/* -*- 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