lemon/fib_heap.h
author Alpar Juttner <alpar@cs.elte.hu>
Sun, 12 Sep 2010 08:32:46 +0200
changeset 905 de428ebb47ab
parent 710 f1fe0ddad6f7
permissions -rw-r--r--
Merge #380
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_FIB_HEAP_H
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#define LEMON_FIB_HEAP_H
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///\file
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///\ingroup heaps
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///\brief Fibonacci heap implementation.
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#include <vector>
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#include <utility>
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#include <functional>
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#include <lemon/math.h>
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namespace lemon {
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  /// \ingroup heaps
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  ///
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  /// \brief Fibonacci heap data structure.
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  ///
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  /// This class implements the \e Fibonacci \e heap data structure.
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  /// It fully conforms to the \ref concepts::Heap "heap concept".
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  ///
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  /// The methods \ref increase() and \ref erase() are not efficient in a
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  /// Fibonacci heap. In case of many calls of these operations, it is
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  /// better to use other heap structure, e.g. \ref BinHeap "binary heap".
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  ///
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  /// \tparam PR Type of the priorities of the items.
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  /// \tparam IM A read-writable item map with \c int values, used
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  /// internally to handle the cross references.
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  /// \tparam CMP A functor class for comparing the priorities.
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  /// The default is \c std::less<PR>.
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#ifdef DOXYGEN
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  template <typename PR, typename IM, typename CMP>
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#else
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  template <typename PR, typename IM, typename CMP = std::less<PR> >
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#endif
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  class FibHeap {
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  public:
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    /// Type of the item-int map.
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    typedef IM ItemIntMap;
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    /// Type of the priorities.
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    typedef PR Prio;
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    /// Type of the items stored in the heap.
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    typedef typename ItemIntMap::Key Item;
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    /// Type of the item-priority pairs.
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    typedef std::pair<Item,Prio> Pair;
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    /// Functor type for comparing the priorities.
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    typedef CMP Compare;
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  private:
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    class Store;
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    std::vector<Store> _data;
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    int _minimum;
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    ItemIntMap &_iim;
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    Compare _comp;
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    int _num;
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  public:
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    /// \brief Type to represent the states of the items.
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    ///
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    /// Each item has a state associated to it. It can be "in heap",
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    /// "pre-heap" or "post-heap". The latter two are indifferent from the
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    /// heap's point of view, but may be useful to the user.
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    ///
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    /// The item-int map must be initialized in such way that it assigns
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    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
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    enum State {
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      IN_HEAP = 0,    ///< = 0.
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      PRE_HEAP = -1,  ///< = -1.
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      POST_HEAP = -2  ///< = -2.
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    };
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    /// \brief Constructor.
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    ///
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    /// Constructor.
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    /// \param map A map that assigns \c int values to the items.
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    /// It is used internally to handle the cross references.
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    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
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    explicit FibHeap(ItemIntMap &map)
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      : _minimum(0), _iim(map), _num() {}
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    /// \brief Constructor.
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    ///
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    /// Constructor.
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    /// \param map A map that assigns \c int values to the items.
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    /// It is used internally to handle the cross references.
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    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
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    /// \param comp The function object used for comparing the priorities.
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    FibHeap(ItemIntMap &map, const Compare &comp)
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      : _minimum(0), _iim(map), _comp(comp), _num() {}
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    /// \brief The number of items stored in the heap.
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    ///
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    /// This function returns the number of items stored in the heap.
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    int size() const { return _num; }
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    /// \brief Check if the heap is empty.
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    ///
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    /// This function returns \c true if the heap is empty.
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    bool empty() const { return _num==0; }
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    /// \brief Make the heap empty.
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    ///
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    /// This functon makes the heap empty.
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    /// It does not change the cross reference map. If you want to reuse
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    /// a heap that is not surely empty, you should first clear it and
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    /// then you should set the cross reference map to \c PRE_HEAP
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    /// for each item.
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    void clear() {
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      _data.clear(); _minimum = 0; _num = 0;
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    }
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    /// \brief Insert an item into the heap with the given priority.
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    ///
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    /// This function inserts the given item into the heap with the
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    /// given priority.
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    /// \param item The item to insert.
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    /// \param prio The priority of the item.
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    /// \pre \e item must not be stored in the heap.
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    void push (const Item& item, const Prio& prio) {
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      int i=_iim[item];
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      if ( i < 0 ) {
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        int s=_data.size();
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        _iim.set( item, s );
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        Store st;
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        st.name=item;
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        _data.push_back(st);
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        i=s;
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      } else {
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        _data[i].parent=_data[i].child=-1;
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        _data[i].degree=0;
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        _data[i].in=true;
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        _data[i].marked=false;
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      }
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      if ( _num ) {
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        _data[_data[_minimum].right_neighbor].left_neighbor=i;
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        _data[i].right_neighbor=_data[_minimum].right_neighbor;
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        _data[_minimum].right_neighbor=i;
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        _data[i].left_neighbor=_minimum;
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        if ( _comp( prio, _data[_minimum].prio) ) _minimum=i;
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      } else {
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        _data[i].right_neighbor=_data[i].left_neighbor=i;
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        _minimum=i;
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      }
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      _data[i].prio=prio;
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      ++_num;
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    }
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    /// \brief Return the item having minimum priority.
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    ///
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    /// This function returns the item having minimum priority.
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    /// \pre The heap must be non-empty.
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    Item top() const { return _data[_minimum].name; }
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    /// \brief The minimum priority.
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    ///
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    /// This function returns the minimum priority.
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    /// \pre The heap must be non-empty.
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    Prio prio() const { return _data[_minimum].prio; }
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    /// \brief Remove the item having minimum priority.
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    ///
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    /// This function removes the item having minimum priority.
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    /// \pre The heap must be non-empty.
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    void pop() {
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      /*The first case is that there are only one root.*/
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      if ( _data[_minimum].left_neighbor==_minimum ) {
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        _data[_minimum].in=false;
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        if ( _data[_minimum].degree!=0 ) {
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          makeRoot(_data[_minimum].child);
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          _minimum=_data[_minimum].child;
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          balance();
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        }
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      } else {
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        int right=_data[_minimum].right_neighbor;
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        unlace(_minimum);
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        _data[_minimum].in=false;
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        if ( _data[_minimum].degree > 0 ) {
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          int left=_data[_minimum].left_neighbor;
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          int child=_data[_minimum].child;
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          int last_child=_data[child].left_neighbor;
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          makeRoot(child);
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          _data[left].right_neighbor=child;
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          _data[child].left_neighbor=left;
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          _data[right].left_neighbor=last_child;
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          _data[last_child].right_neighbor=right;
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        }
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        _minimum=right;
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        balance();
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      } // the case where there are more roots
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      --_num;
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    }
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    /// \brief Remove the given item from the heap.
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    ///
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    /// This function removes the given item from the heap if it is
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    /// already stored.
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    /// \param item The item to delete.
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    /// \pre \e item must be in the heap.
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    void erase (const Item& item) {
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      int i=_iim[item];
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      if ( i >= 0 && _data[i].in ) {
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        if ( _data[i].parent!=-1 ) {
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          int p=_data[i].parent;
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          cut(i,p);
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          cascade(p);
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        }
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        _minimum=i;     //As if its prio would be -infinity
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        pop();
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      }
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    }
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    /// \brief The priority of the given item.
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    ///
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    /// This function returns the priority of the given item.
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    /// \param item The item.
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    /// \pre \e item must be in the heap.
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    Prio operator[](const Item& item) const {
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      return _data[_iim[item]].prio;
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    }
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    /// \brief Set the priority of an item or insert it, if it is
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    /// not stored in the heap.
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    ///
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    /// This method sets the priority of the given item if it is
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    /// already stored in the heap. Otherwise it inserts the given
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    /// item into the heap with the given priority.
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    /// \param item The item.
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    /// \param prio The priority.
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    void set (const Item& item, const Prio& prio) {
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      int i=_iim[item];
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      if ( i >= 0 && _data[i].in ) {
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        if ( _comp(prio, _data[i].prio) ) decrease(item, prio);
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        if ( _comp(_data[i].prio, prio) ) increase(item, prio);
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      } else push(item, prio);
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    }
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    /// \brief Decrease the priority of an item to the given value.
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    ///
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    /// This function decreases the priority of an item to the given value.
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    /// \param item The item.
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    /// \param prio The priority.
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    /// \pre \e item must be stored in the heap with priority at least \e prio.
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    void decrease (const Item& item, const Prio& prio) {
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      int i=_iim[item];
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      _data[i].prio=prio;
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      int p=_data[i].parent;
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      if ( p!=-1 && _comp(prio, _data[p].prio) ) {
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        cut(i,p);
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        cascade(p);
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      }
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      if ( _comp(prio, _data[_minimum].prio) ) _minimum=i;
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    }
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    /// \brief Increase the priority of an item to the given value.
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    ///
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    /// This function increases the priority of an item to the given value.
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    /// \param item The item.
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    /// \param prio The priority.
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    /// \pre \e item must be stored in the heap with priority at most \e prio.
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    void increase (const Item& item, const Prio& prio) {
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      erase(item);
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      push(item, prio);
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    }
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    /// \brief Return the state of an item.
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    ///
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    /// This method returns \c PRE_HEAP if the given item has never
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    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
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    /// and \c POST_HEAP otherwise.
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    /// In the latter case it is possible that the item will get back
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    /// to the heap again.
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    /// \param item The item.
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    State state(const Item &item) const {
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      int i=_iim[item];
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      if( i>=0 ) {
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        if ( _data[i].in ) i=0;
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        else i=-2;
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      }
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      return State(i);
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    }
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    /// \brief Set the state of an item in the heap.
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    ///
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    /// This function sets the state of the given item in the heap.
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    /// It can be used to manually clear the heap when it is important
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    /// to achive better time complexity.
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    /// \param i The item.
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    /// \param st The state. It should not be \c IN_HEAP.
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    void state(const Item& i, State st) {
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      switch (st) {
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      case POST_HEAP:
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      case PRE_HEAP:
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        if (state(i) == IN_HEAP) {
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          erase(i);
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        }
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        _iim[i] = st;
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        break;
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      case IN_HEAP:
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        break;
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      }
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    }
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  private:
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    void balance() {
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      int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
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      std::vector<int> A(maxdeg,-1);
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      /*
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       *Recall that now minimum does not point to the minimum prio element.
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       *We set minimum to this during balance().
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       */
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      int anchor=_data[_minimum].left_neighbor;
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      int next=_minimum;
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      bool end=false;
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      do {
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        int active=next;
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        if ( anchor==active ) end=true;
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        int d=_data[active].degree;
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        next=_data[active].right_neighbor;
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        while (A[d]!=-1) {
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          if( _comp(_data[active].prio, _data[A[d]].prio) ) {
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            fuse(active,A[d]);
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          } else {
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            fuse(A[d],active);
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            active=A[d];
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          }
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          A[d]=-1;
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          ++d;
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        }
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        A[d]=active;
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      } while ( !end );
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      while ( _data[_minimum].parent >=0 )
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        _minimum=_data[_minimum].parent;
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      int s=_minimum;
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      int m=_minimum;
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      do {
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        if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
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        s=_data[s].right_neighbor;
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      } while ( s != m );
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    }
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    void makeRoot(int c) {
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      int s=c;
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      do {
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        _data[s].parent=-1;
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        s=_data[s].right_neighbor;
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      } while ( s != c );
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    }
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    void cut(int a, int b) {
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      /*
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       *Replacing a from the children of b.
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       */
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      --_data[b].degree;
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      if ( _data[b].degree !=0 ) {
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        int child=_data[b].child;
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        if ( child==a )
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          _data[b].child=_data[child].right_neighbor;
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        unlace(a);
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      }
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      /*Lacing a to the roots.*/
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      int right=_data[_minimum].right_neighbor;
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      _data[_minimum].right_neighbor=a;
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      _data[a].left_neighbor=_minimum;
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      _data[a].right_neighbor=right;
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      _data[right].left_neighbor=a;
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      _data[a].parent=-1;
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      _data[a].marked=false;
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    }
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    void cascade(int a) {
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      if ( _data[a].parent!=-1 ) {
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        int p=_data[a].parent;
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        if ( _data[a].marked==false ) _data[a].marked=true;
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        else {
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          cut(a,p);
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          cascade(p);
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        }
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      }
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    }
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    void fuse(int a, int b) {
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      unlace(b);
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      /*Lacing b under a.*/
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      _data[b].parent=a;
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      if (_data[a].degree==0) {
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        _data[b].left_neighbor=b;
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        _data[b].right_neighbor=b;
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        _data[a].child=b;
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      } else {
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        int child=_data[a].child;
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        int last_child=_data[child].left_neighbor;
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        _data[child].left_neighbor=b;
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        _data[b].right_neighbor=child;
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        _data[last_child].right_neighbor=b;
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        _data[b].left_neighbor=last_child;
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      }
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      ++_data[a].degree;
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      _data[b].marked=false;
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    }
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    /*
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     *It is invoked only if a has siblings.
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     */
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    void unlace(int a) {
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      int leftn=_data[a].left_neighbor;
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      int rightn=_data[a].right_neighbor;
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      _data[leftn].right_neighbor=rightn;
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      _data[rightn].left_neighbor=leftn;
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    }
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   454
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    class Store {
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   456
      friend class FibHeap;
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   457
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      Item name;
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      int parent;
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      int left_neighbor;
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      int right_neighbor;
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      int child;
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      int degree;
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      bool marked;
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      bool in;
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      Prio prio;
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      Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
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    };
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  };
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} //namespace lemon
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   474
#endif //LEMON_FIB_HEAP_H
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