lemon/binom_heap.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 05 Oct 2009 20:21:54 +0200
changeset 750 b7e3662faf02
parent 703 bb3392fe91f2
permissions -rw-r--r--
Merge #317
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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_BINOM_HEAP_H
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#define LEMON_BINOM_HEAP_H
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///\file
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///\ingroup heaps
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///\brief Binomial 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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#include <lemon/counter.h>
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namespace lemon {
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  /// \ingroup heaps
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  ///
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  ///\brief Binomial heap data structure.
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  ///
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  /// This class implements the \e binomial \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
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  /// in a binomial heap. In case of many calls of these operations,
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  /// it is better to use other heap structure, e.g. \ref BinHeap
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  /// "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 BinomHeap {
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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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    /// Functor type for comparing the priorities.
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    typedef CMP Compare;
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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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  private:
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    class Store;
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    std::vector<Store> _data;
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    int _min, _head;
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    ItemIntMap &_iim;
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    Compare _comp;
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    int _num_items;
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  public:
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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 BinomHeap(ItemIntMap &map)
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      : _min(0), _head(-1), _iim(map), _num_items(0) {}
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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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    BinomHeap(ItemIntMap &map, const Compare &comp)
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      : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {}
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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_items; }
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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_items==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(); _min=0; _num_items=0; _head=-1;
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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 value The priority.
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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 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 value 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& 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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        st.prio=value;
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        _data.push_back(st);
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        i=s;
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      }
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      else {
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        _data[i].parent=_data[i].right_neighbor=_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].prio=value;
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      }
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      if( 0==_num_items ) {
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        _head=i;
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        _min=i;
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      } else {
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        merge(i);
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        if( _comp(_data[i].prio, _data[_min].prio) ) _min=i;
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      }
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      ++_num_items;
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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[_min].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[_min].prio; }
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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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    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 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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      _data[_min].in=false;
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      int head_child=-1;
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      if ( _data[_min].child!=-1 ) {
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        int child=_data[_min].child;
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        int neighb;
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        while( child!=-1 ) {
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          neighb=_data[child].right_neighbor;
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          _data[child].parent=-1;
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          _data[child].right_neighbor=head_child;
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          head_child=child;
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          child=neighb;
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        }
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      }
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      if ( _data[_head].right_neighbor==-1 ) {
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        // there was only one root
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        _head=head_child;
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      }
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      else {
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        // there were more roots
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        if( _head!=_min )  { unlace(_min); }
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        else { _head=_data[_head].right_neighbor; }
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        merge(head_child);
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      }
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      _min=findMin();
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      --_num_items;
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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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        decrease( item, _data[_min].prio-1 );
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        pop();
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      }
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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 value The priority.
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    /// \pre \e item must be stored in the heap with priority at least \e value.
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    void decrease (Item item, const Prio& value) {
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      int i=_iim[item];
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      int p=_data[i].parent;
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      _data[i].prio=value;
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      while( p!=-1 && _comp(value, _data[p].prio) ) {
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        _data[i].name=_data[p].name;
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        _data[i].prio=_data[p].prio;
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        _data[p].name=item;
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        _data[p].prio=value;
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        _iim[_data[i].name]=i;
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        i=p;
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        p=_data[p].parent;
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      }
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      _iim[item]=i;
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      if ( _comp(value, _data[_min].prio) ) _min=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 value The priority.
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    /// \pre \e item must be stored in the heap with priority at most \e value.
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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 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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    // Find the minimum of the roots
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    int findMin() {
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      if( _head!=-1 ) {
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        int min_loc=_head, min_val=_data[_head].prio;
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        for( int x=_data[_head].right_neighbor; x!=-1;
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             x=_data[x].right_neighbor ) {
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          if( _comp( _data[x].prio,min_val ) ) {
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            min_val=_data[x].prio;
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            min_loc=x;
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          }
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        }
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        return min_loc;
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      }
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      else return -1;
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    }
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    // Merge the heap with another heap starting at the given position
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    void merge(int a) {
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      if( _head==-1 || a==-1 ) return;
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      if( _data[a].right_neighbor==-1 &&
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          _data[a].degree<=_data[_head].degree ) {
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        _data[a].right_neighbor=_head;
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        _head=a;
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      } else {
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        interleave(a);
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      }
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      if( _data[_head].right_neighbor==-1 ) return;
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      int x=_head;
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      int x_prev=-1, x_next=_data[x].right_neighbor;
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      while( x_next!=-1 ) {
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        if( _data[x].degree!=_data[x_next].degree ||
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            ( _data[x_next].right_neighbor!=-1 &&
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              _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {
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          x_prev=x;
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          x=x_next;
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        }
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        else {
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          if( _comp(_data[x_next].prio,_data[x].prio) ) {
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            if( x_prev==-1 ) {
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              _head=x_next;
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            } else {
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              _data[x_prev].right_neighbor=x_next;
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            }
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            fuse(x,x_next);
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            x=x_next;
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          }
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          else {
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            _data[x].right_neighbor=_data[x_next].right_neighbor;
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            fuse(x_next,x);
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          }
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        }
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        x_next=_data[x].right_neighbor;
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      }
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    }
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    // Interleave the elements of the given list into the list of the roots
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    void interleave(int a) {
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      int p=_head, q=a;
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      int curr=_data.size();
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      _data.push_back(Store());
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      while( p!=-1 || q!=-1 ) {
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        if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) {
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          _data[curr].right_neighbor=p;
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          curr=p;
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          p=_data[p].right_neighbor;
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        }
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        else {
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          _data[curr].right_neighbor=q;
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          curr=q;
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          q=_data[q].right_neighbor;
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        }
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      }
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      _head=_data.back().right_neighbor;
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      _data.pop_back();
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    }
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    // Lace node a under node b
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    void fuse(int a, int b) {
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      _data[a].parent=b;
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      _data[a].right_neighbor=_data[b].child;
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      _data[b].child=a;
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      ++_data[b].degree;
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    }
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    // Unlace node a (if it has siblings)
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    void unlace(int a) {
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      int neighb=_data[a].right_neighbor;
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      int other=_head;
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      while( _data[other].right_neighbor!=a )
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        other=_data[other].right_neighbor;
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      _data[other].right_neighbor=neighb;
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    }
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  private:
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    class Store {
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      friend class BinomHeap;
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      Item name;
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      int parent;
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      int right_neighbor;
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      int child;
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      int degree;
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      bool in;
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      Prio prio;
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      Store() : parent(-1), right_neighbor(-1), child(-1), degree(0),
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        in(true) {}
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    };
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  };
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} //namespace lemon
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#endif //LEMON_BINOM_HEAP_H
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