lemon/binom_heap.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 20 Feb 2010 18:39:03 +0100
changeset 839 f3bc4e9b5f3a
parent 703 bb3392fe91f2
permissions -rw-r--r--
New heuristics for MCF algorithms (#340)
and some implementation improvements.

- A useful heuristic is added to NetworkSimplex to make the
initial pivots faster.
- A powerful global update heuristic is added to CostScaling
and the implementation is reworked with various improvements.
- Better relabeling in CostScaling to improve numerical stability
and make the code faster.
- A small improvement is made in CapacityScaling for better
delta computation.
- Add notes to the classes about the usage of vector<char> instead
of vector<bool> for efficiency reasons.
kpeter@703
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@701
     2
 *
kpeter@703
     3
 * This file is a part of LEMON, a generic C++ optimization library.
kpeter@701
     4
 *
kpeter@703
     5
 * Copyright (C) 2003-2009
kpeter@701
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@701
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@701
     8
 *
kpeter@701
     9
 * Permission to use, modify and distribute this software is granted
kpeter@701
    10
 * provided that this copyright notice appears in all copies. For
kpeter@701
    11
 * precise terms see the accompanying LICENSE file.
kpeter@701
    12
 *
kpeter@701
    13
 * This software is provided "AS IS" with no warranty of any kind,
kpeter@701
    14
 * express or implied, and with no claim as to its suitability for any
kpeter@701
    15
 * purpose.
kpeter@701
    16
 *
kpeter@701
    17
 */
kpeter@701
    18
kpeter@701
    19
#ifndef LEMON_BINOM_HEAP_H
kpeter@701
    20
#define LEMON_BINOM_HEAP_H
kpeter@701
    21
kpeter@701
    22
///\file
kpeter@703
    23
///\ingroup heaps
kpeter@701
    24
///\brief Binomial Heap implementation.
kpeter@701
    25
kpeter@701
    26
#include <vector>
kpeter@703
    27
#include <utility>
kpeter@701
    28
#include <functional>
kpeter@701
    29
#include <lemon/math.h>
kpeter@701
    30
#include <lemon/counter.h>
kpeter@701
    31
kpeter@701
    32
namespace lemon {
kpeter@701
    33
kpeter@703
    34
  /// \ingroup heaps
kpeter@701
    35
  ///
kpeter@703
    36
  ///\brief Binomial heap data structure.
kpeter@701
    37
  ///
kpeter@703
    38
  /// This class implements the \e binomial \e heap data structure.
kpeter@703
    39
  /// It fully conforms to the \ref concepts::Heap "heap concept".
kpeter@701
    40
  ///
kpeter@703
    41
  /// The methods \ref increase() and \ref erase() are not efficient
kpeter@703
    42
  /// in a binomial heap. In case of many calls of these operations,
kpeter@703
    43
  /// it is better to use other heap structure, e.g. \ref BinHeap
kpeter@703
    44
  /// "binary heap".
kpeter@701
    45
  ///
kpeter@703
    46
  /// \tparam PR Type of the priorities of the items.
kpeter@703
    47
  /// \tparam IM A read-writable item map with \c int values, used
kpeter@703
    48
  /// internally to handle the cross references.
kpeter@703
    49
  /// \tparam CMP A functor class for comparing the priorities.
kpeter@703
    50
  /// The default is \c std::less<PR>.
kpeter@701
    51
#ifdef DOXYGEN
kpeter@703
    52
  template <typename PR, typename IM, typename CMP>
kpeter@701
    53
#else
kpeter@703
    54
  template <typename PR, typename IM, typename CMP = std::less<PR> >
kpeter@701
    55
#endif
kpeter@701
    56
  class BinomHeap {
kpeter@701
    57
  public:
kpeter@703
    58
    /// Type of the item-int map.
kpeter@703
    59
    typedef IM ItemIntMap;
kpeter@703
    60
    /// Type of the priorities.
kpeter@703
    61
    typedef PR Prio;
kpeter@703
    62
    /// Type of the items stored in the heap.
kpeter@701
    63
    typedef typename ItemIntMap::Key Item;
kpeter@703
    64
    /// Functor type for comparing the priorities.
kpeter@703
    65
    typedef CMP Compare;
kpeter@703
    66
kpeter@703
    67
    /// \brief Type to represent the states of the items.
kpeter@703
    68
    ///
kpeter@703
    69
    /// Each item has a state associated to it. It can be "in heap",
kpeter@703
    70
    /// "pre-heap" or "post-heap". The latter two are indifferent from the
kpeter@703
    71
    /// heap's point of view, but may be useful to the user.
kpeter@703
    72
    ///
kpeter@703
    73
    /// The item-int map must be initialized in such way that it assigns
kpeter@703
    74
    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
kpeter@703
    75
    enum State {
kpeter@703
    76
      IN_HEAP = 0,    ///< = 0.
kpeter@703
    77
      PRE_HEAP = -1,  ///< = -1.
kpeter@703
    78
      POST_HEAP = -2  ///< = -2.
kpeter@703
    79
    };
kpeter@701
    80
kpeter@701
    81
  private:
kpeter@707
    82
    class Store;
kpeter@701
    83
kpeter@707
    84
    std::vector<Store> _data;
kpeter@703
    85
    int _min, _head;
kpeter@703
    86
    ItemIntMap &_iim;
kpeter@703
    87
    Compare _comp;
kpeter@703
    88
    int _num_items;
kpeter@701
    89
kpeter@701
    90
  public:
kpeter@703
    91
    /// \brief Constructor.
kpeter@703
    92
    ///
kpeter@703
    93
    /// Constructor.
kpeter@703
    94
    /// \param map A map that assigns \c int values to the items.
kpeter@703
    95
    /// It is used internally to handle the cross references.
kpeter@703
    96
    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@703
    97
    explicit BinomHeap(ItemIntMap &map)
kpeter@703
    98
      : _min(0), _head(-1), _iim(map), _num_items(0) {}
kpeter@701
    99
kpeter@703
   100
    /// \brief Constructor.
kpeter@701
   101
    ///
kpeter@703
   102
    /// Constructor.
kpeter@703
   103
    /// \param map A map that assigns \c int values to the items.
kpeter@703
   104
    /// It is used internally to handle the cross references.
kpeter@703
   105
    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@703
   106
    /// \param comp The function object used for comparing the priorities.
kpeter@703
   107
    BinomHeap(ItemIntMap &map, const Compare &comp)
kpeter@703
   108
      : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {}
kpeter@701
   109
kpeter@701
   110
    /// \brief The number of items stored in the heap.
kpeter@701
   111
    ///
kpeter@703
   112
    /// This function returns the number of items stored in the heap.
kpeter@703
   113
    int size() const { return _num_items; }
kpeter@701
   114
kpeter@703
   115
    /// \brief Check if the heap is empty.
kpeter@701
   116
    ///
kpeter@703
   117
    /// This function returns \c true if the heap is empty.
kpeter@703
   118
    bool empty() const { return _num_items==0; }
kpeter@701
   119
kpeter@703
   120
    /// \brief Make the heap empty.
kpeter@701
   121
    ///
kpeter@703
   122
    /// This functon makes the heap empty.
kpeter@703
   123
    /// It does not change the cross reference map. If you want to reuse
kpeter@703
   124
    /// a heap that is not surely empty, you should first clear it and
kpeter@703
   125
    /// then you should set the cross reference map to \c PRE_HEAP
kpeter@703
   126
    /// for each item.
kpeter@701
   127
    void clear() {
kpeter@703
   128
      _data.clear(); _min=0; _num_items=0; _head=-1;
kpeter@701
   129
    }
kpeter@701
   130
kpeter@703
   131
    /// \brief Set the priority of an item or insert it, if it is
kpeter@703
   132
    /// not stored in the heap.
kpeter@701
   133
    ///
kpeter@703
   134
    /// This method sets the priority of the given item if it is
kpeter@703
   135
    /// already stored in the heap. Otherwise it inserts the given
kpeter@703
   136
    /// item into the heap with the given priority.
kpeter@703
   137
    /// \param item The item.
kpeter@703
   138
    /// \param value The priority.
kpeter@701
   139
    void set (const Item& item, const Prio& value) {
kpeter@703
   140
      int i=_iim[item];
kpeter@703
   141
      if ( i >= 0 && _data[i].in ) {
kpeter@703
   142
        if ( _comp(value, _data[i].prio) ) decrease(item, value);
kpeter@703
   143
        if ( _comp(_data[i].prio, value) ) increase(item, value);
kpeter@701
   144
      } else push(item, value);
kpeter@701
   145
    }
kpeter@701
   146
kpeter@703
   147
    /// \brief Insert an item into the heap with the given priority.
kpeter@701
   148
    ///
kpeter@703
   149
    /// This function inserts the given item into the heap with the
kpeter@703
   150
    /// given priority.
kpeter@703
   151
    /// \param item The item to insert.
kpeter@703
   152
    /// \param value The priority of the item.
kpeter@703
   153
    /// \pre \e item must not be stored in the heap.
kpeter@701
   154
    void push (const Item& item, const Prio& value) {
kpeter@703
   155
      int i=_iim[item];
kpeter@701
   156
      if ( i<0 ) {
kpeter@703
   157
        int s=_data.size();
kpeter@703
   158
        _iim.set( item,s );
kpeter@707
   159
        Store st;
kpeter@701
   160
        st.name=item;
kpeter@707
   161
        st.prio=value;
kpeter@703
   162
        _data.push_back(st);
kpeter@701
   163
        i=s;
kpeter@701
   164
      }
kpeter@701
   165
      else {
kpeter@703
   166
        _data[i].parent=_data[i].right_neighbor=_data[i].child=-1;
kpeter@703
   167
        _data[i].degree=0;
kpeter@703
   168
        _data[i].in=true;
kpeter@707
   169
        _data[i].prio=value;
kpeter@701
   170
      }
kpeter@701
   171
kpeter@707
   172
      if( 0==_num_items ) {
kpeter@707
   173
        _head=i;
kpeter@707
   174
        _min=i;
kpeter@707
   175
      } else {
kpeter@707
   176
        merge(i);
kpeter@707
   177
        if( _comp(_data[i].prio, _data[_min].prio) ) _min=i;
kpeter@707
   178
      }
kpeter@703
   179
      ++_num_items;
kpeter@701
   180
    }
kpeter@701
   181
kpeter@703
   182
    /// \brief Return the item having minimum priority.
kpeter@701
   183
    ///
kpeter@703
   184
    /// This function returns the item having minimum priority.
kpeter@703
   185
    /// \pre The heap must be non-empty.
kpeter@703
   186
    Item top() const { return _data[_min].name; }
kpeter@701
   187
kpeter@703
   188
    /// \brief The minimum priority.
kpeter@701
   189
    ///
kpeter@703
   190
    /// This function returns the minimum priority.
kpeter@703
   191
    /// \pre The heap must be non-empty.
kpeter@703
   192
    Prio prio() const { return _data[_min].prio; }
kpeter@701
   193
kpeter@703
   194
    /// \brief The priority of the given item.
kpeter@701
   195
    ///
kpeter@703
   196
    /// This function returns the priority of the given item.
kpeter@703
   197
    /// \param item The item.
kpeter@703
   198
    /// \pre \e item must be in the heap.
kpeter@701
   199
    const Prio& operator[](const Item& item) const {
kpeter@703
   200
      return _data[_iim[item]].prio;
kpeter@701
   201
    }
kpeter@701
   202
kpeter@703
   203
    /// \brief Remove the item having minimum priority.
kpeter@701
   204
    ///
kpeter@703
   205
    /// This function removes the item having minimum priority.
kpeter@701
   206
    /// \pre The heap must be non-empty.
kpeter@701
   207
    void pop() {
kpeter@703
   208
      _data[_min].in=false;
kpeter@701
   209
kpeter@701
   210
      int head_child=-1;
kpeter@703
   211
      if ( _data[_min].child!=-1 ) {
kpeter@703
   212
        int child=_data[_min].child;
kpeter@701
   213
        int neighb;
kpeter@701
   214
        while( child!=-1 ) {
kpeter@703
   215
          neighb=_data[child].right_neighbor;
kpeter@703
   216
          _data[child].parent=-1;
kpeter@707
   217
          _data[child].right_neighbor=head_child;
kpeter@701
   218
          head_child=child;
kpeter@701
   219
          child=neighb;
kpeter@701
   220
        }
kpeter@701
   221
      }
kpeter@701
   222
kpeter@707
   223
      if ( _data[_head].right_neighbor==-1 ) {
kpeter@707
   224
        // there was only one root
kpeter@703
   225
        _head=head_child;
kpeter@701
   226
      }
kpeter@701
   227
      else {
kpeter@707
   228
        // there were more roots
kpeter@703
   229
        if( _head!=_min )  { unlace(_min); }
kpeter@703
   230
        else { _head=_data[_head].right_neighbor; }
kpeter@701
   231
        merge(head_child);
kpeter@701
   232
      }
kpeter@703
   233
      _min=findMin();
kpeter@703
   234
      --_num_items;
kpeter@701
   235
    }
kpeter@701
   236
kpeter@703
   237
    /// \brief Remove the given item from the heap.
kpeter@701
   238
    ///
kpeter@703
   239
    /// This function removes the given item from the heap if it is
kpeter@703
   240
    /// already stored.
kpeter@703
   241
    /// \param item The item to delete.
kpeter@703
   242
    /// \pre \e item must be in the heap.
kpeter@701
   243
    void erase (const Item& item) {
kpeter@703
   244
      int i=_iim[item];
kpeter@703
   245
      if ( i >= 0 && _data[i].in ) {
kpeter@703
   246
        decrease( item, _data[_min].prio-1 );
kpeter@701
   247
        pop();
kpeter@701
   248
      }
kpeter@701
   249
    }
kpeter@701
   250
kpeter@703
   251
    /// \brief Decrease the priority of an item to the given value.
kpeter@701
   252
    ///
kpeter@703
   253
    /// This function decreases the priority of an item to the given value.
kpeter@703
   254
    /// \param item The item.
kpeter@703
   255
    /// \param value The priority.
kpeter@703
   256
    /// \pre \e item must be stored in the heap with priority at least \e value.
kpeter@701
   257
    void decrease (Item item, const Prio& value) {
kpeter@703
   258
      int i=_iim[item];
kpeter@707
   259
      int p=_data[i].parent;
kpeter@707
   260
      _data[i].prio=value;
kpeter@707
   261
      
kpeter@707
   262
      while( p!=-1 && _comp(value, _data[p].prio) ) {
kpeter@707
   263
        _data[i].name=_data[p].name;
kpeter@707
   264
        _data[i].prio=_data[p].prio;
kpeter@707
   265
        _data[p].name=item;
kpeter@707
   266
        _data[p].prio=value;
kpeter@707
   267
        _iim[_data[i].name]=i;
kpeter@707
   268
        i=p;
kpeter@707
   269
        p=_data[p].parent;
kpeter@701
   270
      }
kpeter@707
   271
      _iim[item]=i;
kpeter@707
   272
      if ( _comp(value, _data[_min].prio) ) _min=i;
kpeter@701
   273
    }
kpeter@701
   274
kpeter@703
   275
    /// \brief Increase the priority of an item to the given value.
kpeter@701
   276
    ///
kpeter@703
   277
    /// This function increases the priority of an item to the given value.
kpeter@703
   278
    /// \param item The item.
kpeter@703
   279
    /// \param value The priority.
kpeter@703
   280
    /// \pre \e item must be stored in the heap with priority at most \e value.
kpeter@701
   281
    void increase (Item item, const Prio& value) {
kpeter@701
   282
      erase(item);
kpeter@701
   283
      push(item, value);
kpeter@701
   284
    }
kpeter@701
   285
kpeter@703
   286
    /// \brief Return the state of an item.
kpeter@701
   287
    ///
kpeter@703
   288
    /// This method returns \c PRE_HEAP if the given item has never
kpeter@703
   289
    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@703
   290
    /// and \c POST_HEAP otherwise.
kpeter@703
   291
    /// In the latter case it is possible that the item will get back
kpeter@703
   292
    /// to the heap again.
kpeter@703
   293
    /// \param item The item.
kpeter@701
   294
    State state(const Item &item) const {
kpeter@703
   295
      int i=_iim[item];
kpeter@701
   296
      if( i>=0 ) {
kpeter@703
   297
        if ( _data[i].in ) i=0;
kpeter@701
   298
        else i=-2;
kpeter@701
   299
      }
kpeter@701
   300
      return State(i);
kpeter@701
   301
    }
kpeter@701
   302
kpeter@703
   303
    /// \brief Set the state of an item in the heap.
kpeter@701
   304
    ///
kpeter@703
   305
    /// This function sets the state of the given item in the heap.
kpeter@703
   306
    /// It can be used to manually clear the heap when it is important
kpeter@703
   307
    /// to achive better time complexity.
kpeter@701
   308
    /// \param i The item.
kpeter@701
   309
    /// \param st The state. It should not be \c IN_HEAP.
kpeter@701
   310
    void state(const Item& i, State st) {
kpeter@701
   311
      switch (st) {
kpeter@701
   312
      case POST_HEAP:
kpeter@701
   313
      case PRE_HEAP:
kpeter@701
   314
        if (state(i) == IN_HEAP) {
kpeter@701
   315
          erase(i);
kpeter@701
   316
        }
kpeter@703
   317
        _iim[i] = st;
kpeter@701
   318
        break;
kpeter@701
   319
      case IN_HEAP:
kpeter@701
   320
        break;
kpeter@701
   321
      }
kpeter@701
   322
    }
kpeter@701
   323
kpeter@701
   324
  private:
kpeter@707
   325
    
kpeter@707
   326
    // Find the minimum of the roots
kpeter@703
   327
    int findMin() {
kpeter@707
   328
      if( _head!=-1 ) {
kpeter@707
   329
        int min_loc=_head, min_val=_data[_head].prio;
kpeter@707
   330
        for( int x=_data[_head].right_neighbor; x!=-1;
kpeter@707
   331
             x=_data[x].right_neighbor ) {
kpeter@703
   332
          if( _comp( _data[x].prio,min_val ) ) {
kpeter@703
   333
            min_val=_data[x].prio;
kpeter@701
   334
            min_loc=x;
kpeter@701
   335
          }
kpeter@701
   336
        }
kpeter@707
   337
        return min_loc;
kpeter@701
   338
      }
kpeter@707
   339
      else return -1;
kpeter@701
   340
    }
kpeter@701
   341
kpeter@707
   342
    // Merge the heap with another heap starting at the given position
kpeter@701
   343
    void merge(int a) {
kpeter@707
   344
      if( _head==-1 || a==-1 ) return;
kpeter@707
   345
      if( _data[a].right_neighbor==-1 &&
kpeter@707
   346
          _data[a].degree<=_data[_head].degree ) {
kpeter@707
   347
        _data[a].right_neighbor=_head;
kpeter@707
   348
        _head=a;
kpeter@707
   349
      } else {
kpeter@707
   350
        interleave(a);
kpeter@707
   351
      }
kpeter@707
   352
      if( _data[_head].right_neighbor==-1 ) return;
kpeter@707
   353
      
kpeter@703
   354
      int x=_head;
kpeter@707
   355
      int x_prev=-1, x_next=_data[x].right_neighbor;
kpeter@707
   356
      while( x_next!=-1 ) {
kpeter@707
   357
        if( _data[x].degree!=_data[x_next].degree ||
kpeter@707
   358
            ( _data[x_next].right_neighbor!=-1 &&
kpeter@707
   359
              _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {
kpeter@707
   360
          x_prev=x;
kpeter@707
   361
          x=x_next;
kpeter@707
   362
        }
kpeter@707
   363
        else {
kpeter@707
   364
          if( _comp(_data[x_next].prio,_data[x].prio) ) {
kpeter@707
   365
            if( x_prev==-1 ) {
kpeter@707
   366
              _head=x_next;
kpeter@707
   367
            } else {
kpeter@707
   368
              _data[x_prev].right_neighbor=x_next;
kpeter@707
   369
            }
kpeter@707
   370
            fuse(x,x_next);
kpeter@701
   371
            x=x_next;
kpeter@701
   372
          }
kpeter@701
   373
          else {
kpeter@707
   374
            _data[x].right_neighbor=_data[x_next].right_neighbor;
kpeter@707
   375
            fuse(x_next,x);
kpeter@701
   376
          }
kpeter@701
   377
        }
kpeter@707
   378
        x_next=_data[x].right_neighbor;
kpeter@701
   379
      }
kpeter@701
   380
    }
kpeter@701
   381
kpeter@707
   382
    // Interleave the elements of the given list into the list of the roots
kpeter@701
   383
    void interleave(int a) {
kpeter@707
   384
      int p=_head, q=a;
kpeter@707
   385
      int curr=_data.size();
kpeter@707
   386
      _data.push_back(Store());
kpeter@707
   387
      
kpeter@707
   388
      while( p!=-1 || q!=-1 ) {
kpeter@707
   389
        if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) {
kpeter@707
   390
          _data[curr].right_neighbor=p;
kpeter@707
   391
          curr=p;
kpeter@707
   392
          p=_data[p].right_neighbor;
kpeter@701
   393
        }
kpeter@701
   394
        else {
kpeter@707
   395
          _data[curr].right_neighbor=q;
kpeter@707
   396
          curr=q;
kpeter@707
   397
          q=_data[q].right_neighbor;
kpeter@701
   398
        }
kpeter@701
   399
      }
kpeter@707
   400
      
kpeter@707
   401
      _head=_data.back().right_neighbor;
kpeter@707
   402
      _data.pop_back();
kpeter@701
   403
    }
kpeter@701
   404
kpeter@707
   405
    // Lace node a under node b
kpeter@701
   406
    void fuse(int a, int b) {
kpeter@703
   407
      _data[a].parent=b;
kpeter@703
   408
      _data[a].right_neighbor=_data[b].child;
kpeter@703
   409
      _data[b].child=a;
kpeter@701
   410
kpeter@703
   411
      ++_data[b].degree;
kpeter@701
   412
    }
kpeter@701
   413
kpeter@707
   414
    // Unlace node a (if it has siblings)
kpeter@701
   415
    void unlace(int a) {
kpeter@703
   416
      int neighb=_data[a].right_neighbor;
kpeter@703
   417
      int other=_head;
kpeter@701
   418
kpeter@703
   419
      while( _data[other].right_neighbor!=a )
kpeter@703
   420
        other=_data[other].right_neighbor;
kpeter@703
   421
      _data[other].right_neighbor=neighb;
kpeter@701
   422
    }
kpeter@701
   423
kpeter@701
   424
  private:
kpeter@701
   425
kpeter@707
   426
    class Store {
kpeter@701
   427
      friend class BinomHeap;
kpeter@701
   428
kpeter@701
   429
      Item name;
kpeter@701
   430
      int parent;
kpeter@701
   431
      int right_neighbor;
kpeter@701
   432
      int child;
kpeter@701
   433
      int degree;
kpeter@701
   434
      bool in;
kpeter@701
   435
      Prio prio;
kpeter@701
   436
kpeter@707
   437
      Store() : parent(-1), right_neighbor(-1), child(-1), degree(0),
kpeter@707
   438
        in(true) {}
kpeter@701
   439
    };
kpeter@701
   440
  };
kpeter@701
   441
kpeter@701
   442
} //namespace lemon
kpeter@701
   443
kpeter@701
   444
#endif //LEMON_BINOM_HEAP_H
kpeter@701
   445