lemon/fib_heap.h
changeset 802 994c7df296c9
parent 681 532697c9fa53
child 709 0747f332c478
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/fib_heap.h	Thu Dec 10 17:05:35 2009 +0100
     1.3 @@ -0,0 +1,468 @@
     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_FIB_HEAP_H
    1.23 +#define LEMON_FIB_HEAP_H
    1.24 +
    1.25 +///\file
    1.26 +///\ingroup auxdat
    1.27 +///\brief Fibonacci Heap implementation.
    1.28 +
    1.29 +#include <vector>
    1.30 +#include <functional>
    1.31 +#include <lemon/math.h>
    1.32 +
    1.33 +namespace lemon {
    1.34 +
    1.35 +  /// \ingroup auxdat
    1.36 +  ///
    1.37 +  ///\brief Fibonacci Heap.
    1.38 +  ///
    1.39 +  ///This class implements the \e Fibonacci \e heap data structure. A \e heap
    1.40 +  ///is a data structure for storing items with specified values called \e
    1.41 +  ///priorities in such a way that finding the item with minimum priority is
    1.42 +  ///efficient. \c CMP specifies the ordering of the priorities. In a heap
    1.43 +  ///one can change the priority of an item, add or erase an item, etc.
    1.44 +  ///
    1.45 +  ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
    1.46 +  ///heap. In case of many calls to these operations, it is better to use a
    1.47 +  ///\ref BinHeap "binary heap".
    1.48 +  ///
    1.49 +  ///\param PRIO Type of the priority of the items.
    1.50 +  ///\param IM A read and writable Item int map, used internally
    1.51 +  ///to handle the cross references.
    1.52 +  ///\param CMP A class for the ordering of the priorities. The
    1.53 +  ///default is \c std::less<PRIO>.
    1.54 +  ///
    1.55 +  ///\sa BinHeap
    1.56 +  ///\sa Dijkstra
    1.57 +#ifdef DOXYGEN
    1.58 +  template <typename PRIO, typename IM, typename CMP>
    1.59 +#else
    1.60 +  template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
    1.61 +#endif
    1.62 +  class FibHeap {
    1.63 +  public:
    1.64 +    ///\e
    1.65 +    typedef IM ItemIntMap;
    1.66 +    ///\e
    1.67 +    typedef PRIO Prio;
    1.68 +    ///\e
    1.69 +    typedef typename ItemIntMap::Key Item;
    1.70 +    ///\e
    1.71 +    typedef std::pair<Item,Prio> Pair;
    1.72 +    ///\e
    1.73 +    typedef CMP Compare;
    1.74 +
    1.75 +  private:
    1.76 +    class Store;
    1.77 +
    1.78 +    std::vector<Store> _data;
    1.79 +    int _minimum;
    1.80 +    ItemIntMap &_iim;
    1.81 +    Compare _comp;
    1.82 +    int _num;
    1.83 +
    1.84 +  public:
    1.85 +
    1.86 +    /// \brief Type to represent the items states.
    1.87 +    ///
    1.88 +    /// Each Item element have a state associated to it. It may be "in heap",
    1.89 +    /// "pre heap" or "post heap". The latter two are indifferent from the
    1.90 +    /// heap's point of view, but may be useful to the user.
    1.91 +    ///
    1.92 +    /// The item-int map must be initialized in such way that it assigns
    1.93 +    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    1.94 +    enum State {
    1.95 +      IN_HEAP = 0,    ///< = 0.
    1.96 +      PRE_HEAP = -1,  ///< = -1.
    1.97 +      POST_HEAP = -2  ///< = -2.
    1.98 +    };
    1.99 +
   1.100 +    /// \brief The constructor
   1.101 +    ///
   1.102 +    /// \c map should be given to the constructor, since it is
   1.103 +    ///   used internally to handle the cross references.
   1.104 +    explicit FibHeap(ItemIntMap &map)
   1.105 +      : _minimum(0), _iim(map), _num() {}
   1.106 +
   1.107 +    /// \brief The constructor
   1.108 +    ///
   1.109 +    /// \c map should be given to the constructor, since it is used
   1.110 +    /// internally to handle the cross references. \c comp is an
   1.111 +    /// object for ordering of the priorities.
   1.112 +    FibHeap(ItemIntMap &map, const Compare &comp)
   1.113 +      : _minimum(0), _iim(map), _comp(comp), _num() {}
   1.114 +
   1.115 +    /// \brief The number of items stored in the heap.
   1.116 +    ///
   1.117 +    /// Returns the number of items stored in the heap.
   1.118 +    int size() const { return _num; }
   1.119 +
   1.120 +    /// \brief Checks if the heap stores no items.
   1.121 +    ///
   1.122 +    ///   Returns \c true if and only if the heap stores no items.
   1.123 +    bool empty() const { return _num==0; }
   1.124 +
   1.125 +    /// \brief Make empty this heap.
   1.126 +    ///
   1.127 +    /// Make empty this heap. It does not change the cross reference
   1.128 +    /// map.  If you want to reuse a heap what is not surely empty you
   1.129 +    /// should first clear the heap and after that you should set the
   1.130 +    /// cross reference map for each item to \c PRE_HEAP.
   1.131 +    void clear() {
   1.132 +      _data.clear(); _minimum = 0; _num = 0;
   1.133 +    }
   1.134 +
   1.135 +    /// \brief \c item gets to the heap with priority \c value independently
   1.136 +    /// if \c item was already there.
   1.137 +    ///
   1.138 +    /// This method calls \ref push(\c item, \c value) if \c item is not
   1.139 +    /// stored in the heap and it calls \ref decrease(\c item, \c value) or
   1.140 +    /// \ref increase(\c item, \c value) otherwise.
   1.141 +    void set (const Item& item, const Prio& value) {
   1.142 +      int i=_iim[item];
   1.143 +      if ( i >= 0 && _data[i].in ) {
   1.144 +        if ( _comp(value, _data[i].prio) ) decrease(item, value);
   1.145 +        if ( _comp(_data[i].prio, value) ) increase(item, value);
   1.146 +      } else push(item, value);
   1.147 +    }
   1.148 +
   1.149 +    /// \brief Adds \c item to the heap with priority \c value.
   1.150 +    ///
   1.151 +    /// Adds \c item to the heap with priority \c value.
   1.152 +    /// \pre \c item must not be stored in the heap.
   1.153 +    void push (const Item& item, const Prio& value) {
   1.154 +      int i=_iim[item];
   1.155 +      if ( i < 0 ) {
   1.156 +        int s=_data.size();
   1.157 +        _iim.set( item, s );
   1.158 +        Store st;
   1.159 +        st.name=item;
   1.160 +        _data.push_back(st);
   1.161 +        i=s;
   1.162 +      } else {
   1.163 +        _data[i].parent=_data[i].child=-1;
   1.164 +        _data[i].degree=0;
   1.165 +        _data[i].in=true;
   1.166 +        _data[i].marked=false;
   1.167 +      }
   1.168 +
   1.169 +      if ( _num ) {
   1.170 +        _data[_data[_minimum].right_neighbor].left_neighbor=i;
   1.171 +        _data[i].right_neighbor=_data[_minimum].right_neighbor;
   1.172 +        _data[_minimum].right_neighbor=i;
   1.173 +        _data[i].left_neighbor=_minimum;
   1.174 +        if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
   1.175 +      } else {
   1.176 +        _data[i].right_neighbor=_data[i].left_neighbor=i;
   1.177 +        _minimum=i;
   1.178 +      }
   1.179 +      _data[i].prio=value;
   1.180 +      ++_num;
   1.181 +    }
   1.182 +
   1.183 +    /// \brief Returns the item with minimum priority relative to \c Compare.
   1.184 +    ///
   1.185 +    /// This method returns the item with minimum priority relative to \c
   1.186 +    /// Compare.
   1.187 +    /// \pre The heap must be nonempty.
   1.188 +    Item top() const { return _data[_minimum].name; }
   1.189 +
   1.190 +    /// \brief Returns the minimum priority relative to \c Compare.
   1.191 +    ///
   1.192 +    /// It returns the minimum priority relative to \c Compare.
   1.193 +    /// \pre The heap must be nonempty.
   1.194 +    const Prio& prio() const { return _data[_minimum].prio; }
   1.195 +
   1.196 +    /// \brief Returns the priority of \c item.
   1.197 +    ///
   1.198 +    /// It returns the priority of \c item.
   1.199 +    /// \pre \c item must be in the heap.
   1.200 +    const Prio& operator[](const Item& item) const {
   1.201 +      return _data[_iim[item]].prio;
   1.202 +    }
   1.203 +
   1.204 +    /// \brief Deletes the item with minimum priority relative to \c Compare.
   1.205 +    ///
   1.206 +    /// This method deletes the item with minimum priority relative to \c
   1.207 +    /// Compare from the heap.
   1.208 +    /// \pre The heap must be non-empty.
   1.209 +    void pop() {
   1.210 +      /*The first case is that there are only one root.*/
   1.211 +      if ( _data[_minimum].left_neighbor==_minimum ) {
   1.212 +        _data[_minimum].in=false;
   1.213 +        if ( _data[_minimum].degree!=0 ) {
   1.214 +          makeroot(_data[_minimum].child);
   1.215 +          _minimum=_data[_minimum].child;
   1.216 +          balance();
   1.217 +        }
   1.218 +      } else {
   1.219 +        int right=_data[_minimum].right_neighbor;
   1.220 +        unlace(_minimum);
   1.221 +        _data[_minimum].in=false;
   1.222 +        if ( _data[_minimum].degree > 0 ) {
   1.223 +          int left=_data[_minimum].left_neighbor;
   1.224 +          int child=_data[_minimum].child;
   1.225 +          int last_child=_data[child].left_neighbor;
   1.226 +
   1.227 +          makeroot(child);
   1.228 +
   1.229 +          _data[left].right_neighbor=child;
   1.230 +          _data[child].left_neighbor=left;
   1.231 +          _data[right].left_neighbor=last_child;
   1.232 +          _data[last_child].right_neighbor=right;
   1.233 +        }
   1.234 +        _minimum=right;
   1.235 +        balance();
   1.236 +      } // the case where there are more roots
   1.237 +      --_num;
   1.238 +    }
   1.239 +
   1.240 +    /// \brief Deletes \c item from the heap.
   1.241 +    ///
   1.242 +    /// This method deletes \c item from the heap, if \c item was already
   1.243 +    /// stored in the heap. It is quite inefficient in Fibonacci heaps.
   1.244 +    void erase (const Item& item) {
   1.245 +      int i=_iim[item];
   1.246 +
   1.247 +      if ( i >= 0 && _data[i].in ) {
   1.248 +        if ( _data[i].parent!=-1 ) {
   1.249 +          int p=_data[i].parent;
   1.250 +          cut(i,p);
   1.251 +          cascade(p);
   1.252 +        }
   1.253 +        _minimum=i;     //As if its prio would be -infinity
   1.254 +        pop();
   1.255 +      }
   1.256 +    }
   1.257 +
   1.258 +    /// \brief Decreases the priority of \c item to \c value.
   1.259 +    ///
   1.260 +    /// This method decreases the priority of \c item to \c value.
   1.261 +    /// \pre \c item must be stored in the heap with priority at least \c
   1.262 +    ///   value relative to \c Compare.
   1.263 +    void decrease (Item item, const Prio& value) {
   1.264 +      int i=_iim[item];
   1.265 +      _data[i].prio=value;
   1.266 +      int p=_data[i].parent;
   1.267 +
   1.268 +      if ( p!=-1 && _comp(value, _data[p].prio) ) {
   1.269 +        cut(i,p);
   1.270 +        cascade(p);
   1.271 +      }
   1.272 +      if ( _comp(value, _data[_minimum].prio) ) _minimum=i;
   1.273 +    }
   1.274 +
   1.275 +    /// \brief Increases the priority of \c item to \c value.
   1.276 +    ///
   1.277 +    /// This method sets the priority of \c item to \c value. Though
   1.278 +    /// there is no precondition on the priority of \c item, this
   1.279 +    /// method should be used only if it is indeed necessary to increase
   1.280 +    /// (relative to \c Compare) the priority of \c item, because this
   1.281 +    /// method is inefficient.
   1.282 +    void increase (Item item, const Prio& value) {
   1.283 +      erase(item);
   1.284 +      push(item, value);
   1.285 +    }
   1.286 +
   1.287 +
   1.288 +    /// \brief Returns if \c item is in, has already been in, or has never
   1.289 +    /// been in the heap.
   1.290 +    ///
   1.291 +    /// This method returns PRE_HEAP if \c item has never been in the
   1.292 +    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   1.293 +    /// otherwise. In the latter case it is possible that \c item will
   1.294 +    /// get back to the heap again.
   1.295 +    State state(const Item &item) const {
   1.296 +      int i=_iim[item];
   1.297 +      if( i>=0 ) {
   1.298 +        if ( _data[i].in ) i=0;
   1.299 +        else i=-2;
   1.300 +      }
   1.301 +      return State(i);
   1.302 +    }
   1.303 +
   1.304 +    /// \brief Sets the state of the \c item in the heap.
   1.305 +    ///
   1.306 +    /// Sets the state of the \c item in the heap. It can be used to
   1.307 +    /// manually clear the heap when it is important to achive the
   1.308 +    /// better time _complexity.
   1.309 +    /// \param i The item.
   1.310 +    /// \param st The state. It should not be \c IN_HEAP.
   1.311 +    void state(const Item& i, State st) {
   1.312 +      switch (st) {
   1.313 +      case POST_HEAP:
   1.314 +      case PRE_HEAP:
   1.315 +        if (state(i) == IN_HEAP) {
   1.316 +          erase(i);
   1.317 +        }
   1.318 +        _iim[i] = st;
   1.319 +        break;
   1.320 +      case IN_HEAP:
   1.321 +        break;
   1.322 +      }
   1.323 +    }
   1.324 +
   1.325 +  private:
   1.326 +
   1.327 +    void balance() {
   1.328 +
   1.329 +      int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
   1.330 +
   1.331 +      std::vector<int> A(maxdeg,-1);
   1.332 +
   1.333 +      /*
   1.334 +       *Recall that now minimum does not point to the minimum prio element.
   1.335 +       *We set minimum to this during balance().
   1.336 +       */
   1.337 +      int anchor=_data[_minimum].left_neighbor;
   1.338 +      int next=_minimum;
   1.339 +      bool end=false;
   1.340 +
   1.341 +      do {
   1.342 +        int active=next;
   1.343 +        if ( anchor==active ) end=true;
   1.344 +        int d=_data[active].degree;
   1.345 +        next=_data[active].right_neighbor;
   1.346 +
   1.347 +        while (A[d]!=-1) {
   1.348 +          if( _comp(_data[active].prio, _data[A[d]].prio) ) {
   1.349 +            fuse(active,A[d]);
   1.350 +          } else {
   1.351 +            fuse(A[d],active);
   1.352 +            active=A[d];
   1.353 +          }
   1.354 +          A[d]=-1;
   1.355 +          ++d;
   1.356 +        }
   1.357 +        A[d]=active;
   1.358 +      } while ( !end );
   1.359 +
   1.360 +
   1.361 +      while ( _data[_minimum].parent >=0 )
   1.362 +        _minimum=_data[_minimum].parent;
   1.363 +      int s=_minimum;
   1.364 +      int m=_minimum;
   1.365 +      do {
   1.366 +        if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
   1.367 +        s=_data[s].right_neighbor;
   1.368 +      } while ( s != m );
   1.369 +    }
   1.370 +
   1.371 +    void makeroot(int c) {
   1.372 +      int s=c;
   1.373 +      do {
   1.374 +        _data[s].parent=-1;
   1.375 +        s=_data[s].right_neighbor;
   1.376 +      } while ( s != c );
   1.377 +    }
   1.378 +
   1.379 +    void cut(int a, int b) {
   1.380 +      /*
   1.381 +       *Replacing a from the children of b.
   1.382 +       */
   1.383 +      --_data[b].degree;
   1.384 +
   1.385 +      if ( _data[b].degree !=0 ) {
   1.386 +        int child=_data[b].child;
   1.387 +        if ( child==a )
   1.388 +          _data[b].child=_data[child].right_neighbor;
   1.389 +        unlace(a);
   1.390 +      }
   1.391 +
   1.392 +
   1.393 +      /*Lacing a to the roots.*/
   1.394 +      int right=_data[_minimum].right_neighbor;
   1.395 +      _data[_minimum].right_neighbor=a;
   1.396 +      _data[a].left_neighbor=_minimum;
   1.397 +      _data[a].right_neighbor=right;
   1.398 +      _data[right].left_neighbor=a;
   1.399 +
   1.400 +      _data[a].parent=-1;
   1.401 +      _data[a].marked=false;
   1.402 +    }
   1.403 +
   1.404 +    void cascade(int a) {
   1.405 +      if ( _data[a].parent!=-1 ) {
   1.406 +        int p=_data[a].parent;
   1.407 +
   1.408 +        if ( _data[a].marked==false ) _data[a].marked=true;
   1.409 +        else {
   1.410 +          cut(a,p);
   1.411 +          cascade(p);
   1.412 +        }
   1.413 +      }
   1.414 +    }
   1.415 +
   1.416 +    void fuse(int a, int b) {
   1.417 +      unlace(b);
   1.418 +
   1.419 +      /*Lacing b under a.*/
   1.420 +      _data[b].parent=a;
   1.421 +
   1.422 +      if (_data[a].degree==0) {
   1.423 +        _data[b].left_neighbor=b;
   1.424 +        _data[b].right_neighbor=b;
   1.425 +        _data[a].child=b;
   1.426 +      } else {
   1.427 +        int child=_data[a].child;
   1.428 +        int last_child=_data[child].left_neighbor;
   1.429 +        _data[child].left_neighbor=b;
   1.430 +        _data[b].right_neighbor=child;
   1.431 +        _data[last_child].right_neighbor=b;
   1.432 +        _data[b].left_neighbor=last_child;
   1.433 +      }
   1.434 +
   1.435 +      ++_data[a].degree;
   1.436 +
   1.437 +      _data[b].marked=false;
   1.438 +    }
   1.439 +
   1.440 +    /*
   1.441 +     *It is invoked only if a has siblings.
   1.442 +     */
   1.443 +    void unlace(int a) {
   1.444 +      int leftn=_data[a].left_neighbor;
   1.445 +      int rightn=_data[a].right_neighbor;
   1.446 +      _data[leftn].right_neighbor=rightn;
   1.447 +      _data[rightn].left_neighbor=leftn;
   1.448 +    }
   1.449 +
   1.450 +
   1.451 +    class Store {
   1.452 +      friend class FibHeap;
   1.453 +
   1.454 +      Item name;
   1.455 +      int parent;
   1.456 +      int left_neighbor;
   1.457 +      int right_neighbor;
   1.458 +      int child;
   1.459 +      int degree;
   1.460 +      bool marked;
   1.461 +      bool in;
   1.462 +      Prio prio;
   1.463 +
   1.464 +      Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
   1.465 +    };
   1.466 +  };
   1.467 +
   1.468 +} //namespace lemon
   1.469 +
   1.470 +#endif //LEMON_FIB_HEAP_H
   1.471 +