/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2007

 * 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_BIN_HEAP_H

#define LEMON_BIN_HEAP_H

///\ingroup auxdat

///\file

///\brief Binary Heap implementation.

#include <vector>

#include <utility>

#include <functional>

namespace lemon {

  /// \ingroup 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 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 Prio, typename ItemIntMap,

	    typename Compare = std::less<Prio> >

  class BinHeap {

  public:

    typedef typename ItemIntMap::Key         ItemType;

    typedef Prio                             PrioType;

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

    typedef ItemIntMap                       ItemIntMapType;

    typedef Compare                          PrioCompare;

    /// \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_enum {

      IN_HEAP = 0,

      PRE_HEAP = -1,

      POST_HEAP = -2

    };

  private:

    std::vector<PairType> data;

    Compare comp;

    ItemIntMap &iim;

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

    /// \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.

    BinHeap(ItemIntMap &_iim, const Compare &_comp) 

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

    /// 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:

    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:

    /// \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 PairType &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 ItemType &i, const Prio &p) { push(PairType(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.  

    ItemType 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() {

      rmidx(0);

    }

    /// \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 ItemType &i) {

      rmidx(iim[i]);

    }

    /// \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 ItemType &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 ItemType &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());

      }

    }

    /// \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 ItemType &i, const Prio &p) {

      int idx = iim[i];

      bubble_up(idx, PairType(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 ItemType &i, const Prio &p) {

      int idx = iim[i];

      bubble_down(idx, PairType(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_enum state(const ItemType &i) const {

      int s = iim[i];

      if( s>=0 )

	s=0;

      return state_enum(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 ItemType& i, state_enum 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 BinHeap

  template <typename V, typename M, typename C>

  int BinHeap<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 V, typename M, typename C>

  int BinHeap<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