lemon/kary_heap.h
changeset 783 ef88c0a30f85
parent 704 7124b2581f72
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/kary_heap.h	Thu Nov 05 15:48:01 2009 +0100
     1.3 @@ -0,0 +1,352 @@
     1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
     1.5 + *
     1.6 + * This file is a part of LEMON, a generic C++ optimization library.
     1.7 + *
     1.8 + * Copyright (C) 2003-2009
     1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11 + *
    1.12 + * Permission to use, modify and distribute this software is granted
    1.13 + * provided that this copyright notice appears in all copies. For
    1.14 + * precise terms see the accompanying LICENSE file.
    1.15 + *
    1.16 + * This software is provided "AS IS" with no warranty of any kind,
    1.17 + * express or implied, and with no claim as to its suitability for any
    1.18 + * purpose.
    1.19 + *
    1.20 + */
    1.21 +
    1.22 +#ifndef LEMON_KARY_HEAP_H
    1.23 +#define LEMON_KARY_HEAP_H
    1.24 +
    1.25 +///\ingroup heaps
    1.26 +///\file
    1.27 +///\brief Fourary heap implementation.
    1.28 +
    1.29 +#include <vector>
    1.30 +#include <utility>
    1.31 +#include <functional>
    1.32 +
    1.33 +namespace lemon {
    1.34 +
    1.35 +  /// \ingroup heaps
    1.36 +  ///
    1.37 +  ///\brief K-ary heap data structure.
    1.38 +  ///
    1.39 +  /// This class implements the \e K-ary \e heap data structure.
    1.40 +  /// It fully conforms to the \ref concepts::Heap "heap concept".
    1.41 +  ///
    1.42 +  /// The \ref KaryHeap "K-ary heap" is a generalization of the
    1.43 +  /// \ref BinHeap "binary heap" structure, its nodes have at most
    1.44 +  /// \c K children, instead of two.
    1.45 +  /// \ref BinHeap and \ref FouraryHeap are specialized implementations
    1.46 +  /// of this structure for <tt>K=2</tt> and <tt>K=4</tt>, respectively.
    1.47 +  ///
    1.48 +  /// \tparam PR Type of the priorities of the items.
    1.49 +  /// \tparam IM A read-writable item map with \c int values, used
    1.50 +  /// internally to handle the cross references.
    1.51 +  /// \tparam K The degree of the heap, each node have at most \e K
    1.52 +  /// children. The default is 16. Powers of two are suggested to use
    1.53 +  /// so that the multiplications and divisions needed to traverse the
    1.54 +  /// nodes of the heap could be performed faster.
    1.55 +  /// \tparam CMP A functor class for comparing the priorities.
    1.56 +  /// The default is \c std::less<PR>.
    1.57 +  ///
    1.58 +  ///\sa BinHeap
    1.59 +  ///\sa FouraryHeap
    1.60 +#ifdef DOXYGEN
    1.61 +  template <typename PR, typename IM, int K, typename CMP>
    1.62 +#else
    1.63 +  template <typename PR, typename IM, int K = 16,
    1.64 +            typename CMP = std::less<PR> >
    1.65 +#endif
    1.66 +  class KaryHeap {
    1.67 +  public:
    1.68 +    /// Type of the item-int map.
    1.69 +    typedef IM ItemIntMap;
    1.70 +    /// Type of the priorities.
    1.71 +    typedef PR Prio;
    1.72 +    /// Type of the items stored in the heap.
    1.73 +    typedef typename ItemIntMap::Key Item;
    1.74 +    /// Type of the item-priority pairs.
    1.75 +    typedef std::pair<Item,Prio> Pair;
    1.76 +    /// Functor type for comparing the priorities.
    1.77 +    typedef CMP Compare;
    1.78 +
    1.79 +    /// \brief Type to represent the states of the items.
    1.80 +    ///
    1.81 +    /// Each item has a state associated to it. It can be "in heap",
    1.82 +    /// "pre-heap" or "post-heap". The latter two are indifferent from the
    1.83 +    /// heap's point of view, but may be useful to the user.
    1.84 +    ///
    1.85 +    /// The item-int map must be initialized in such way that it assigns
    1.86 +    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    1.87 +    enum State {
    1.88 +      IN_HEAP = 0,    ///< = 0.
    1.89 +      PRE_HEAP = -1,  ///< = -1.
    1.90 +      POST_HEAP = -2  ///< = -2.
    1.91 +    };
    1.92 +
    1.93 +  private:
    1.94 +    std::vector<Pair> _data;
    1.95 +    Compare _comp;
    1.96 +    ItemIntMap &_iim;
    1.97 +
    1.98 +  public:
    1.99 +    /// \brief Constructor.
   1.100 +    ///
   1.101 +    /// Constructor.
   1.102 +    /// \param map A map that assigns \c int values to the items.
   1.103 +    /// It is used internally to handle the cross references.
   1.104 +    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   1.105 +    explicit KaryHeap(ItemIntMap &map) : _iim(map) {}
   1.106 +
   1.107 +    /// \brief Constructor.
   1.108 +    ///
   1.109 +    /// Constructor.
   1.110 +    /// \param map A map that assigns \c int values to the items.
   1.111 +    /// It is used internally to handle the cross references.
   1.112 +    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   1.113 +    /// \param comp The function object used for comparing the priorities.
   1.114 +    KaryHeap(ItemIntMap &map, const Compare &comp)
   1.115 +      : _iim(map), _comp(comp) {}
   1.116 +
   1.117 +    /// \brief The number of items stored in the heap.
   1.118 +    ///
   1.119 +    /// This function returns the number of items stored in the heap.
   1.120 +    int size() const { return _data.size(); }
   1.121 +
   1.122 +    /// \brief Check if the heap is empty.
   1.123 +    ///
   1.124 +    /// This function returns \c true if the heap is empty.
   1.125 +    bool empty() const { return _data.empty(); }
   1.126 +
   1.127 +    /// \brief Make the heap empty.
   1.128 +    ///
   1.129 +    /// This functon makes the heap empty.
   1.130 +    /// It does not change the cross reference map. If you want to reuse
   1.131 +    /// a heap that is not surely empty, you should first clear it and
   1.132 +    /// then you should set the cross reference map to \c PRE_HEAP
   1.133 +    /// for each item.
   1.134 +    void clear() { _data.clear(); }
   1.135 +
   1.136 +  private:
   1.137 +    int parent(int i) { return (i-1)/K; }
   1.138 +    int firstChild(int i) { return K*i+1; }
   1.139 +
   1.140 +    bool less(const Pair &p1, const Pair &p2) const {
   1.141 +      return _comp(p1.second, p2.second);
   1.142 +    }
   1.143 +
   1.144 +    void bubbleUp(int hole, Pair p) {
   1.145 +      int par = parent(hole);
   1.146 +      while( hole>0 && less(p,_data[par]) ) {
   1.147 +        move(_data[par],hole);
   1.148 +        hole = par;
   1.149 +        par = parent(hole);
   1.150 +      }
   1.151 +      move(p, hole);
   1.152 +    }
   1.153 +
   1.154 +    void bubbleDown(int hole, Pair p, int length) {
   1.155 +      if( length>1 ) {
   1.156 +        int child = firstChild(hole);
   1.157 +        while( child+K<=length ) {
   1.158 +          int min=child;
   1.159 +          for (int i=1; i<K; ++i) {
   1.160 +            if( less(_data[child+i], _data[min]) )
   1.161 +              min=child+i;
   1.162 +          }
   1.163 +          if( !less(_data[min], p) )
   1.164 +            goto ok;
   1.165 +          move(_data[min], hole);
   1.166 +          hole = min;
   1.167 +          child = firstChild(hole);
   1.168 +        }
   1.169 +        if ( child<length ) {
   1.170 +          int min = child;
   1.171 +          while (++child < length) {
   1.172 +            if( less(_data[child], _data[min]) )
   1.173 +              min=child;
   1.174 +          }
   1.175 +          if( less(_data[min], p) ) {
   1.176 +            move(_data[min], hole);
   1.177 +            hole = min;
   1.178 +          }
   1.179 +        }
   1.180 +      }
   1.181 +    ok:
   1.182 +      move(p, hole);
   1.183 +    }
   1.184 +
   1.185 +    void move(const Pair &p, int i) {
   1.186 +      _data[i] = p;
   1.187 +      _iim.set(p.first, i);
   1.188 +    }
   1.189 +
   1.190 +  public:
   1.191 +    /// \brief Insert a pair of item and priority into the heap.
   1.192 +    ///
   1.193 +    /// This function inserts \c p.first to the heap with priority
   1.194 +    /// \c p.second.
   1.195 +    /// \param p The pair to insert.
   1.196 +    /// \pre \c p.first must not be stored in the heap.
   1.197 +    void push(const Pair &p) {
   1.198 +      int n = _data.size();
   1.199 +      _data.resize(n+1);
   1.200 +      bubbleUp(n, p);
   1.201 +    }
   1.202 +
   1.203 +    /// \brief Insert an item into the heap with the given priority.
   1.204 +    ///
   1.205 +    /// This function inserts the given item into the heap with the
   1.206 +    /// given priority.
   1.207 +    /// \param i The item to insert.
   1.208 +    /// \param p The priority of the item.
   1.209 +    /// \pre \e i must not be stored in the heap.
   1.210 +    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
   1.211 +
   1.212 +    /// \brief Return the item having minimum priority.
   1.213 +    ///
   1.214 +    /// This function returns the item having minimum priority.
   1.215 +    /// \pre The heap must be non-empty.
   1.216 +    Item top() const { return _data[0].first; }
   1.217 +
   1.218 +    /// \brief The minimum priority.
   1.219 +    ///
   1.220 +    /// This function returns the minimum priority.
   1.221 +    /// \pre The heap must be non-empty.
   1.222 +    Prio prio() const { return _data[0].second; }
   1.223 +
   1.224 +    /// \brief Remove the item having minimum priority.
   1.225 +    ///
   1.226 +    /// This function removes the item having minimum priority.
   1.227 +    /// \pre The heap must be non-empty.
   1.228 +    void pop() {
   1.229 +      int n = _data.size()-1;
   1.230 +      _iim.set(_data[0].first, POST_HEAP);
   1.231 +      if (n>0) bubbleDown(0, _data[n], n);
   1.232 +      _data.pop_back();
   1.233 +    }
   1.234 +
   1.235 +    /// \brief Remove the given item from the heap.
   1.236 +    ///
   1.237 +    /// This function removes the given item from the heap if it is
   1.238 +    /// already stored.
   1.239 +    /// \param i The item to delete.
   1.240 +    /// \pre \e i must be in the heap.
   1.241 +    void erase(const Item &i) {
   1.242 +      int h = _iim[i];
   1.243 +      int n = _data.size()-1;
   1.244 +      _iim.set(_data[h].first, POST_HEAP);
   1.245 +      if( h<n ) {
   1.246 +        if( less(_data[parent(h)], _data[n]) )
   1.247 +          bubbleDown(h, _data[n], n);
   1.248 +        else
   1.249 +          bubbleUp(h, _data[n]);
   1.250 +      }
   1.251 +      _data.pop_back();
   1.252 +    }
   1.253 +
   1.254 +    /// \brief The priority of the given item.
   1.255 +    ///
   1.256 +    /// This function returns the priority of the given item.
   1.257 +    /// \param i The item.
   1.258 +    /// \pre \e i must be in the heap.
   1.259 +    Prio operator[](const Item &i) const {
   1.260 +      int idx = _iim[i];
   1.261 +      return _data[idx].second;
   1.262 +    }
   1.263 +
   1.264 +    /// \brief Set the priority of an item or insert it, if it is
   1.265 +    /// not stored in the heap.
   1.266 +    ///
   1.267 +    /// This method sets the priority of the given item if it is
   1.268 +    /// already stored in the heap. Otherwise it inserts the given
   1.269 +    /// item into the heap with the given priority.
   1.270 +    /// \param i The item.
   1.271 +    /// \param p The priority.
   1.272 +    void set(const Item &i, const Prio &p) {
   1.273 +      int idx = _iim[i];
   1.274 +      if( idx<0 )
   1.275 +        push(i,p);
   1.276 +      else if( _comp(p, _data[idx].second) )
   1.277 +        bubbleUp(idx, Pair(i,p));
   1.278 +      else
   1.279 +        bubbleDown(idx, Pair(i,p), _data.size());
   1.280 +    }
   1.281 +
   1.282 +    /// \brief Decrease the priority of an item to the given value.
   1.283 +    ///
   1.284 +    /// This function decreases the priority of an item to the given value.
   1.285 +    /// \param i The item.
   1.286 +    /// \param p The priority.
   1.287 +    /// \pre \e i must be stored in the heap with priority at least \e p.
   1.288 +    void decrease(const Item &i, const Prio &p) {
   1.289 +      int idx = _iim[i];
   1.290 +      bubbleUp(idx, Pair(i,p));
   1.291 +    }
   1.292 +
   1.293 +    /// \brief Increase the priority of an item to the given value.
   1.294 +    ///
   1.295 +    /// This function increases the priority of an item to the given value.
   1.296 +    /// \param i The item.
   1.297 +    /// \param p The priority.
   1.298 +    /// \pre \e i must be stored in the heap with priority at most \e p.
   1.299 +    void increase(const Item &i, const Prio &p) {
   1.300 +      int idx = _iim[i];
   1.301 +      bubbleDown(idx, Pair(i,p), _data.size());
   1.302 +    }
   1.303 +
   1.304 +    /// \brief Return the state of an item.
   1.305 +    ///
   1.306 +    /// This method returns \c PRE_HEAP if the given item has never
   1.307 +    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
   1.308 +    /// and \c POST_HEAP otherwise.
   1.309 +    /// In the latter case it is possible that the item will get back
   1.310 +    /// to the heap again.
   1.311 +    /// \param i The item.
   1.312 +    State state(const Item &i) const {
   1.313 +      int s = _iim[i];
   1.314 +      if (s>=0) s=0;
   1.315 +      return State(s);
   1.316 +    }
   1.317 +
   1.318 +    /// \brief Set the state of an item in the heap.
   1.319 +    ///
   1.320 +    /// This function sets the state of the given item in the heap.
   1.321 +    /// It can be used to manually clear the heap when it is important
   1.322 +    /// to achive better time complexity.
   1.323 +    /// \param i The item.
   1.324 +    /// \param st The state. It should not be \c IN_HEAP.
   1.325 +    void state(const Item& i, State st) {
   1.326 +      switch (st) {
   1.327 +        case POST_HEAP:
   1.328 +        case PRE_HEAP:
   1.329 +          if (state(i) == IN_HEAP) erase(i);
   1.330 +          _iim[i] = st;
   1.331 +          break;
   1.332 +        case IN_HEAP:
   1.333 +          break;
   1.334 +      }
   1.335 +    }
   1.336 +
   1.337 +    /// \brief Replace an item in the heap.
   1.338 +    ///
   1.339 +    /// This function replaces item \c i with item \c j.
   1.340 +    /// Item \c i must be in the heap, while \c j must be out of the heap.
   1.341 +    /// After calling this method, item \c i will be out of the
   1.342 +    /// heap and \c j will be in the heap with the same prioriority
   1.343 +    /// as item \c i had before.
   1.344 +    void replace(const Item& i, const Item& j) {
   1.345 +      int idx=_iim[i];
   1.346 +      _iim.set(i, _iim[j]);
   1.347 +      _iim.set(j, idx);
   1.348 +      _data[idx].first=j;
   1.349 +    }
   1.350 +
   1.351 +  }; // class KaryHeap
   1.352 +
   1.353 +} // namespace lemon
   1.354 +
   1.355 +#endif // LEMON_KARY_HEAP_H