/* -*- 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_KARY_HEAP_H

#define LEMON_KARY_HEAP_H

///\ingroup auxdat

///\file

///\brief Kary Heap implementation.

#include <iostream>

#include <vector>

#include <utility>

#include <functional>

namespace lemon {

  ///\ingroup auxdat

  ///

  ///\brief A Kary Heap implementation.

  ///

  ///This class implements the \e Kary \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 _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

  ///\author Dorian Batha

  template <typename _Prio, typename _ItemIntMap,

            typename _Compare = std::less<_Prio> >

  class KaryHeap {

  public:

    ///\e

    typedef _ItemIntMap ItemIntMap;

    ///\e

    typedef _Prio Prio;

    ///\e

    typedef typename ItemIntMap::Key Item;

    ///\e

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

    ///\e

    typedef _Compare Compare;

    ///\e

    /// \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:

    std::vector<Pair> data;

    Compare comp;

    ItemIntMap &iim;

    int K;

  public:

    /// \brief The constructor.

    ///

    /// The constructor.

    /// \param _iim 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.

    explicit KaryHeap(ItemIntMap &_iim, const int &_K=32) : iim(_iim), K(_K) {}

    /// \brief The constructor.

    ///

    /// The constructor.

    /// \param _iim 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 _comp The comparator function object.

    KaryHeap(ItemIntMap &_iim, const Compare &_comp, const int &_K=32)

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

    /// 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 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() { data.clear(); }

  private:

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

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

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

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

    }

    int find_min(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 bubble_up(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 bubble_down(int hole, Pair p, int length) {

      if( length>1 ) {

        int child = first_child(hole);

        while( child<length ) {

          child = find_min(child, length);

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

            goto ok;

          move(data[child], hole);

          hole = child;

          child = first_child(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.

    ///

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

    /// \param p The pair to insert.

    void push(const Pair &p) {

      int n = data.size();

      data.resize(n+1);

      bubble_up(n, p);

    }

    /// \brief Insert an item into the heap with the given heap.

    ///

    /// 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) { push(Pair(i,p)); }

    /// \brief 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; }

    /// \brief 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; }

    /// \brief 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() {

      int n = data.size()-1;

      iim.set(data[0].first, POST_HEAP);

      if (n>0) bubble_down(0, data[n], n);

      data.pop_back();

    }

    /// \brief Deletes \c i from the heap.

    ///

    /// This method deletes item \c i from the heap.

    /// \param i The item to erase.

    /// \pre The item should 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]) )

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

        else

          bubble_up(h, data[n]);

      }

      data.pop_back();

    }

    /// \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].second;

    }

    /// \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.

    /// \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) )

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

      else

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

    }

    /// \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 relative to \c Compare.

    /// \param i The item.

    /// \param p The priority.

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

      int idx = iim[i];

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

    }

    /// \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 relative to \c Compare.

    /// \param i The item.

    /// \param p The priority.

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

      int idx = iim[i];

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

    }

    /// \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;

      }

    }

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

    ///

    /// The \c i item is replaced with \c j item. The \c i item should

    /// be in the heap, while the \c j should be out of the heap. The

    /// \c i item will out of the heap and \c j will be in the heap

    /// with the same prioriority as prevoiusly the \c i item.

    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