/* -*- 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_PAIRING_HEAP_H

 #define LEMON_PAIRING_HEAP_H

 ///\file

 ///\ingroup auxdat

 ///\brief Pairing Heap implementation.

 #include <vector>

 #include <functional>

 #include <lemon/math.h>

 namespace lemon {

   /// \ingroup auxdat

   ///

   ///\brief Pairing Heap.

   ///

   ///This class implements the \e Pairing \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.

   ///

   ///The methods \ref increase and \ref erase are not efficient in a Pairing

   ///heap. In case of many calls to these operations, it is better to use a

   ///\ref BinHeap "binary heap".

   ///

   ///\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 BinHeap

   ///\sa Dijkstra

   ///\author Dorian Batha

 #ifdef DOXYGEN

   template <typename _Prio,

             typename _ItemIntMap,

             typename _Compare>

 #else

   template <typename _Prio,

             typename _ItemIntMap,

             typename _Compare = std::less<_Prio> >

 #endif

   class PairingHeap {

   public:

     typedef _ItemIntMap ItemIntMap;

     typedef _Prio Prio;

     typedef typename ItemIntMap::Key Item;

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

     typedef _Compare Compare;

   private:

     class store;

     std::vector<store> container;

     int minimum;

     ItemIntMap &iimap;

     Compare comp;

     int num_items;

   public:

     ///Status of the nodes

     enum State {

       ///The node is in the heap

       IN_HEAP = 0,

       ///The node has never been in the heap

       PRE_HEAP = -1,

       ///The node was in the heap but it got out of it

       POST_HEAP = -2

     };

     /// \brief The constructor

     ///

     /// \c _iimap should be given to the constructor, since it is

     ///   used internally to handle the cross references.

     explicit PairingHeap(ItemIntMap &_iimap)

       : minimum(0), iimap(_iimap), num_items(0) {}

     /// \brief The constructor

     ///

     /// \c _iimap should be given to the constructor, since it is used

     /// internally to handle the cross references. \c _comp is an

     /// object for ordering of the priorities.

     PairingHeap(ItemIntMap &_iimap, const Compare &_comp)

       : minimum(0), iimap(_iimap), comp(_comp), num_items(0) {}

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

     ///

     /// Returns the number of items stored in the heap.

     int size() const { return num_items; }

     /// \brief Checks if the heap stores no items.

     ///

     ///   Returns \c true if and only if the heap stores no items.

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

     /// \brief Make empty this heap.

     ///

     /// Make empty this heap. It does not change the cross reference

     /// map.  If you want to reuse a heap 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() {

       container.clear();

       minimum = 0;

       num_items = 0;

     }

     /// \brief \c item gets to the heap with priority \c value independently

     /// if \c item was already there.

     ///

     /// This method calls \ref push(\c item, \c value) if \c item is not

     /// stored in the heap and it calls \ref decrease(\c item, \c value) or

     /// \ref increase(\c item, \c value) otherwise.

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

       int i=iimap[item];

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

         if ( comp(value, container[i].prio) ) decrease(item, value);

         if ( comp(container[i].prio, value) ) increase(item, value);

       } else push(item, value);

     }

     /// \brief Adds \c item to the heap with priority \c value.

     ///

     /// Adds \c item to the heap with priority \c value.

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

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

       int i=iimap[item];

       if( i<0 ) {

         int s=container.size();

         iimap.set(item, s);

         store st;

         st.name=item;

         container.push_back(st);

         i=s;

       } else {

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

         container[i].left_child=false;

         container[i].degree=0;

         container[i].in=true;

       }

       container[i].prio=value;

       if ( num_items!=0 ) {

         if ( comp( value, container[minimum].prio) ) {

           fuse(i,minimum);

           minimum=i;

         }

         else fuse(minimum,i);

       }

       else minimum=i;

       ++num_items;

     }

     /// \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 container[minimum].name; }

     /// \brief Returns the minimum priority relative to \c Compare.

     ///

     /// It returns the minimum priority relative to \c Compare.

     /// \pre The heap must be nonempty.

     const Prio& prio() const { return container[minimum].prio; }

     /// \brief Returns the priority of \c item.

     ///

     /// It returns the priority of \c item.

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

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

       return container[iimap[item]].prio;

     }

     /// \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 TreeArray[num_items];

       int i=0, num_child=0, child_right = 0;

       container[minimum].in=false;

       if( -1!=container[minimum].child ) {

         i=container[minimum].child;

         TreeArray[num_child] = i;

         container[i].parent = -1;

         container[minimum].child = -1;

         ++num_child;

         int ch=-1;

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

           ch=container[i].child;

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

             i=ch;

             //break;

           } else {

             if( container[ch].left_child ) {

               child_right=container[ch].parent;

               container[ch].parent = i;

               --container[i].degree;

             }

             else {

               child_right=ch;

               container[i].child=-1;

               container[i].degree=0;

             }

             container[child_right].parent = -1;

             TreeArray[num_child] = child_right;

             i = child_right;

             ++num_child;

           }

         }

         int other;

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

           if ( !comp(container[TreeArray[i]].prio,

                      container[TreeArray[i+1]].prio) ) {

             other=TreeArray[i];

             TreeArray[i]=TreeArray[i+1];

             TreeArray[i+1]=other;

           }

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

         }

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

         while(i>=2) {

           if ( comp(container[TreeArray[i]].prio,

                     container[TreeArray[i-2]].prio) ) {

             other=TreeArray[i];

             TreeArray[i]=TreeArray[i-2];

             TreeArray[i-2]=other;

           }

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

           i-=2;

         }

         minimum = TreeArray[0];

       }

       if ( 0==num_child ) {

         minimum = container[minimum].child;

       }

       if (minimum >= 0) container[minimum].left_child = false;

       --num_items;

     }

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

     ///

     /// This method deletes \c item from the heap, if \c item was already

     /// stored in the heap. It is quite inefficient in Pairing heaps.

     void erase (const Item& item) {

       int i=iimap[item];

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

         decrease( item, container[minimum].prio-1 );

         pop();

       }

     }

     /// \brief Decreases the priority of \c item to \c value.

     ///

     /// This method decreases the priority of \c item to \c value.

     /// \pre \c item must be stored in the heap with priority at least \c

     ///   value relative to \c Compare.

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

       int i=iimap[item];

       container[i].prio=value;

       int p=container[i].parent;

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

         p=container[p].parent;

       }

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

         cut(i,p);

         if ( comp(container[minimum].prio,value) ) {

           fuse(minimum,i);

         } else {

           fuse(i,minimum);

           minimum=i;

         }

       }

     }

     /// \brief Increases the priority of \c item to \c value.

     ///

     /// This method sets the priority of \c item to \c value. Though

     /// there is no precondition on the priority of \c item, this

     /// method should be used only if it is indeed necessary to increase

     /// (relative to \c Compare) the priority of \c item, because this

     /// method is inefficient.

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

       erase(item);

       push(item,value);

     }

     /// \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.

     State state(const Item &item) const {

       int i=iimap[item];

       if( i>=0 ) {

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

         else i=-2;

       }

       return State(i);

     }

     /// \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);

         iimap[i]=st;

         break;

       case IN_HEAP:

         break;

       }

     }

   private:

     void cut(int a, int b) {

       int child_a;

       switch (container[a].degree) {

         case 2:

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

           if( container[a].left_child ) {

             container[child_a].left_child=true;

             container[b].child=child_a;

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

           }

           else {

             container[child_a].left_child=false;

             container[child_a].parent=b;

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

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

             else

               container[b].child=child_a;

           }

           --container[a].degree;

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

           break;

         case 1:

           child_a = container[a].child;

           if( !container[child_a].left_child ) {

             --container[a].degree;

             if( container[a].left_child ) {

               container[child_a].left_child=true;

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

               container[b].child=child_a;

             }

             else {

               container[child_a].left_child=false;

               container[child_a].parent=b;

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

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

               else

                 container[b].child=child_a;

             }

             container[a].child=-1;

           }

           else {

             --container[b].degree;

             if( container[a].left_child ) {

               container[b].child =

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

             } else {

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

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

               else

                 container[b].child=-1;

             }

           }

           break;

         case 0:

           --container[b].degree;

           if( container[a].left_child ) {

             container[b].child =

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

           } else {

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

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

             else

               container[b].child=-1;

           }

           break;

       }

       container[a].parent=-1;

       container[a].left_child=false;

     }

     void fuse(int a, int b) {

       int child_a = container[a].child;

       int child_b = container[b].child;

       container[a].child=b;

       container[b].parent=a;

       container[b].left_child=true;

       if( -1!=child_a ) {

         container[b].child=child_a;

         container[child_a].parent=b;

         container[child_a].left_child=false;

         ++container[b].degree;

         if( -1!=child_b ) {

            container[b].child=child_b;

            container[child_b].parent=child_a;

         }

       }

       else { ++container[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