/* -*- 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);

    }

    int findMin(const int child, const int length) {

      int min=child, i=1;

      while( i<K && child+i<length ) {

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

          min=child+i;

        ++i;

      }

      return min;

    }

    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<length ) {

          child = findMin(child, length);

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

            goto ok;

          move(_data[child], hole);

          hole = child;

          child = firstChild(hole);

        }

      }

    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