;

       _iim.set(p.first, i);

     }

   public:

     /// \brief Insert a pair of item and priority into the heap.

     ///

     /// This function inserts \c p.first to the heap with priority

     /// \c p.second.

     /// \param p The pair to insert.

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

     void push(const Pair &p) {

       int n = _data.size();

       _data.resize(n+1);

       bubbleUp(n, p);

     }

     /// \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.

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

     /// \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 { return _data[0].first; }

     /// \brief The minimum priority.

     ///

     /// This function returns the minimum priority.

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

     Prio prio() const { return _data[0].second; }

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

     ///

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

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

     void pop() {

       int n = _data.size()-1;

       _iim.set(_data[0].first, POST_HEAP);

       if (n>0) bubbleDown(0, _data[n], n);

       _data.pop_back();

     }

     /// \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 h = _iim[i];

       int n = _data.size()-1;

       _iim.set(_data[h].first, POST_HEAP);

       if( h<n ) {

         if( less(_data[parent(h)], _data[n]) )

           bubbleDown(h, _data[n], n);

         else

           bubbleUp(h, _data[n]);

       }

       _data.pop_back();

     }

     /// \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].second;

     }

     /// \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.

     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) )

         bubbleUp(idx, Pair(i,p));

       else

         bubbleDown(idx, Pair(i,p), _data.size());

     }

     /// \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.

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

       int idx = _iim[i];

       bubbleUp(idx, Pair(i,p));

     }

     /// \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];

       bubbleDown(idx, Pair(i,p), _data.size());

     }

     /// \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;

       }

     }

     /// \brief Replace an item in the heap.

     ///

     /// This function replaces item \c i with item \c j.

     /// Item \c i must be in the heap, while \c j must be out of the heap.

     /// After calling this method, item \c i will be out of the

     /// heap and \c j will be in the heap with the same prioriority

     /// as item \c i had before.

     void replace(const Item& i, const Item& j) {

       int idx=_iim[i];

       _iim.set(i, _iim[j]);

       _iim.set(j, idx);

       _data[idx].first=j;

     }

   }; // class KaryHeap

 } // namespace lemon

 #endif // LEMON_KARY_HEAP_H