lemon/bin_heap.h
changeset 598 a3402913cffe
parent 440 88ed40ad0d4f
child 584 33c6b6e755cd
equal deleted inserted replaced
3:1b95d0e13262 4:3a0046a8da26
    31 
    31 
    32   ///\ingroup auxdat
    32   ///\ingroup auxdat
    33   ///
    33   ///
    34   ///\brief A Binary Heap implementation.
    34   ///\brief A Binary Heap implementation.
    35   ///
    35   ///
    36   ///This class implements the \e binary \e heap data structure. A \e heap
    36   ///This class implements the \e binary \e heap data structure. 
    37   ///is a data structure for storing items with specified values called \e
    37   /// 
    38   ///priorities in such a way that finding the item with minimum priority is
    38   ///A \e heap is a data structure for storing items with specified values
    39   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
    39   ///called \e priorities in such a way that finding the item with minimum
    40   ///one can change the priority of an item, add or erase an item, etc.
    40   ///priority is efficient. \c Comp specifies the ordering of the priorities.
       
    41   ///In a heap one can change the priority of an item, add or erase an
       
    42   ///item, etc.
    41   ///
    43   ///
    42   ///\tparam _Prio Type of the priority of the items.
    44   ///\tparam PR Type of the priority of the items.
    43   ///\tparam _ItemIntMap A read and writable Item int map, used internally
    45   ///\tparam IM A read and writable item map with int values, used internally
    44   ///to handle the cross references.
    46   ///to handle the cross references.
    45   ///\tparam _Compare A class for the ordering of the priorities. The
    47   ///\tparam Comp A functor class for the ordering of the priorities.
    46   ///default is \c std::less<_Prio>.
    48   ///The default is \c std::less<PR>.
    47   ///
    49   ///
    48   ///\sa FibHeap
    50   ///\sa FibHeap
    49   ///\sa Dijkstra
    51   ///\sa Dijkstra
    50   template <typename _Prio, typename _ItemIntMap,
    52   template <typename PR, typename IM, typename Comp = std::less<PR> >
    51             typename _Compare = std::less<_Prio> >
       
    52   class BinHeap {
    53   class BinHeap {
    53 
    54 
    54   public:
    55   public:
    55     ///\e
    56     ///\e
    56     typedef _ItemIntMap ItemIntMap;
    57     typedef IM ItemIntMap;
    57     ///\e
    58     ///\e
    58     typedef _Prio Prio;
    59     typedef PR Prio;
    59     ///\e
    60     ///\e
    60     typedef typename ItemIntMap::Key Item;
    61     typedef typename ItemIntMap::Key Item;
    61     ///\e
    62     ///\e
    62     typedef std::pair<Item,Prio> Pair;
    63     typedef std::pair<Item,Prio> Pair;
    63     ///\e
    64     ///\e
    64     typedef _Compare Compare;
    65     typedef Comp Compare;
    65 
    66 
    66     /// \brief Type to represent the items states.
    67     /// \brief Type to represent the items states.
    67     ///
    68     ///
    68     /// Each Item element have a state associated to it. It may be "in heap",
    69     /// Each Item element have a state associated to it. It may be "in heap",
    69     /// "pre heap" or "post heap". The latter two are indifferent from the
    70     /// "pre heap" or "post heap". The latter two are indifferent from the
    70     /// heap's point of view, but may be useful to the user.
    71     /// heap's point of view, but may be useful to the user.
    71     ///
    72     ///
    72     /// The ItemIntMap \e should be initialized in such way that it maps
    73     /// The item-int map must be initialized in such way that it assigns
    73     /// PRE_HEAP (-1) to any element to be put in the heap...
    74     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
    74     enum State {
    75     enum State {
    75       IN_HEAP = 0,
    76       IN_HEAP = 0,    ///< \e
    76       PRE_HEAP = -1,
    77       PRE_HEAP = -1,  ///< \e
    77       POST_HEAP = -2
    78       POST_HEAP = -2  ///< \e
    78     };
    79     };
    79 
    80 
    80   private:
    81   private:
    81     std::vector<Pair> data;
    82     std::vector<Pair> _data;
    82     Compare comp;
    83     Compare _comp;
    83     ItemIntMap &iim;
    84     ItemIntMap &_iim;
    84 
    85 
    85   public:
    86   public:
    86     /// \brief The constructor.
    87     /// \brief The constructor.
    87     ///
    88     ///
    88     /// The constructor.
    89     /// The constructor.
    89     /// \param _iim should be given to the constructor, since it is used
    90     /// \param map should be given to the constructor, since it is used
       
    91     /// internally to handle the cross references. The value of the map
       
    92     /// must be \c PRE_HEAP (<tt>-1</tt>) for every item.
       
    93     explicit BinHeap(ItemIntMap &map) : _iim(map) {}
       
    94 
       
    95     /// \brief The constructor.
       
    96     ///
       
    97     /// The constructor.
       
    98     /// \param map should be given to the constructor, since it is used
    90     /// internally to handle the cross references. The value of the map
    99     /// internally to handle the cross references. The value of the map
    91     /// should be PRE_HEAP (-1) for each element.
   100     /// should be PRE_HEAP (-1) for each element.
    92     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
   101     ///
    93 
   102     /// \param comp The comparator function object.
    94     /// \brief The constructor.
   103     BinHeap(ItemIntMap &map, const Compare &comp)
    95     ///
   104       : _iim(map), _comp(comp) {}
    96     /// The constructor.
       
    97     /// \param _iim should be given to the constructor, since it is used
       
    98     /// internally to handle the cross references. The value of the map
       
    99     /// should be PRE_HEAP (-1) for each element.
       
   100     ///
       
   101     /// \param _comp The comparator function object.
       
   102     BinHeap(ItemIntMap &_iim, const Compare &_comp)
       
   103       : iim(_iim), comp(_comp) {}
       
   104 
   105 
   105 
   106 
   106     /// The number of items stored in the heap.
   107     /// The number of items stored in the heap.
   107     ///
   108     ///
   108     /// \brief Returns the number of items stored in the heap.
   109     /// \brief Returns the number of items stored in the heap.
   109     int size() const { return data.size(); }
   110     int size() const { return _data.size(); }
   110 
   111 
   111     /// \brief Checks if the heap stores no items.
   112     /// \brief Checks if the heap stores no items.
   112     ///
   113     ///
   113     /// Returns \c true if and only if the heap stores no items.
   114     /// Returns \c true if and only if the heap stores no items.
   114     bool empty() const { return data.empty(); }
   115     bool empty() const { return _data.empty(); }
   115 
   116 
   116     /// \brief Make empty this heap.
   117     /// \brief Make empty this heap.
   117     ///
   118     ///
   118     /// Make empty this heap. It does not change the cross reference map.
   119     /// Make empty this heap. It does not change the cross reference map.
   119     /// If you want to reuse what is not surely empty you should first clear
   120     /// If you want to reuse what is not surely empty you should first clear
   120     /// the heap and after that you should set the cross reference map for
   121     /// the heap and after that you should set the cross reference map for
   121     /// each item to \c PRE_HEAP.
   122     /// each item to \c PRE_HEAP.
   122     void clear() {
   123     void clear() {
   123       data.clear();
   124       _data.clear();
   124     }
   125     }
   125 
   126 
   126   private:
   127   private:
   127     static int parent(int i) { return (i-1)/2; }
   128     static int parent(int i) { return (i-1)/2; }
   128 
   129 
   129     static int second_child(int i) { return 2*i+2; }
   130     static int second_child(int i) { return 2*i+2; }
   130     bool less(const Pair &p1, const Pair &p2) const {
   131     bool less(const Pair &p1, const Pair &p2) const {
   131       return comp(p1.second, p2.second);
   132       return _comp(p1.second, p2.second);
   132     }
   133     }
   133 
   134 
   134     int bubble_up(int hole, Pair p) {
   135     int bubble_up(int hole, Pair p) {
   135       int par = parent(hole);
   136       int par = parent(hole);
   136       while( hole>0 && less(p,data[par]) ) {
   137       while( hole>0 && less(p,_data[par]) ) {
   137         move(data[par],hole);
   138         move(_data[par],hole);
   138         hole = par;
   139         hole = par;
   139         par = parent(hole);
   140         par = parent(hole);
   140       }
   141       }
   141       move(p, hole);
   142       move(p, hole);
   142       return hole;
   143       return hole;
   143     }
   144     }
   144 
   145 
   145     int bubble_down(int hole, Pair p, int length) {
   146     int bubble_down(int hole, Pair p, int length) {
   146       int child = second_child(hole);
   147       int child = second_child(hole);
   147       while(child < length) {
   148       while(child < length) {
   148         if( less(data[child-1], data[child]) ) {
   149         if( less(_data[child-1], _data[child]) ) {
   149           --child;
   150           --child;
   150         }
   151         }
   151         if( !less(data[child], p) )
   152         if( !less(_data[child], p) )
   152           goto ok;
   153           goto ok;
   153         move(data[child], hole);
   154         move(_data[child], hole);
   154         hole = child;
   155         hole = child;
   155         child = second_child(hole);
   156         child = second_child(hole);
   156       }
   157       }
   157       child--;
   158       child--;
   158       if( child<length && less(data[child], p) ) {
   159       if( child<length && less(_data[child], p) ) {
   159         move(data[child], hole);
   160         move(_data[child], hole);
   160         hole=child;
   161         hole=child;
   161       }
   162       }
   162     ok:
   163     ok:
   163       move(p, hole);
   164       move(p, hole);
   164       return hole;
   165       return hole;
   165     }
   166     }
   166 
   167 
   167     void move(const Pair &p, int i) {
   168     void move(const Pair &p, int i) {
   168       data[i] = p;
   169       _data[i] = p;
   169       iim.set(p.first, i);
   170       _iim.set(p.first, i);
   170     }
   171     }
   171 
   172 
   172   public:
   173   public:
   173     /// \brief Insert a pair of item and priority into the heap.
   174     /// \brief Insert a pair of item and priority into the heap.
   174     ///
   175     ///
   175     /// Adds \c p.first to the heap with priority \c p.second.
   176     /// Adds \c p.first to the heap with priority \c p.second.
   176     /// \param p The pair to insert.
   177     /// \param p The pair to insert.
   177     void push(const Pair &p) {
   178     void push(const Pair &p) {
   178       int n = data.size();
   179       int n = _data.size();
   179       data.resize(n+1);
   180       _data.resize(n+1);
   180       bubble_up(n, p);
   181       bubble_up(n, p);
   181     }
   182     }
   182 
   183 
   183     /// \brief Insert an item into the heap with the given heap.
   184     /// \brief Insert an item into the heap with the given heap.
   184     ///
   185     ///
   191     ///
   192     ///
   192     /// This method returns the item with minimum priority relative to \c
   193     /// This method returns the item with minimum priority relative to \c
   193     /// Compare.
   194     /// Compare.
   194     /// \pre The heap must be nonempty.
   195     /// \pre The heap must be nonempty.
   195     Item top() const {
   196     Item top() const {
   196       return data[0].first;
   197       return _data[0].first;
   197     }
   198     }
   198 
   199 
   199     /// \brief Returns the minimum priority relative to \c Compare.
   200     /// \brief Returns the minimum priority relative to \c Compare.
   200     ///
   201     ///
   201     /// It returns the minimum priority relative to \c Compare.
   202     /// It returns the minimum priority relative to \c Compare.
   202     /// \pre The heap must be nonempty.
   203     /// \pre The heap must be nonempty.
   203     Prio prio() const {
   204     Prio prio() const {
   204       return data[0].second;
   205       return _data[0].second;
   205     }
   206     }
   206 
   207 
   207     /// \brief Deletes the item with minimum priority relative to \c Compare.
   208     /// \brief Deletes the item with minimum priority relative to \c Compare.
   208     ///
   209     ///
   209     /// This method deletes the item with minimum priority relative to \c
   210     /// This method deletes the item with minimum priority relative to \c
   210     /// Compare from the heap.
   211     /// Compare from the heap.
   211     /// \pre The heap must be non-empty.
   212     /// \pre The heap must be non-empty.
   212     void pop() {
   213     void pop() {
   213       int n = data.size()-1;
   214       int n = _data.size()-1;
   214       iim.set(data[0].first, POST_HEAP);
   215       _iim.set(_data[0].first, POST_HEAP);
   215       if (n > 0) {
   216       if (n > 0) {
   216         bubble_down(0, data[n], n);
   217         bubble_down(0, _data[n], n);
   217       }
   218       }
   218       data.pop_back();
   219       _data.pop_back();
   219     }
   220     }
   220 
   221 
   221     /// \brief Deletes \c i from the heap.
   222     /// \brief Deletes \c i from the heap.
   222     ///
   223     ///
   223     /// This method deletes item \c i from the heap.
   224     /// This method deletes item \c i from the heap.
   224     /// \param i The item to erase.
   225     /// \param i The item to erase.
   225     /// \pre The item should be in the heap.
   226     /// \pre The item should be in the heap.
   226     void erase(const Item &i) {
   227     void erase(const Item &i) {
   227       int h = iim[i];
   228       int h = _iim[i];
   228       int n = data.size()-1;
   229       int n = _data.size()-1;
   229       iim.set(data[h].first, POST_HEAP);
   230       _iim.set(_data[h].first, POST_HEAP);
   230       if( h < n ) {
   231       if( h < n ) {
   231         if ( bubble_up(h, data[n]) == h) {
   232         if ( bubble_up(h, _data[n]) == h) {
   232           bubble_down(h, data[n], n);
   233           bubble_down(h, _data[n], n);
   233         }
   234         }
   234       }
   235       }
   235       data.pop_back();
   236       _data.pop_back();
   236     }
   237     }
   237 
   238 
   238 
   239 
   239     /// \brief Returns the priority of \c i.
   240     /// \brief Returns the priority of \c i.
   240     ///
   241     ///
   241     /// This function returns the priority of item \c i.
   242     /// This function returns the priority of item \c i.
       
   243     /// \param i The item.
   242     /// \pre \c i must be in the heap.
   244     /// \pre \c i must be in the heap.
   243     /// \param i The item.
       
   244     Prio operator[](const Item &i) const {
   245     Prio operator[](const Item &i) const {
   245       int idx = iim[i];
   246       int idx = _iim[i];
   246       return data[idx].second;
   247       return _data[idx].second;
   247     }
   248     }
   248 
   249 
   249     /// \brief \c i gets to the heap with priority \c p independently
   250     /// \brief \c i gets to the heap with priority \c p independently
   250     /// if \c i was already there.
   251     /// if \c i was already there.
   251     ///
   252     ///
   252     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   253     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   253     /// in the heap and sets the priority of \c i to \c p otherwise.
   254     /// in the heap and sets the priority of \c i to \c p otherwise.
   254     /// \param i The item.
   255     /// \param i The item.
   255     /// \param p The priority.
   256     /// \param p The priority.
   256     void set(const Item &i, const Prio &p) {
   257     void set(const Item &i, const Prio &p) {
   257       int idx = iim[i];
   258       int idx = _iim[i];
   258       if( idx < 0 ) {
   259       if( idx < 0 ) {
   259         push(i,p);
   260         push(i,p);
   260       }
   261       }
   261       else if( comp(p, data[idx].second) ) {
   262       else if( _comp(p, _data[idx].second) ) {
   262         bubble_up(idx, Pair(i,p));
   263         bubble_up(idx, Pair(i,p));
   263       }
   264       }
   264       else {
   265       else {
   265         bubble_down(idx, Pair(i,p), data.size());
   266         bubble_down(idx, Pair(i,p), _data.size());
   266       }
   267       }
   267     }
   268     }
   268 
   269 
   269     /// \brief Decreases the priority of \c i to \c p.
   270     /// \brief Decreases the priority of \c i to \c p.
   270     ///
   271     ///
   271     /// This method decreases the priority of item \c i to \c p.
   272     /// This method decreases the priority of item \c i to \c p.
       
   273     /// \param i The item.
       
   274     /// \param p The priority.
   272     /// \pre \c i must be stored in the heap with priority at least \c
   275     /// \pre \c i must be stored in the heap with priority at least \c
   273     /// p relative to \c Compare.
   276     /// p relative to \c Compare.
       
   277     void decrease(const Item &i, const Prio &p) {
       
   278       int idx = _iim[i];
       
   279       bubble_up(idx, Pair(i,p));
       
   280     }
       
   281 
       
   282     /// \brief Increases the priority of \c i to \c p.
       
   283     ///
       
   284     /// This method sets the priority of item \c i to \c p.
   274     /// \param i The item.
   285     /// \param i The item.
   275     /// \param p The priority.
   286     /// \param p The priority.
   276     void decrease(const Item &i, const Prio &p) {
       
   277       int idx = iim[i];
       
   278       bubble_up(idx, Pair(i,p));
       
   279     }
       
   280 
       
   281     /// \brief Increases the priority of \c i to \c p.
       
   282     ///
       
   283     /// This method sets the priority of item \c i to \c p.
       
   284     /// \pre \c i must be stored in the heap with priority at most \c
   287     /// \pre \c i must be stored in the heap with priority at most \c
   285     /// p relative to \c Compare.
   288     /// p relative to \c Compare.
   286     /// \param i The item.
       
   287     /// \param p The priority.
       
   288     void increase(const Item &i, const Prio &p) {
   289     void increase(const Item &i, const Prio &p) {
   289       int idx = iim[i];
   290       int idx = _iim[i];
   290       bubble_down(idx, Pair(i,p), data.size());
   291       bubble_down(idx, Pair(i,p), _data.size());
   291     }
   292     }
   292 
   293 
   293     /// \brief Returns if \c item is in, has already been in, or has
   294     /// \brief Returns if \c item is in, has already been in, or has
   294     /// never been in the heap.
   295     /// never been in the heap.
   295     ///
   296     ///
   297     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   298     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   298     /// otherwise. In the latter case it is possible that \c item will
   299     /// otherwise. In the latter case it is possible that \c item will
   299     /// get back to the heap again.
   300     /// get back to the heap again.
   300     /// \param i The item.
   301     /// \param i The item.
   301     State state(const Item &i) const {
   302     State state(const Item &i) const {
   302       int s = iim[i];
   303       int s = _iim[i];
   303       if( s>=0 )
   304       if( s>=0 )
   304         s=0;
   305         s=0;
   305       return State(s);
   306       return State(s);
   306     }
   307     }
   307 
   308 
   317       case POST_HEAP:
   318       case POST_HEAP:
   318       case PRE_HEAP:
   319       case PRE_HEAP:
   319         if (state(i) == IN_HEAP) {
   320         if (state(i) == IN_HEAP) {
   320           erase(i);
   321           erase(i);
   321         }
   322         }
   322         iim[i] = st;
   323         _iim[i] = st;
   323         break;
   324         break;
   324       case IN_HEAP:
   325       case IN_HEAP:
   325         break;
   326         break;
   326       }
   327       }
   327     }
   328     }
   331     /// The \c i item is replaced with \c j item. The \c i item should
   332     /// The \c i item is replaced with \c j item. The \c i item should
   332     /// be in the heap, while the \c j should be out of the heap. The
   333     /// be in the heap, while the \c j should be out of the heap. The
   333     /// \c i item will out of the heap and \c j will be in the heap
   334     /// \c i item will out of the heap and \c j will be in the heap
   334     /// with the same prioriority as prevoiusly the \c i item.
   335     /// with the same prioriority as prevoiusly the \c i item.
   335     void replace(const Item& i, const Item& j) {
   336     void replace(const Item& i, const Item& j) {
   336       int idx = iim[i];
   337       int idx = _iim[i];
   337       iim.set(i, iim[j]);
   338       _iim.set(i, _iim[j]);
   338       iim.set(j, idx);
   339       _iim.set(j, idx);
   339       data[idx].first = j;
   340       _data[idx].first = j;
   340     }
   341     }
   341 
   342 
   342   }; // class BinHeap
   343   }; // class BinHeap
   343 
   344 
   344 } // namespace lemon
   345 } // namespace lemon