/* -*- 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