lemon/fib_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Thu, 09 Jul 2009 02:38:01 +0200
changeset 701 d1a9224f1e30
parent 681 532697c9fa53
child 709 0747f332c478
permissions -rw-r--r--
Add fourary, k-ary, pairing and binomial heaps (#301)
These structures were implemented by Dorian Batha.
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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 auxdat
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///\brief Fibonacci Heap implementation.
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#include <vector>
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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 auxdat
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  ///
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  ///\brief Fibonacci Heap.
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  ///
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  ///This class implements the \e Fibonacci \e heap data structure. A \e heap
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  ///is a data structure for storing items with specified values called \e
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  ///priorities in such a way that finding the item with minimum priority is
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  ///efficient. \c CMP specifies the ordering of the priorities. In a heap
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  ///one can change the priority of an item, add or erase an item, etc.
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  ///
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  ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
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  ///heap. In case of many calls to these operations, it is better to use a
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  ///\ref BinHeap "binary heap".
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  ///
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  ///\param PRIO Type of the priority of the items.
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  ///\param IM A read and writable Item int map, used internally
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  ///to handle the cross references.
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  ///\param CMP A class for the ordering of the priorities. The
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  ///default is \c std::less<PRIO>.
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  ///
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  ///\sa BinHeap
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  ///\sa Dijkstra
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#ifdef DOXYGEN
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  template <typename PRIO, typename IM, typename CMP>
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#else
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  template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
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#endif
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  class FibHeap {
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  public:
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    ///\e
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    typedef IM ItemIntMap;
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    ///\e
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    typedef PRIO Prio;
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    ///\e
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    typedef typename ItemIntMap::Key Item;
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    ///\e
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    typedef std::pair<Item,Prio> Pair;
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    ///\e
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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 items states.
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    ///
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    /// Each Item element have a state associated to it. It may 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 The constructor
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    ///
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    /// \c map should be given to the constructor, since it is
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    ///   used internally to handle the cross references.
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    explicit FibHeap(ItemIntMap &map)
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      : _minimum(0), _iim(map), _num() {}
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    /// \brief The constructor
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    ///
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    /// \c map should be given to the constructor, since it is used
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    /// internally to handle the cross references. \c comp is an
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    /// object for ordering of 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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    /// Returns the number of items stored in the heap.
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    int size() const { return _num; }
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    /// \brief Checks if the heap stores no items.
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    ///
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    ///   Returns \c true if and only if the heap stores no items.
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    bool empty() const { return _num==0; }
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    /// \brief Make empty this heap.
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    ///
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    /// Make empty this heap. It does not change the cross reference
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    /// map.  If you want to reuse a heap what is not surely empty you
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    /// should first clear the heap and after that you should set the
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    /// cross reference map for each item to \c PRE_HEAP.
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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 \c item gets to the heap with priority \c value independently
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    /// if \c item was already there.
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    ///
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    /// This method calls \ref push(\c item, \c value) if \c item is not
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    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
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    /// \ref increase(\c item, \c value) otherwise.
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    void set (const Item& item, const Prio& value) {
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      int i=_iim[item];
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      if ( i >= 0 && _data[i].in ) {
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        if ( _comp(value, _data[i].prio) ) decrease(item, value);
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        if ( _comp(_data[i].prio, value) ) increase(item, value);
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      } else push(item, value);
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    }
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    /// \brief Adds \c item to the heap with priority \c value.
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    ///
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    /// Adds \c item to the heap with priority \c value.
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    /// \pre \c item must not be stored in the heap.
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    void push (const Item& item, const Prio& value) {
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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( value, _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=value;
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      ++_num;
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    }
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    /// \brief Returns the item with minimum priority relative to \c Compare.
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    ///
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    /// This method returns the item with minimum priority relative to \c
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    /// Compare.
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    /// \pre The heap must be nonempty.
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    Item top() const { return _data[_minimum].name; }
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    /// \brief Returns the minimum priority relative to \c Compare.
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    ///
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    /// It returns the minimum priority relative to \c Compare.
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    /// \pre The heap must be nonempty.
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    const Prio& prio() const { return _data[_minimum].prio; }
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    /// \brief Returns the priority of \c item.
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    ///
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    /// It returns the priority of \c item.
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    /// \pre \c item must be in the heap.
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    const Prio& operator[](const Item& item) const {
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      return _data[_iim[item]].prio;
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    }
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    /// \brief Deletes the item with minimum priority relative to \c Compare.
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    ///
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    /// This method deletes the item with minimum priority relative to \c
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    /// Compare from the heap.
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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 Deletes \c item from the heap.
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    ///
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    /// This method deletes \c item from the heap, if \c item was already
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    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
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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 Decreases the priority of \c item to \c value.
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    ///
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    /// This method decreases the priority of \c item to \c value.
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    /// \pre \c item must be stored in the heap with priority at least \c
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    ///   value relative to \c Compare.
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    void decrease (Item item, const Prio& value) {
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      int i=_iim[item];
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      _data[i].prio=value;
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      int p=_data[i].parent;
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      if ( p!=-1 && _comp(value, _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(value, _data[_minimum].prio) ) _minimum=i;
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    }
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    /// \brief Increases the priority of \c item to \c value.
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    ///
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    /// This method sets the priority of \c item to \c value. Though
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    /// there is no precondition on the priority of \c item, this
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    /// method should be used only if it is indeed necessary to increase
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    /// (relative to \c Compare) the priority of \c item, because this
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    /// method is inefficient.
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    void increase (Item item, const Prio& value) {
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      erase(item);
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      push(item, value);
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    }
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    /// \brief Returns if \c item is in, has already been in, or has never
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    /// been in the heap.
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    ///
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    /// This method returns PRE_HEAP if \c item has never been in the
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    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
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    /// otherwise. In the latter case it is possible that \c item will
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    /// get back to the heap again.
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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 Sets the state of the \c item in the heap.
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    ///
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    /// Sets the state of the \c item in the heap. It can be used to
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    /// manually clear the heap when it is important to achive the
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    /// 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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    class Store {
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      friend class FibHeap;
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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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#endif //LEMON_FIB_HEAP_H
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