lemon/bin_heap.h
changeset 2547 f393a8162688
parent 2546 b5eba564bb60
child 2548 a3ba22ebccc6
equal deleted inserted replaced
13:8a5bb5b89a25 14:b6db6581cf03
    37   ///is a data structure for storing items with specified values called \e
    37   ///is a data structure for storing items with specified values called \e
    38   ///priorities in such a way that finding the item with minimum priority is
    38   ///priorities in such a way that finding the item with minimum priority is
    39   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
    39   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
    40   ///one can change the priority of an item, add or erase an item, etc.
    40   ///one can change the priority of an item, add or erase an item, etc.
    41   ///
    41   ///
    42   ///\param Prio Type of the priority of the items.
    42   ///\param _Prio Type of the priority of the items.
    43   ///\param ItemIntMap A read and writable Item int map, used internally
    43   ///\param _ItemIntMap A read and writable Item int map, used internally
    44   ///to handle the cross references.
    44   ///to handle the cross references.
    45   ///\param Compare A class for the ordering of the priorities. The
    45   ///\param _Compare A class for the ordering of the priorities. The
    46   ///default is \c std::less<Prio>.
    46   ///default is \c std::less<_Prio>.
    47   ///
    47   ///
    48   ///\sa FibHeap
    48   ///\sa FibHeap
    49   ///\sa Dijkstra
    49   ///\sa Dijkstra
    50   template <typename Prio, typename ItemIntMap,
    50   template <typename _Prio, typename _ItemIntMap,
    51 	    typename Compare = std::less<Prio> >
    51 	    typename _Compare = std::less<_Prio> >
    52   class BinHeap {
    52   class BinHeap {
    53 
    53 
    54   public:
    54   public:
    55     typedef typename ItemIntMap::Key         ItemType;
    55     typedef _ItemIntMap ItemIntMap;
    56     typedef Prio                             PrioType;
    56     typedef _Prio Prio;
    57     typedef std::pair<ItemType,PrioType>     PairType;
    57     typedef typename ItemIntMap::Key Item;
    58     typedef ItemIntMap                       ItemIntMapType;
    58     typedef std::pair<Item,Prio> Pair;
    59     typedef Compare                          PrioCompare;
    59     typedef _Compare Compare;
    60 
    60 
    61     /// \brief Type to represent the items states.
    61     /// \brief Type to represent the items states.
    62     ///
    62     ///
    63     /// Each Item element have a state associated to it. It may be "in heap",
    63     /// Each Item element have a state associated to it. It may be "in heap",
    64     /// "pre heap" or "post heap". The latter two are indifferent from the
    64     /// "pre heap" or "post heap". The latter two are indifferent from the
    65     /// heap's point of view, but may be useful to the user.
    65     /// heap's point of view, but may be useful to the user.
    66     ///
    66     ///
    67     /// The ItemIntMap \e should be initialized in such way that it maps
    67     /// The ItemIntMap \e should be initialized in such way that it maps
    68     /// PRE_HEAP (-1) to any element to be put in the heap...
    68     /// PRE_HEAP (-1) to any element to be put in the heap...
    69     enum state_enum {
    69     enum State {
    70       IN_HEAP = 0,
    70       IN_HEAP = 0,
    71       PRE_HEAP = -1,
    71       PRE_HEAP = -1,
    72       POST_HEAP = -2
    72       POST_HEAP = -2
    73     };
    73     };
    74 
    74 
    75   private:
    75   private:
    76     std::vector<PairType> data;
    76     std::vector<Pair> data;
    77     Compare comp;
    77     Compare comp;
    78     ItemIntMap &iim;
    78     ItemIntMap &iim;
    79 
    79 
    80   public:
    80   public:
    81     /// \brief The constructor.
    81     /// \brief The constructor.
   120 
   120 
   121   private:
   121   private:
   122     static int parent(int i) { return (i-1)/2; }
   122     static int parent(int i) { return (i-1)/2; }
   123 
   123 
   124     static int second_child(int i) { return 2*i+2; }
   124     static int second_child(int i) { return 2*i+2; }
   125     bool less(const PairType &p1, const PairType &p2) const {
   125     bool less(const Pair &p1, const Pair &p2) const {
   126       return comp(p1.second, p2.second);
   126       return comp(p1.second, p2.second);
   127     }
   127     }
   128 
   128 
   129     int bubble_up(int hole, PairType p) {
   129     int bubble_up(int hole, Pair p) {
   130       int par = parent(hole);
   130       int par = parent(hole);
   131       while( hole>0 && less(p,data[par]) ) {
   131       while( hole>0 && less(p,data[par]) ) {
   132 	move(data[par],hole);
   132 	move(data[par],hole);
   133 	hole = par;
   133 	hole = par;
   134 	par = parent(hole);
   134 	par = parent(hole);
   135       }
   135       }
   136       move(p, hole);
   136       move(p, hole);
   137       return hole;
   137       return hole;
   138     }
   138     }
   139 
   139 
   140     int bubble_down(int hole, PairType p, int length) {
   140     int bubble_down(int hole, Pair p, int length) {
   141       int child = second_child(hole);
   141       int child = second_child(hole);
   142       while(child < length) {
   142       while(child < length) {
   143 	if( less(data[child-1], data[child]) ) {
   143 	if( less(data[child-1], data[child]) ) {
   144 	  --child;
   144 	  --child;
   145 	}
   145 	}
   157     ok:
   157     ok:
   158       move(p, hole);
   158       move(p, hole);
   159       return hole;
   159       return hole;
   160     }
   160     }
   161 
   161 
   162     void move(const PairType &p, int i) {
   162     void move(const Pair &p, int i) {
   163       data[i] = p;
   163       data[i] = p;
   164       iim.set(p.first, i);
   164       iim.set(p.first, i);
   165     }
   165     }
   166 
   166 
   167   public:
   167   public:
   168     /// \brief Insert a pair of item and priority into the heap.
   168     /// \brief Insert a pair of item and priority into the heap.
   169     ///
   169     ///
   170     /// Adds \c p.first to the heap with priority \c p.second.
   170     /// Adds \c p.first to the heap with priority \c p.second.
   171     /// \param p The pair to insert.
   171     /// \param p The pair to insert.
   172     void push(const PairType &p) {
   172     void push(const Pair &p) {
   173       int n = data.size();
   173       int n = data.size();
   174       data.resize(n+1);
   174       data.resize(n+1);
   175       bubble_up(n, p);
   175       bubble_up(n, p);
   176     }
   176     }
   177 
   177 
   178     /// \brief Insert an item into the heap with the given heap.
   178     /// \brief Insert an item into the heap with the given heap.
   179     ///    
   179     ///    
   180     /// Adds \c i to the heap with priority \c p. 
   180     /// Adds \c i to the heap with priority \c p. 
   181     /// \param i The item to insert.
   181     /// \param i The item to insert.
   182     /// \param p The priority of the item.
   182     /// \param p The priority of the item.
   183     void push(const ItemType &i, const Prio &p) { push(PairType(i,p)); }
   183     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
   184 
   184 
   185     /// \brief Returns the item with minimum priority relative to \c Compare.
   185     /// \brief Returns the item with minimum priority relative to \c Compare.
   186     ///
   186     ///
   187     /// This method returns the item with minimum priority relative to \c
   187     /// This method returns the item with minimum priority relative to \c
   188     /// Compare.  
   188     /// Compare.  
   189     /// \pre The heap must be nonempty.  
   189     /// \pre The heap must be nonempty.  
   190     ItemType top() const {
   190     Item top() const {
   191       return data[0].first;
   191       return data[0].first;
   192     }
   192     }
   193 
   193 
   194     /// \brief Returns the minimum priority relative to \c Compare.
   194     /// \brief Returns the minimum priority relative to \c Compare.
   195     ///
   195     ///
   216     /// \brief Deletes \c i from the heap.
   216     /// \brief Deletes \c i from the heap.
   217     ///
   217     ///
   218     /// This method deletes item \c i from the heap.
   218     /// This method deletes item \c i from the heap.
   219     /// \param i The item to erase.
   219     /// \param i The item to erase.
   220     /// \pre The item should be in the heap.
   220     /// \pre The item should be in the heap.
   221     void erase(const ItemType &i) {
   221     void erase(const Item &i) {
   222       int h = iim[i];
   222       int h = iim[i];
   223       int n = data.size()-1;
   223       int n = data.size()-1;
   224       iim.set(data[h].first, POST_HEAP);
   224       iim.set(data[h].first, POST_HEAP);
   225       if( h < n ) {
   225       if( h < n ) {
   226 	if ( bubble_up(h, data[n]) == h) {
   226 	if ( bubble_up(h, data[n]) == h) {
   234     /// \brief Returns the priority of \c i.
   234     /// \brief Returns the priority of \c i.
   235     ///
   235     ///
   236     /// This function returns the priority of item \c i.  
   236     /// This function returns the priority of item \c i.  
   237     /// \pre \c i must be in the heap.
   237     /// \pre \c i must be in the heap.
   238     /// \param i The item.
   238     /// \param i The item.
   239     Prio operator[](const ItemType &i) const {
   239     Prio operator[](const Item &i) const {
   240       int idx = iim[i];
   240       int idx = iim[i];
   241       return data[idx].second;
   241       return data[idx].second;
   242     }
   242     }
   243 
   243 
   244     /// \brief \c i gets to the heap with priority \c p independently 
   244     /// \brief \c i gets to the heap with priority \c p independently 
   246     ///
   246     ///
   247     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   247     /// This method calls \ref push(\c i, \c p) if \c i is not stored
   248     /// in the heap and sets the priority of \c i to \c p otherwise.
   248     /// in the heap and sets the priority of \c i to \c p otherwise.
   249     /// \param i The item.
   249     /// \param i The item.
   250     /// \param p The priority.
   250     /// \param p The priority.
   251     void set(const ItemType &i, const Prio &p) {
   251     void set(const Item &i, const Prio &p) {
   252       int idx = iim[i];
   252       int idx = iim[i];
   253       if( idx < 0 ) {
   253       if( idx < 0 ) {
   254 	push(i,p);
   254 	push(i,p);
   255       }
   255       }
   256       else if( comp(p, data[idx].second) ) {
   256       else if( comp(p, data[idx].second) ) {
   257 	bubble_up(idx, PairType(i,p));
   257 	bubble_up(idx, Pair(i,p));
   258       }
   258       }
   259       else {
   259       else {
   260 	bubble_down(idx, PairType(i,p), data.size());
   260 	bubble_down(idx, Pair(i,p), data.size());
   261       }
   261       }
   262     }
   262     }
   263 
   263 
   264     /// \brief Decreases the priority of \c i to \c p.
   264     /// \brief Decreases the priority of \c i to \c p.
   265     ///
   265     ///
   266     /// This method decreases the priority of item \c i to \c p.
   266     /// This method decreases the priority of item \c i to \c p.
   267     /// \pre \c i must be stored in the heap with priority at least \c
   267     /// \pre \c i must be stored in the heap with priority at least \c
   268     /// p relative to \c Compare.
   268     /// p relative to \c Compare.
   269     /// \param i The item.
   269     /// \param i The item.
   270     /// \param p The priority.
   270     /// \param p The priority.
   271     void decrease(const ItemType &i, const Prio &p) {
   271     void decrease(const Item &i, const Prio &p) {
   272       int idx = iim[i];
   272       int idx = iim[i];
   273       bubble_up(idx, PairType(i,p));
   273       bubble_up(idx, Pair(i,p));
   274     }
   274     }
   275     
   275     
   276     /// \brief Increases the priority of \c i to \c p.
   276     /// \brief Increases the priority of \c i to \c p.
   277     ///
   277     ///
   278     /// This method sets the priority of item \c i to \c p. 
   278     /// This method sets the priority of item \c i to \c p. 
   279     /// \pre \c i must be stored in the heap with priority at most \c
   279     /// \pre \c i must be stored in the heap with priority at most \c
   280     /// p relative to \c Compare.
   280     /// p relative to \c Compare.
   281     /// \param i The item.
   281     /// \param i The item.
   282     /// \param p The priority.
   282     /// \param p The priority.
   283     void increase(const ItemType &i, const Prio &p) {
   283     void increase(const Item &i, const Prio &p) {
   284       int idx = iim[i];
   284       int idx = iim[i];
   285       bubble_down(idx, PairType(i,p), data.size());
   285       bubble_down(idx, Pair(i,p), data.size());
   286     }
   286     }
   287 
   287 
   288     /// \brief Returns if \c item is in, has already been in, or has 
   288     /// \brief Returns if \c item is in, has already been in, or has 
   289     /// never been in the heap.
   289     /// never been in the heap.
   290     ///
   290     ///
   291     /// This method returns PRE_HEAP if \c item has never been in the
   291     /// This method returns PRE_HEAP if \c item has never been in the
   292     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   292     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   293     /// otherwise. In the latter case it is possible that \c item will
   293     /// otherwise. In the latter case it is possible that \c item will
   294     /// get back to the heap again.
   294     /// get back to the heap again.
   295     /// \param i The item.
   295     /// \param i The item.
   296     state_enum state(const ItemType &i) const {
   296     State state(const Item &i) const {
   297       int s = iim[i];
   297       int s = iim[i];
   298       if( s>=0 )
   298       if( s>=0 )
   299 	s=0;
   299 	s=0;
   300       return state_enum(s);
   300       return State(s);
   301     }
   301     }
   302 
   302 
   303     /// \brief Sets the state of the \c item in the heap.
   303     /// \brief Sets the state of the \c item in the heap.
   304     ///
   304     ///
   305     /// Sets the state of the \c item in the heap. It can be used to
   305     /// Sets the state of the \c item in the heap. It can be used to
   306     /// manually clear the heap when it is important to achive the
   306     /// manually clear the heap when it is important to achive the
   307     /// better time complexity.
   307     /// better time complexity.
   308     /// \param i The item.
   308     /// \param i The item.
   309     /// \param st The state. It should not be \c IN_HEAP. 
   309     /// \param st The state. It should not be \c IN_HEAP. 
   310     void state(const ItemType& i, state_enum st) {
   310     void state(const Item& i, State st) {
   311       switch (st) {
   311       switch (st) {
   312       case POST_HEAP:
   312       case POST_HEAP:
   313       case PRE_HEAP:
   313       case PRE_HEAP:
   314         if (state(i) == IN_HEAP) {
   314         if (state(i) == IN_HEAP) {
   315           erase(i);
   315           erase(i);