/* -*- 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_PAIRING_HEAP_H

#define LEMON_PAIRING_HEAP_H

///\file

///\ingroup heaps

///\brief Pairing heap implementation.

#include <vector>

#include <utility>

#include <functional>

#include <lemon/math.h>

namespace lemon {

  /// \ingroup heaps

  ///

  ///\brief Pairing Heap.

  ///

  /// This class implements the \e pairing \e heap data structure.

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

  ///

  /// The methods \ref increase() and \ref erase() are not efficient

  /// in a pairing heap. In case of many calls of these operations,

  /// it is better to use other heap structure, e.g. \ref BinHeap

  /// "binary heap".

  ///

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

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

#ifdef DOXYGEN

  template <typename PR, typename IM, typename CMP>

#else

  template <typename PR, typename IM, typename CMP = std::less<PR> >

#endif

  class PairingHeap {

  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;

    /// 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:

    class store;

    std::vector<store> _data;

    int _min;

    ItemIntMap &_iim;

    Compare _comp;

    int _num_items;

  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 PairingHeap(ItemIntMap &map)

      : _min(0), _iim(map), _num_items(0) {}

    /// \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.

    PairingHeap(ItemIntMap &map, const Compare &comp)

      : _min(0), _iim(map), _comp(comp), _num_items(0) {}

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

    ///

    /// This function returns the number of items stored in the heap.

    int size() const { return _num_items; }

    /// \brief Check if the heap is empty.

    ///

    /// This function returns \c true if the heap is empty.

    bool empty() const { return _num_items==0; }

    /// \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();

      _min = 0;

      _num_items = 0;

    }

    /// \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 item The item.

    /// \param value The priority.

    void set (const Item& item, const Prio& value) {

      int i=_iim[item];

      if ( i>=0 && _data[i].in ) {

        if ( _comp(value, _data[i].prio) ) decrease(item, value);

        if ( _comp(_data[i].prio, value) ) increase(item, value);

      } else push(item, value);

    }

    /// \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 item The item to insert.

    /// \param value The priority of the item.

    /// \pre \e item must not be stored in the heap.

    void push (const Item& item, const Prio& value) {

      int i=_iim[item];

      if( i<0 ) {

        int s=_data.size();

        _iim.set(item, s);

        store st;

        st.name=item;

        _data.push_back(st);

        i=s;

      } else {

        _data[i].parent=_data[i].child=-1;

        _data[i].left_child=false;

        _data[i].degree=0;

        _data[i].in=true;

      }

      _data[i].prio=value;

      if ( _num_items!=0 ) {

        if ( _comp( value, _data[_min].prio) ) {

          fuse(i,_min);

          _min=i;

        }

        else fuse(_min,i);

      }

      else _min=i;

      ++_num_items;

    }

    /// \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[_min].name; }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

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

    const Prio& prio() const { return _data[_min].prio; }

    /// \brief The priority of the given item.

    ///

    /// This function returns the priority of the given item.

    /// \param item The item.

    /// \pre \e item must be in the heap.

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

      return _data[_iim[item]].prio;

    }

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

    ///

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

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

    void pop() {

      std::vector<int> trees;

      int i=0, child_right = 0;

      _data[_min].in=false;

      if( -1!=_data[_min].child ) {

        i=_data[_min].child;

        trees.push_back(i);

        _data[i].parent = -1;

        _data[_min].child = -1;

        int ch=-1;

        while( _data[i].child!=-1 ) {

          ch=_data[i].child;

          if( _data[ch].left_child && i==_data[ch].parent ) {

            break;

          } else {

            if( _data[ch].left_child ) {

              child_right=_data[ch].parent;

              _data[ch].parent = i;

              --_data[i].degree;

            }

            else {

              child_right=ch;

              _data[i].child=-1;

              _data[i].degree=0;

            }

            _data[child_right].parent = -1;

            trees.push_back(child_right);

            i = child_right;

          }

        }

        int num_child = trees.size();

        int other;

        for( i=0; i<num_child-1; i+=2 ) {

          if ( !_comp(_data[trees[i]].prio, _data[trees[i+1]].prio) ) {

            other=trees[i];

            trees[i]=trees[i+1];

            trees[i+1]=other;

          }

          fuse( trees[i], trees[i+1] );

        }

        i = (0==(num_child % 2)) ? num_child-2 : num_child-1;

        while(i>=2) {

          if ( _comp(_data[trees[i]].prio, _data[trees[i-2]].prio) ) {

            other=trees[i];

            trees[i]=trees[i-2];

            trees[i-2]=other;

          }

          fuse( trees[i-2], trees[i] );

          i-=2;

        }

        _min = trees[0];

      }

      else {

        _min = _data[_min].child;

      }

      if (_min >= 0) _data[_min].left_child = false;

      --_num_items;

    }

    /// \brief Remove the given item from the heap.

    ///

    /// This function removes the given item from the heap if it is

    /// already stored.

    /// \param item The item to delete.

    /// \pre \e item must be in the heap.

    void erase (const Item& item) {

      int i=_iim[item];

      if ( i>=0 && _data[i].in ) {

        decrease( item, _data[_min].prio-1 );

        pop();

      }

    }

    /// \brief Decrease the priority of an item to the given value.

    ///

    /// This function decreases the priority of an item to the given value.

    /// \param item The item.

    /// \param value The priority.

    /// \pre \e item must be stored in the heap with priority at least \e value.

    void decrease (Item item, const Prio& value) {

      int i=_iim[item];

      _data[i].prio=value;

      int p=_data[i].parent;

      if( _data[i].left_child && i!=_data[p].child ) {

        p=_data[p].parent;

      }

      if ( p!=-1 && _comp(value,_data[p].prio) ) {

        cut(i,p);

        if ( _comp(_data[_min].prio,value) ) {

          fuse(_min,i);

        } else {

          fuse(i,_min);

          _min=i;

        }

      }

    }

    /// \brief Increase the priority of an item to the given value.

    ///

    /// This function increases the priority of an item to the given value.

    /// \param item The item.

    /// \param value The priority.

    /// \pre \e item must be stored in the heap with priority at most \e value.

    void increase (Item item, const Prio& value) {

      erase(item);

      push(item,value);

    }

    /// \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 item The item.

    State state(const Item &item) const {

      int i=_iim[item];

      if( i>=0 ) {

        if( _data[i].in ) i=0;

        else i=-2;

      }

      return State(i);

    }

    /// \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;

      }

    }

  private:

    void cut(int a, int b) {

      int child_a;

      switch (_data[a].degree) {

        case 2:

          child_a = _data[_data[a].child].parent;

          if( _data[a].left_child ) {

            _data[child_a].left_child=true;

            _data[b].child=child_a;

            _data[child_a].parent=_data[a].parent;

          }

          else {

            _data[child_a].left_child=false;

            _data[child_a].parent=b;

            if( a!=_data[b].child )

              _data[_data[b].child].parent=child_a;

            else

              _data[b].child=child_a;

          }

          --_data[a].degree;

          _data[_data[a].child].parent=a;

          break;

        case 1:

          child_a = _data[a].child;

          if( !_data[child_a].left_child ) {

            --_data[a].degree;

            if( _data[a].left_child ) {

              _data[child_a].left_child=true;

              _data[child_a].parent=_data[a].parent;

              _data[b].child=child_a;

            }

            else {

              _data[child_a].left_child=false;

              _data[child_a].parent=b;

              if( a!=_data[b].child )

                _data[_data[b].child].parent=child_a;

              else

                _data[b].child=child_a;

            }

            _data[a].child=-1;

          }

          else {

            --_data[b].degree;

            if( _data[a].left_child ) {

              _data[b].child =

                (1==_data[b].degree) ? _data[a].parent : -1;

            } else {

              if (1==_data[b].degree)

                _data[_data[b].child].parent=b;

              else

                _data[b].child=-1;

            }

          }

          break;

        case 0:

          --_data[b].degree;

          if( _data[a].left_child ) {

            _data[b].child =

              (0!=_data[b].degree) ? _data[a].parent : -1;

          } else {

            if( 0!=_data[b].degree )

              _data[_data[b].child].parent=b;

            else

              _data[b].child=-1;

          }

          break;

      }

      _data[a].parent=-1;

      _data[a].left_child=false;

    }

    void fuse(int a, int b) {

      int child_a = _data[a].child;

      int child_b = _data[b].child;

      _data[a].child=b;

      _data[b].parent=a;

      _data[b].left_child=true;

      if( -1!=child_a ) {

        _data[b].child=child_a;

        _data[child_a].parent=b;

        _data[child_a].left_child=false;

        ++_data[b].degree;

        if( -1!=child_b ) {

           _data[b].child=child_b;

           _data[child_b].parent=child_a;

        }

      }

      else { ++_data[a].degree; }

    }

    class store {

      friend class PairingHeap;

      Item name;

      int parent;

      int child;

      bool left_child;

      int degree;

      bool in;

      Prio prio;

      store() : parent(-1), child(-1), left_child(false), degree(0), in(true) {}

    };

  };

} //namespace lemon

#endif //LEMON_PAIRING_HEAP_H