lemon/pairing_heap.h
changeset 717 684964884a2e
parent 703 bb3392fe91f2
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/pairing_heap.h	Fri Sep 25 09:13:03 2009 +0200
     1.3 @@ -0,0 +1,474 @@
     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_PAIRING_HEAP_H
    1.23 +#define LEMON_PAIRING_HEAP_H
    1.24 +
    1.25 +///\file
    1.26 +///\ingroup heaps
    1.27 +///\brief Pairing heap implementation.
    1.28 +
    1.29 +#include <vector>
    1.30 +#include <utility>
    1.31 +#include <functional>
    1.32 +#include <lemon/math.h>
    1.33 +
    1.34 +namespace lemon {
    1.35 +
    1.36 +  /// \ingroup heaps
    1.37 +  ///
    1.38 +  ///\brief Pairing Heap.
    1.39 +  ///
    1.40 +  /// This class implements the \e pairing \e heap data structure.
    1.41 +  /// It fully conforms to the \ref concepts::Heap "heap concept".
    1.42 +  ///
    1.43 +  /// The methods \ref increase() and \ref erase() are not efficient
    1.44 +  /// in a pairing heap. In case of many calls of these operations,
    1.45 +  /// it is better to use other heap structure, e.g. \ref BinHeap
    1.46 +  /// "binary heap".
    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 CMP A functor class for comparing the priorities.
    1.52 +  /// The default is \c std::less<PR>.
    1.53 +#ifdef DOXYGEN
    1.54 +  template <typename PR, typename IM, typename CMP>
    1.55 +#else
    1.56 +  template <typename PR, typename IM, typename CMP = std::less<PR> >
    1.57 +#endif
    1.58 +  class PairingHeap {
    1.59 +  public:
    1.60 +    /// Type of the item-int map.
    1.61 +    typedef IM ItemIntMap;
    1.62 +    /// Type of the priorities.
    1.63 +    typedef PR Prio;
    1.64 +    /// Type of the items stored in the heap.
    1.65 +    typedef typename ItemIntMap::Key Item;
    1.66 +    /// Functor type for comparing the priorities.
    1.67 +    typedef CMP Compare;
    1.68 +
    1.69 +    /// \brief Type to represent the states of the items.
    1.70 +    ///
    1.71 +    /// Each item has a state associated to it. It can be "in heap",
    1.72 +    /// "pre-heap" or "post-heap". The latter two are indifferent from the
    1.73 +    /// heap's point of view, but may be useful to the user.
    1.74 +    ///
    1.75 +    /// The item-int map must be initialized in such way that it assigns
    1.76 +    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    1.77 +    enum State {
    1.78 +      IN_HEAP = 0,    ///< = 0.
    1.79 +      PRE_HEAP = -1,  ///< = -1.
    1.80 +      POST_HEAP = -2  ///< = -2.
    1.81 +    };
    1.82 +
    1.83 +  private:
    1.84 +    class store;
    1.85 +
    1.86 +    std::vector<store> _data;
    1.87 +    int _min;
    1.88 +    ItemIntMap &_iim;
    1.89 +    Compare _comp;
    1.90 +    int _num_items;
    1.91 +
    1.92 +  public:
    1.93 +    /// \brief Constructor.
    1.94 +    ///
    1.95 +    /// Constructor.
    1.96 +    /// \param map A map that assigns \c int values to the items.
    1.97 +    /// It is used internally to handle the cross references.
    1.98 +    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
    1.99 +    explicit PairingHeap(ItemIntMap &map)
   1.100 +      : _min(0), _iim(map), _num_items(0) {}
   1.101 +
   1.102 +    /// \brief Constructor.
   1.103 +    ///
   1.104 +    /// Constructor.
   1.105 +    /// \param map A map that assigns \c int values to the items.
   1.106 +    /// It is used internally to handle the cross references.
   1.107 +    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
   1.108 +    /// \param comp The function object used for comparing the priorities.
   1.109 +    PairingHeap(ItemIntMap &map, const Compare &comp)
   1.110 +      : _min(0), _iim(map), _comp(comp), _num_items(0) {}
   1.111 +
   1.112 +    /// \brief The number of items stored in the heap.
   1.113 +    ///
   1.114 +    /// This function returns the number of items stored in the heap.
   1.115 +    int size() const { return _num_items; }
   1.116 +
   1.117 +    /// \brief Check if the heap is empty.
   1.118 +    ///
   1.119 +    /// This function returns \c true if the heap is empty.
   1.120 +    bool empty() const { return _num_items==0; }
   1.121 +
   1.122 +    /// \brief Make the heap empty.
   1.123 +    ///
   1.124 +    /// This functon makes the heap empty.
   1.125 +    /// It does not change the cross reference map. If you want to reuse
   1.126 +    /// a heap that is not surely empty, you should first clear it and
   1.127 +    /// then you should set the cross reference map to \c PRE_HEAP
   1.128 +    /// for each item.
   1.129 +    void clear() {
   1.130 +      _data.clear();
   1.131 +      _min = 0;
   1.132 +      _num_items = 0;
   1.133 +    }
   1.134 +
   1.135 +    /// \brief Set the priority of an item or insert it, if it is
   1.136 +    /// not stored in the heap.
   1.137 +    ///
   1.138 +    /// This method sets the priority of the given item if it is
   1.139 +    /// already stored in the heap. Otherwise it inserts the given
   1.140 +    /// item into the heap with the given priority.
   1.141 +    /// \param item The item.
   1.142 +    /// \param value The priority.
   1.143 +    void set (const Item& item, const Prio& value) {
   1.144 +      int i=_iim[item];
   1.145 +      if ( i>=0 && _data[i].in ) {
   1.146 +        if ( _comp(value, _data[i].prio) ) decrease(item, value);
   1.147 +        if ( _comp(_data[i].prio, value) ) increase(item, value);
   1.148 +      } else push(item, value);
   1.149 +    }
   1.150 +
   1.151 +    /// \brief Insert an item into the heap with the given priority.
   1.152 +    ///
   1.153 +    /// This function inserts the given item into the heap with the
   1.154 +    /// given priority.
   1.155 +    /// \param item The item to insert.
   1.156 +    /// \param value The priority of the item.
   1.157 +    /// \pre \e item must not be stored in the heap.
   1.158 +    void push (const Item& item, const Prio& value) {
   1.159 +      int i=_iim[item];
   1.160 +      if( i<0 ) {
   1.161 +        int s=_data.size();
   1.162 +        _iim.set(item, s);
   1.163 +        store st;
   1.164 +        st.name=item;
   1.165 +        _data.push_back(st);
   1.166 +        i=s;
   1.167 +      } else {
   1.168 +        _data[i].parent=_data[i].child=-1;
   1.169 +        _data[i].left_child=false;
   1.170 +        _data[i].degree=0;
   1.171 +        _data[i].in=true;
   1.172 +      }
   1.173 +
   1.174 +      _data[i].prio=value;
   1.175 +
   1.176 +      if ( _num_items!=0 ) {
   1.177 +        if ( _comp( value, _data[_min].prio) ) {
   1.178 +          fuse(i,_min);
   1.179 +          _min=i;
   1.180 +        }
   1.181 +        else fuse(_min,i);
   1.182 +      }
   1.183 +      else _min=i;
   1.184 +
   1.185 +      ++_num_items;
   1.186 +    }
   1.187 +
   1.188 +    /// \brief Return the item having minimum priority.
   1.189 +    ///
   1.190 +    /// This function returns the item having minimum priority.
   1.191 +    /// \pre The heap must be non-empty.
   1.192 +    Item top() const { return _data[_min].name; }
   1.193 +
   1.194 +    /// \brief The minimum priority.
   1.195 +    ///
   1.196 +    /// This function returns the minimum priority.
   1.197 +    /// \pre The heap must be non-empty.
   1.198 +    const Prio& prio() const { return _data[_min].prio; }
   1.199 +
   1.200 +    /// \brief The priority of the given item.
   1.201 +    ///
   1.202 +    /// This function returns the priority of the given item.
   1.203 +    /// \param item The item.
   1.204 +    /// \pre \e item must be in the heap.
   1.205 +    const Prio& operator[](const Item& item) const {
   1.206 +      return _data[_iim[item]].prio;
   1.207 +    }
   1.208 +
   1.209 +    /// \brief Remove the item having minimum priority.
   1.210 +    ///
   1.211 +    /// This function removes the item having minimum priority.
   1.212 +    /// \pre The heap must be non-empty.
   1.213 +    void pop() {
   1.214 +      std::vector<int> trees;
   1.215 +      int i=0, child_right = 0;
   1.216 +      _data[_min].in=false;
   1.217 +
   1.218 +      if( -1!=_data[_min].child ) {
   1.219 +        i=_data[_min].child;
   1.220 +        trees.push_back(i);
   1.221 +        _data[i].parent = -1;
   1.222 +        _data[_min].child = -1;
   1.223 +
   1.224 +        int ch=-1;
   1.225 +        while( _data[i].child!=-1 ) {
   1.226 +          ch=_data[i].child;
   1.227 +          if( _data[ch].left_child && i==_data[ch].parent ) {
   1.228 +            break;
   1.229 +          } else {
   1.230 +            if( _data[ch].left_child ) {
   1.231 +              child_right=_data[ch].parent;
   1.232 +              _data[ch].parent = i;
   1.233 +              --_data[i].degree;
   1.234 +            }
   1.235 +            else {
   1.236 +              child_right=ch;
   1.237 +              _data[i].child=-1;
   1.238 +              _data[i].degree=0;
   1.239 +            }
   1.240 +            _data[child_right].parent = -1;
   1.241 +            trees.push_back(child_right);
   1.242 +            i = child_right;
   1.243 +          }
   1.244 +        }
   1.245 +
   1.246 +        int num_child = trees.size();
   1.247 +        int other;
   1.248 +        for( i=0; i<num_child-1; i+=2 ) {
   1.249 +          if ( !_comp(_data[trees[i]].prio, _data[trees[i+1]].prio) ) {
   1.250 +            other=trees[i];
   1.251 +            trees[i]=trees[i+1];
   1.252 +            trees[i+1]=other;
   1.253 +          }
   1.254 +          fuse( trees[i], trees[i+1] );
   1.255 +        }
   1.256 +
   1.257 +        i = (0==(num_child % 2)) ? num_child-2 : num_child-1;
   1.258 +        while(i>=2) {
   1.259 +          if ( _comp(_data[trees[i]].prio, _data[trees[i-2]].prio) ) {
   1.260 +            other=trees[i];
   1.261 +            trees[i]=trees[i-2];
   1.262 +            trees[i-2]=other;
   1.263 +          }
   1.264 +          fuse( trees[i-2], trees[i] );
   1.265 +          i-=2;
   1.266 +        }
   1.267 +        _min = trees[0];
   1.268 +      }
   1.269 +      else {
   1.270 +        _min = _data[_min].child;
   1.271 +      }
   1.272 +
   1.273 +      if (_min >= 0) _data[_min].left_child = false;
   1.274 +      --_num_items;
   1.275 +    }
   1.276 +
   1.277 +    /// \brief Remove the given item from the heap.
   1.278 +    ///
   1.279 +    /// This function removes the given item from the heap if it is
   1.280 +    /// already stored.
   1.281 +    /// \param item The item to delete.
   1.282 +    /// \pre \e item must be in the heap.
   1.283 +    void erase (const Item& item) {
   1.284 +      int i=_iim[item];
   1.285 +      if ( i>=0 && _data[i].in ) {
   1.286 +        decrease( item, _data[_min].prio-1 );
   1.287 +        pop();
   1.288 +      }
   1.289 +    }
   1.290 +
   1.291 +    /// \brief Decrease the priority of an item to the given value.
   1.292 +    ///
   1.293 +    /// This function decreases the priority of an item to the given value.
   1.294 +    /// \param item The item.
   1.295 +    /// \param value The priority.
   1.296 +    /// \pre \e item must be stored in the heap with priority at least \e value.
   1.297 +    void decrease (Item item, const Prio& value) {
   1.298 +      int i=_iim[item];
   1.299 +      _data[i].prio=value;
   1.300 +      int p=_data[i].parent;
   1.301 +
   1.302 +      if( _data[i].left_child && i!=_data[p].child ) {
   1.303 +        p=_data[p].parent;
   1.304 +      }
   1.305 +
   1.306 +      if ( p!=-1 && _comp(value,_data[p].prio) ) {
   1.307 +        cut(i,p);
   1.308 +        if ( _comp(_data[_min].prio,value) ) {
   1.309 +          fuse(_min,i);
   1.310 +        } else {
   1.311 +          fuse(i,_min);
   1.312 +          _min=i;
   1.313 +        }
   1.314 +      }
   1.315 +    }
   1.316 +
   1.317 +    /// \brief Increase the priority of an item to the given value.
   1.318 +    ///
   1.319 +    /// This function increases the priority of an item to the given value.
   1.320 +    /// \param item The item.
   1.321 +    /// \param value The priority.
   1.322 +    /// \pre \e item must be stored in the heap with priority at most \e value.
   1.323 +    void increase (Item item, const Prio& value) {
   1.324 +      erase(item);
   1.325 +      push(item,value);
   1.326 +    }
   1.327 +
   1.328 +    /// \brief Return the state of an item.
   1.329 +    ///
   1.330 +    /// This method returns \c PRE_HEAP if the given item has never
   1.331 +    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
   1.332 +    /// and \c POST_HEAP otherwise.
   1.333 +    /// In the latter case it is possible that the item will get back
   1.334 +    /// to the heap again.
   1.335 +    /// \param item The item.
   1.336 +    State state(const Item &item) const {
   1.337 +      int i=_iim[item];
   1.338 +      if( i>=0 ) {
   1.339 +        if( _data[i].in ) i=0;
   1.340 +        else i=-2;
   1.341 +      }
   1.342 +      return State(i);
   1.343 +    }
   1.344 +
   1.345 +    /// \brief Set the state of an item in the heap.
   1.346 +    ///
   1.347 +    /// This function sets the state of the given item in the heap.
   1.348 +    /// It can be used to manually clear the heap when it is important
   1.349 +    /// to achive better time complexity.
   1.350 +    /// \param i The item.
   1.351 +    /// \param st The state. It should not be \c IN_HEAP.
   1.352 +    void state(const Item& i, State st) {
   1.353 +      switch (st) {
   1.354 +      case POST_HEAP:
   1.355 +      case PRE_HEAP:
   1.356 +        if (state(i) == IN_HEAP) erase(i);
   1.357 +        _iim[i]=st;
   1.358 +        break;
   1.359 +      case IN_HEAP:
   1.360 +        break;
   1.361 +      }
   1.362 +    }
   1.363 +
   1.364 +  private:
   1.365 +
   1.366 +    void cut(int a, int b) {
   1.367 +      int child_a;
   1.368 +      switch (_data[a].degree) {
   1.369 +        case 2:
   1.370 +          child_a = _data[_data[a].child].parent;
   1.371 +          if( _data[a].left_child ) {
   1.372 +            _data[child_a].left_child=true;
   1.373 +            _data[b].child=child_a;
   1.374 +            _data[child_a].parent=_data[a].parent;
   1.375 +          }
   1.376 +          else {
   1.377 +            _data[child_a].left_child=false;
   1.378 +            _data[child_a].parent=b;
   1.379 +            if( a!=_data[b].child )
   1.380 +              _data[_data[b].child].parent=child_a;
   1.381 +            else
   1.382 +              _data[b].child=child_a;
   1.383 +          }
   1.384 +          --_data[a].degree;
   1.385 +          _data[_data[a].child].parent=a;
   1.386 +          break;
   1.387 +
   1.388 +        case 1:
   1.389 +          child_a = _data[a].child;
   1.390 +          if( !_data[child_a].left_child ) {
   1.391 +            --_data[a].degree;
   1.392 +            if( _data[a].left_child ) {
   1.393 +              _data[child_a].left_child=true;
   1.394 +              _data[child_a].parent=_data[a].parent;
   1.395 +              _data[b].child=child_a;
   1.396 +            }
   1.397 +            else {
   1.398 +              _data[child_a].left_child=false;
   1.399 +              _data[child_a].parent=b;
   1.400 +              if( a!=_data[b].child )
   1.401 +                _data[_data[b].child].parent=child_a;
   1.402 +              else
   1.403 +                _data[b].child=child_a;
   1.404 +            }
   1.405 +            _data[a].child=-1;
   1.406 +          }
   1.407 +          else {
   1.408 +            --_data[b].degree;
   1.409 +            if( _data[a].left_child ) {
   1.410 +              _data[b].child =
   1.411 +                (1==_data[b].degree) ? _data[a].parent : -1;
   1.412 +            } else {
   1.413 +              if (1==_data[b].degree)
   1.414 +                _data[_data[b].child].parent=b;
   1.415 +              else
   1.416 +                _data[b].child=-1;
   1.417 +            }
   1.418 +          }
   1.419 +          break;
   1.420 +
   1.421 +        case 0:
   1.422 +          --_data[b].degree;
   1.423 +          if( _data[a].left_child ) {
   1.424 +            _data[b].child =
   1.425 +              (0!=_data[b].degree) ? _data[a].parent : -1;
   1.426 +          } else {
   1.427 +            if( 0!=_data[b].degree )
   1.428 +              _data[_data[b].child].parent=b;
   1.429 +            else
   1.430 +              _data[b].child=-1;
   1.431 +          }
   1.432 +          break;
   1.433 +      }
   1.434 +      _data[a].parent=-1;
   1.435 +      _data[a].left_child=false;
   1.436 +    }
   1.437 +
   1.438 +    void fuse(int a, int b) {
   1.439 +      int child_a = _data[a].child;
   1.440 +      int child_b = _data[b].child;
   1.441 +      _data[a].child=b;
   1.442 +      _data[b].parent=a;
   1.443 +      _data[b].left_child=true;
   1.444 +
   1.445 +      if( -1!=child_a ) {
   1.446 +        _data[b].child=child_a;
   1.447 +        _data[child_a].parent=b;
   1.448 +        _data[child_a].left_child=false;
   1.449 +        ++_data[b].degree;
   1.450 +
   1.451 +        if( -1!=child_b ) {
   1.452 +           _data[b].child=child_b;
   1.453 +           _data[child_b].parent=child_a;
   1.454 +        }
   1.455 +      }
   1.456 +      else { ++_data[a].degree; }
   1.457 +    }
   1.458 +
   1.459 +    class store {
   1.460 +      friend class PairingHeap;
   1.461 +
   1.462 +      Item name;
   1.463 +      int parent;
   1.464 +      int child;
   1.465 +      bool left_child;
   1.466 +      int degree;
   1.467 +      bool in;
   1.468 +      Prio prio;
   1.469 +
   1.470 +      store() : parent(-1), child(-1), left_child(false), degree(0), in(true) {}
   1.471 +    };
   1.472 +  };
   1.473 +
   1.474 +} //namespace lemon
   1.475 +
   1.476 +#endif //LEMON_PAIRING_HEAP_H
   1.477 +