diff --git a/lemon/radix_heap.h b/lemon/radix_heap.h --- a/lemon/radix_heap.h +++ b/lemon/radix_heap.h @@ -19,9 +19,9 @@ #ifndef LEMON_RADIX_HEAP_H #define LEMON_RADIX_HEAP_H -///\ingroup auxdat +///\ingroup heaps ///\file -///\brief Radix Heap implementation. +///\brief Radix heap implementation. #include #include @@ -29,56 +29,54 @@ namespace lemon { - /// \ingroup auxdata + /// \ingroup heaps /// - /// \brief A Radix Heap implementation. + /// \brief Radix heap data structure. /// - /// This class implements the \e radix \e heap data structure. A \e heap - /// is a data structure for storing items with specified values called \e - /// priorities in such a way that finding the item with minimum priority is - /// efficient. This heap type can store only items with \e int priority. - /// In a heap one can change the priority of an item, add or erase an - /// item, but the priority cannot be decreased under the last removed - /// item's priority. + /// This class implements the \e radix \e heap data structure. + /// It practically conforms to the \ref concepts::Heap "heap concept", + /// but it has some limitations due its special implementation. + /// The type of the priorities must be \c int and the priority of an + /// item cannot be decreased under the priority of the last removed item. /// - /// \param IM A read and writable Item int map, used internally - /// to handle the cross references. - /// - /// \see BinHeap - /// \see Dijkstra + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. template class RadixHeap { public: - typedef typename IM::Key Item; + + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. typedef int Prio; - typedef IM ItemIntMap; + /// Type of the items stored in the heap. + typedef typename ItemIntMap::Key Item; /// \brief Exception thrown by RadixHeap. /// - /// This Exception is thrown when a smaller priority - /// is inserted into the \e RadixHeap then the last time erased. + /// This exception is thrown when an item is inserted into a + /// RadixHeap with a priority smaller than the last erased one. /// \see RadixHeap - - class UnderFlowPriorityError : public Exception { + class PriorityUnderflowError : public Exception { public: virtual const char* what() const throw() { - return "lemon::RadixHeap::UnderFlowPriorityError"; + return "lemon::RadixHeap::PriorityUnderflowError"; } }; - /// \brief Type to represent the items states. + /// \brief Type to represent the states of the items. /// - /// Each Item element have a state associated to it. It may be "in heap", - /// "pre heap" or "post heap". The latter two are indifferent from the + /// Each item has a state associated to it. It can be "in heap", + /// "pre-heap" or "post-heap". The latter two are indifferent from the /// heap's point of view, but may be useful to the user. /// - /// The ItemIntMap \e should be initialized in such way that it maps - /// PRE_HEAP (-1) to any element to be put in the heap... + /// The item-int map must be initialized in such way that it assigns + /// \c PRE_HEAP (-1) to any element to be put in the heap. enum State { - IN_HEAP = 0, - PRE_HEAP = -1, - POST_HEAP = -2 + IN_HEAP = 0, ///< = 0. + PRE_HEAP = -1, ///< = -1. + POST_HEAP = -2 ///< = -2. }; private: @@ -96,52 +94,55 @@ RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} }; - std::vector data; - std::vector boxes; + std::vector _data; + std::vector _boxes; ItemIntMap &_iim; + public: - public: - /// \brief The constructor. + /// \brief Constructor. /// - /// The constructor. - /// - /// \param map It should be given to the constructor, since it is used - /// internally to handle the cross references. The value of the map - /// should be PRE_HEAP (-1) for each element. - /// - /// \param minimal The initial minimal value of the heap. - /// \param capacity It determines the initial capacity of the heap. - RadixHeap(ItemIntMap &map, int minimal = 0, int capacity = 0) - : _iim(map) { - boxes.push_back(RadixBox(minimal, 1)); - boxes.push_back(RadixBox(minimal + 1, 1)); - while (lower(boxes.size() - 1, capacity + minimal - 1)) { + /// Constructor. + /// \param map A map that assigns \c int values to the items. + /// It is used internally to handle the cross references. + /// The assigned value must be \c PRE_HEAP (-1) for each item. + /// \param minimum The initial minimum value of the heap. + /// \param capacity The initial capacity of the heap. + RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0) + : _iim(map) + { + _boxes.push_back(RadixBox(minimum, 1)); + _boxes.push_back(RadixBox(minimum + 1, 1)); + while (lower(_boxes.size() - 1, capacity + minimum - 1)) { extend(); } } - /// The number of items stored in the heap. + /// \brief The number of items stored in the heap. /// - /// \brief Returns the number of items stored in the heap. - int size() const { return data.size(); } - /// \brief Checks if the heap stores no items. + /// This function returns the number of items stored in the heap. + int size() const { return _data.size(); } + + /// \brief Check if the heap is empty. /// - /// Returns \c true if and only if the heap stores no items. - bool empty() const { return data.empty(); } + /// This function returns \c true if the heap is empty. + bool empty() const { return _data.empty(); } - /// \brief Make empty this heap. + /// \brief Make the heap empty. /// - /// Make empty this heap. It does not change the cross reference - /// map. If you want to reuse a heap what is not surely empty you - /// should first clear the heap and after that you should set the - /// cross reference map for each item to \c PRE_HEAP. - void clear(int minimal = 0, int capacity = 0) { - data.clear(); boxes.clear(); - boxes.push_back(RadixBox(minimal, 1)); - boxes.push_back(RadixBox(minimal + 1, 1)); - while (lower(boxes.size() - 1, capacity + minimal - 1)) { + /// This functon makes the heap empty. + /// It does not change the cross reference map. If you want to reuse + /// a heap that is not surely empty, you should first clear it and + /// then you should set the cross reference map to \c PRE_HEAP + /// for each item. + /// \param minimum The minimum value of the heap. + /// \param capacity The capacity of the heap. + void clear(int minimum = 0, int capacity = 0) { + _data.clear(); _boxes.clear(); + _boxes.push_back(RadixBox(minimum, 1)); + _boxes.push_back(RadixBox(minimum + 1, 1)); + while (lower(_boxes.size() - 1, capacity + minimum - 1)) { extend(); } } @@ -149,255 +150,259 @@ private: bool upper(int box, Prio pr) { - return pr < boxes[box].min; + return pr < _boxes[box].min; } bool lower(int box, Prio pr) { - return pr >= boxes[box].min + boxes[box].size; + return pr >= _boxes[box].min + _boxes[box].size; } - /// \brief Remove item from the box list. + // Remove item from the box list void remove(int index) { - if (data[index].prev >= 0) { - data[data[index].prev].next = data[index].next; + if (_data[index].prev >= 0) { + _data[_data[index].prev].next = _data[index].next; } else { - boxes[data[index].box].first = data[index].next; + _boxes[_data[index].box].first = _data[index].next; } - if (data[index].next >= 0) { - data[data[index].next].prev = data[index].prev; + if (_data[index].next >= 0) { + _data[_data[index].next].prev = _data[index].prev; } } - /// \brief Insert item into the box list. + // Insert item into the box list void insert(int box, int index) { - if (boxes[box].first == -1) { - boxes[box].first = index; - data[index].next = data[index].prev = -1; + if (_boxes[box].first == -1) { + _boxes[box].first = index; + _data[index].next = _data[index].prev = -1; } else { - data[index].next = boxes[box].first; - data[boxes[box].first].prev = index; - data[index].prev = -1; - boxes[box].first = index; + _data[index].next = _boxes[box].first; + _data[_boxes[box].first].prev = index; + _data[index].prev = -1; + _boxes[box].first = index; } - data[index].box = box; + _data[index].box = box; } - /// \brief Add a new box to the box list. + // Add a new box to the box list void extend() { - int min = boxes.back().min + boxes.back().size; - int bs = 2 * boxes.back().size; - boxes.push_back(RadixBox(min, bs)); + int min = _boxes.back().min + _boxes.back().size; + int bs = 2 * _boxes.back().size; + _boxes.push_back(RadixBox(min, bs)); } - /// \brief Move an item up into the proper box. - void bubble_up(int index) { - if (!lower(data[index].box, data[index].prio)) return; + // Move an item up into the proper box. + void bubbleUp(int index) { + if (!lower(_data[index].box, _data[index].prio)) return; remove(index); - int box = findUp(data[index].box, data[index].prio); + int box = findUp(_data[index].box, _data[index].prio); insert(box, index); } - /// \brief Find up the proper box for the item with the given prio. + // Find up the proper box for the item with the given priority int findUp(int start, int pr) { while (lower(start, pr)) { - if (++start == int(boxes.size())) { + if (++start == int(_boxes.size())) { extend(); } } return start; } - /// \brief Move an item down into the proper box. - void bubble_down(int index) { - if (!upper(data[index].box, data[index].prio)) return; + // Move an item down into the proper box + void bubbleDown(int index) { + if (!upper(_data[index].box, _data[index].prio)) return; remove(index); - int box = findDown(data[index].box, data[index].prio); + int box = findDown(_data[index].box, _data[index].prio); insert(box, index); } - /// \brief Find up the proper box for the item with the given prio. + // Find down the proper box for the item with the given priority int findDown(int start, int pr) { while (upper(start, pr)) { - if (--start < 0) throw UnderFlowPriorityError(); + if (--start < 0) throw PriorityUnderflowError(); } return start; } - /// \brief Find the first not empty box. + // Find the first non-empty box int findFirst() { int first = 0; - while (boxes[first].first == -1) ++first; + while (_boxes[first].first == -1) ++first; return first; } - /// \brief Gives back the minimal prio of the box. + // Gives back the minimum priority of the given box int minValue(int box) { - int min = data[boxes[box].first].prio; - for (int k = boxes[box].first; k != -1; k = data[k].next) { - if (data[k].prio < min) min = data[k].prio; + int min = _data[_boxes[box].first].prio; + for (int k = _boxes[box].first; k != -1; k = _data[k].next) { + if (_data[k].prio < min) min = _data[k].prio; } return min; } - /// \brief Rearrange the items of the heap and makes the - /// first box not empty. + // Rearrange the items of the heap and make the first box non-empty void moveDown() { int box = findFirst(); if (box == 0) return; int min = minValue(box); for (int i = 0; i <= box; ++i) { - boxes[i].min = min; - min += boxes[i].size; + _boxes[i].min = min; + min += _boxes[i].size; } - int curr = boxes[box].first, next; + int curr = _boxes[box].first, next; while (curr != -1) { - next = data[curr].next; - bubble_down(curr); + next = _data[curr].next; + bubbleDown(curr); curr = next; } } - void relocate_last(int index) { - if (index != int(data.size()) - 1) { - data[index] = data.back(); - if (data[index].prev != -1) { - data[data[index].prev].next = index; + void relocateLast(int index) { + if (index != int(_data.size()) - 1) { + _data[index] = _data.back(); + if (_data[index].prev != -1) { + _data[_data[index].prev].next = index; } else { - boxes[data[index].box].first = index; + _boxes[_data[index].box].first = index; } - if (data[index].next != -1) { - data[data[index].next].prev = index; + if (_data[index].next != -1) { + _data[_data[index].next].prev = index; } - _iim[data[index].item] = index; + _iim[_data[index].item] = index; } - data.pop_back(); + _data.pop_back(); } public: /// \brief Insert an item into the heap with the given priority. /// - /// Adds \c i to the heap with priority \c p. + /// This function inserts the given item into the heap with the + /// given priority. /// \param i The item to insert. /// \param p The priority of the item. + /// \pre \e i must not be stored in the heap. + /// \warning This method may throw an \c UnderFlowPriorityException. void push(const Item &i, const Prio &p) { - int n = data.size(); + int n = _data.size(); _iim.set(i, n); - data.push_back(RadixItem(i, p)); - while (lower(boxes.size() - 1, p)) { + _data.push_back(RadixItem(i, p)); + while (lower(_boxes.size() - 1, p)) { extend(); } - int box = findDown(boxes.size() - 1, p); + int box = findDown(_boxes.size() - 1, p); insert(box, n); } - /// \brief Returns the item with minimum priority. + /// \brief Return the item having minimum priority. /// - /// This method returns the item with minimum priority. - /// \pre The heap must be nonempty. + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. Item top() const { const_cast&>(*this).moveDown(); - return data[boxes[0].first].item; + return _data[_boxes[0].first].item; } - /// \brief Returns the minimum priority. + /// \brief The minimum priority. /// - /// It returns the minimum priority. - /// \pre The heap must be nonempty. + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. Prio prio() const { const_cast&>(*this).moveDown(); - return data[boxes[0].first].prio; + return _data[_boxes[0].first].prio; } - /// \brief Deletes the item with minimum priority. + /// \brief Remove the item having minimum priority. /// - /// This method deletes the item with minimum priority. + /// This function removes the item having minimum priority. /// \pre The heap must be non-empty. void pop() { moveDown(); - int index = boxes[0].first; - _iim[data[index].item] = POST_HEAP; + int index = _boxes[0].first; + _iim[_data[index].item] = POST_HEAP; remove(index); - relocate_last(index); + relocateLast(index); } - /// \brief Deletes \c i from the heap. + /// \brief Remove the given item from the heap. /// - /// This method deletes item \c i from the heap, if \c i was - /// already stored in the heap. - /// \param i The item to erase. + /// This function removes the given item from the heap if it is + /// already stored. + /// \param i The item to delete. + /// \pre \e i must be in the heap. void erase(const Item &i) { int index = _iim[i]; _iim[i] = POST_HEAP; remove(index); - relocate_last(index); + relocateLast(index); } - /// \brief Returns the priority of \c i. + /// \brief The priority of the given item. /// - /// This function returns the priority of item \c i. - /// \pre \c i must be in the heap. + /// This function returns the priority of the given item. /// \param i The item. + /// \pre \e i must be in the heap. Prio operator[](const Item &i) const { int idx = _iim[i]; - return data[idx].prio; + return _data[idx].prio; } - /// \brief \c i gets to the heap with priority \c p independently - /// if \c i was already there. + /// \brief Set the priority of an item or insert it, if it is + /// not stored in the heap. /// - /// This method calls \ref push(\c i, \c p) if \c i is not stored - /// in the heap and sets the priority of \c i to \c p otherwise. - /// It may throw an \e UnderFlowPriorityException. + /// This method sets the priority of the given item if it is + /// already stored in the heap. Otherwise it inserts the given + /// item into the heap with the given priority. /// \param i The item. /// \param p The priority. + /// \pre \e i must be in the heap. + /// \warning This method may throw an \c UnderFlowPriorityException. void set(const Item &i, const Prio &p) { int idx = _iim[i]; if( idx < 0 ) { push(i, p); } - else if( p >= data[idx].prio ) { - data[idx].prio = p; - bubble_up(idx); + else if( p >= _data[idx].prio ) { + _data[idx].prio = p; + bubbleUp(idx); } else { - data[idx].prio = p; - bubble_down(idx); + _data[idx].prio = p; + bubbleDown(idx); } } - - /// \brief Decreases the priority of \c i to \c p. + /// \brief Decrease the priority of an item to the given value. /// - /// This method decreases the priority of item \c i to \c p. - /// \pre \c i must be stored in the heap with priority at least \c p, and - /// \c should be greater or equal to the last removed item's priority. + /// This function decreases the priority of an item to the given value. /// \param i The item. /// \param p The priority. + /// \pre \e i must be stored in the heap with priority at least \e p. + /// \warning This method may throw an \c UnderFlowPriorityException. void decrease(const Item &i, const Prio &p) { int idx = _iim[i]; - data[idx].prio = p; - bubble_down(idx); + _data[idx].prio = p; + bubbleDown(idx); } - /// \brief Increases the priority of \c i to \c p. + /// \brief Increase the priority of an item to the given value. /// - /// This method sets the priority of item \c i to \c p. - /// \pre \c i must be stored in the heap with priority at most \c p + /// This function increases the priority of an item to the given value. /// \param i The item. /// \param p The priority. + /// \pre \e i must be stored in the heap with priority at most \e p. void increase(const Item &i, const Prio &p) { int idx = _iim[i]; - data[idx].prio = p; - bubble_up(idx); + _data[idx].prio = p; + bubbleUp(idx); } - /// \brief Returns if \c item is in, has already been in, or has - /// never been in the heap. + /// \brief Return the state of an item. /// - /// This method returns PRE_HEAP if \c item has never been in the - /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP - /// otherwise. In the latter case it is possible that \c item will - /// get back to the heap again. + /// This method returns \c PRE_HEAP if the given item has never + /// been in the heap, \c IN_HEAP if it is in the heap at the moment, + /// and \c POST_HEAP otherwise. + /// In the latter case it is possible that the item will get back + /// to the heap again. /// \param i The item. State state(const Item &i) const { int s = _iim[i]; @@ -405,11 +410,11 @@ return State(s); } - /// \brief Sets the state of the \c item in the heap. + /// \brief Set the state of an item in the heap. /// - /// Sets the state of the \c item in the heap. It can be used to - /// manually clear the heap when it is important to achive the - /// better time complexity. + /// This function sets the state of the given item in the heap. + /// It can be used to manually clear the heap when it is important + /// to achive better time complexity. /// \param i The item. /// \param st The state. It should not be \c IN_HEAP. void state(const Item& i, State st) {