diff --git a/lemon/binom_heap.h b/lemon/binom_heap.h --- a/lemon/binom_heap.h +++ b/lemon/binom_heap.h @@ -1,8 +1,8 @@ -/* -*- C++ -*- +/* -*- mode: C++; indent-tabs-mode: nil; -*- * - * This file is a part of LEMON, a generic C++ optimization library + * This file is a part of LEMON, a generic C++ optimization library. * - * Copyright (C) 2003-2008 + * Copyright (C) 2003-2009 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). * @@ -20,193 +20,199 @@ #define LEMON_BINOM_HEAP_H ///\file -///\ingroup auxdat +///\ingroup heaps ///\brief Binomial Heap implementation. #include +#include #include #include #include namespace lemon { - /// \ingroup auxdat + /// \ingroup heaps /// - ///\brief Binomial Heap. + ///\brief Binomial heap data structure. /// - ///This class implements the \e Binomial \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. \c Compare specifies the ordering of the priorities. In a heap - ///one can change the priority of an item, add or erase an item, etc. + /// This class implements the \e binomial \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". /// - ///The methods \ref increase and \ref erase are not efficient in a Binomial - ///heap. In case of many calls to these operations, it is better to use a - ///\ref BinHeap "binary heap". + /// The methods \ref increase() and \ref erase() are not efficient + /// in a binomial heap. In case of many calls of these operations, + /// it is better to use other heap structure, e.g. \ref BinHeap + /// "binary heap". /// - ///\param _Prio Type of the priority of the items. - ///\param _ItemIntMap A read and writable Item int map, used internally - ///to handle the cross references. - ///\param _Compare A class for the ordering of the priorities. The - ///default is \c std::less<_Prio>. - /// - ///\sa BinHeap - ///\sa Dijkstra - ///\author Dorian Batha - + /// \tparam PR Type of the priorities of the items. + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam CMP A functor class for comparing the priorities. + /// The default is \c std::less. #ifdef DOXYGEN - template + template #else - template > + template > #endif class BinomHeap { public: - typedef _ItemIntMap ItemIntMap; - typedef _Prio Prio; + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef PR Prio; + /// Type of the items stored in the heap. typedef typename ItemIntMap::Key Item; - typedef std::pair Pair; - typedef _Compare Compare; + /// Functor type for comparing the priorities. + typedef CMP Compare; + + /// \brief Type to represent the states of the items. + /// + /// 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 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, ///< = 0. + PRE_HEAP = -1, ///< = -1. + POST_HEAP = -2 ///< = -2. + }; private: class store; - std::vector container; - int minimum, head; - ItemIntMap &iimap; - Compare comp; - int num_items; + std::vector _data; + int _min, _head; + ItemIntMap &_iim; + Compare _comp; + int _num_items; public: - ///Status of the nodes - enum State { - ///The node is in the heap - IN_HEAP = 0, - ///The node has never been in the heap - PRE_HEAP = -1, - ///The node was in the heap but it got out of it - POST_HEAP = -2 - }; + /// \brief Constructor. + /// + /// 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. + explicit BinomHeap(ItemIntMap &map) + : _min(0), _head(-1), _iim(map), _num_items(0) {} - /// \brief The constructor + /// \brief Constructor. /// - /// \c _iimap should be given to the constructor, since it is - /// used internally to handle the cross references. - explicit BinomHeap(ItemIntMap &_iimap) - : minimum(0), head(-1), iimap(_iimap), num_items() {} - - /// \brief The constructor - /// - /// \c _iimap should be given to the constructor, since it is used - /// internally to handle the cross references. \c _comp is an - /// object for ordering of the priorities. - BinomHeap(ItemIntMap &_iimap, const Compare &_comp) - : minimum(0), head(-1), iimap(_iimap), comp(_comp), num_items() {} + /// 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 comp The function object used for comparing the priorities. + BinomHeap(ItemIntMap &map, const Compare &comp) + : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {} /// \brief The number of items stored in the heap. /// - /// Returns the number of items stored in the heap. - int size() const { return num_items; } + /// This function returns the number of items stored in the heap. + int size() const { return _num_items; } - /// \brief Checks if the heap stores no items. + /// \brief Check if the heap is empty. /// - /// Returns \c true if and only if the heap stores no items. - bool empty() const { return num_items==0; } + /// This function returns \c true if the heap is empty. + bool empty() const { return _num_items==0; } - /// \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. + /// 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. void clear() { - container.clear(); minimum=0; num_items=0; head=-1; + _data.clear(); _min=0; _num_items=0; _head=-1; } - /// \brief \c item gets to the heap with priority \c value independently - /// if \c item 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 item, \c value) if \c item is not - /// stored in the heap and it calls \ref decrease(\c item, \c value) or - /// \ref increase(\c item, \c value) otherwise. + /// 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 item The item. + /// \param value The priority. void set (const Item& item, const Prio& value) { - int i=iimap[item]; - if ( i >= 0 && container[i].in ) { - if ( comp(value, container[i].prio) ) decrease(item, value); - if ( comp(container[i].prio, value) ) increase(item, value); + int i=_iim[item]; + if ( i >= 0 && _data[i].in ) { + if ( _comp(value, _data[i].prio) ) decrease(item, value); + if ( _comp(_data[i].prio, value) ) increase(item, value); } else push(item, value); } - /// \brief Adds \c item to the heap with priority \c value. + /// \brief Insert an item into the heap with the given priority. /// - /// Adds \c item to the heap with priority \c value. - /// \pre \c item must not be stored in the heap. + /// This function inserts the given item into the heap with the + /// given priority. + /// \param item The item to insert. + /// \param value The priority of the item. + /// \pre \e item must not be stored in the heap. void push (const Item& item, const Prio& value) { - int i=iimap[item]; + int i=_iim[item]; if ( i<0 ) { - int s=container.size(); - iimap.set( item,s ); + int s=_data.size(); + _iim.set( item,s ); store st; st.name=item; - container.push_back(st); + _data.push_back(st); i=s; } else { - container[i].parent=container[i].right_neighbor=container[i].child=-1; - container[i].degree=0; - container[i].in=true; + _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; + _data[i].degree=0; + _data[i].in=true; } - container[i].prio=value; + _data[i].prio=value; - if( 0==num_items ) { head=i; minimum=i; } + if( 0==_num_items ) { _head=i; _min=i; } else { merge(i); } - minimum = find_min(); + _min = findMin(); - ++num_items; + ++_num_items; } - /// \brief Returns the item with minimum priority relative to \c Compare. + /// \brief Return the item having minimum priority. /// - /// This method returns the item with minimum priority relative to \c - /// Compare. - /// \pre The heap must be nonempty. - Item top() const { return container[minimum].name; } + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { return _data[_min].name; } - /// \brief Returns the minimum priority relative to \c Compare. + /// \brief The minimum priority. /// - /// It returns the minimum priority relative to \c Compare. - /// \pre The heap must be nonempty. - const Prio& prio() const { return container[minimum].prio; } + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { return _data[_min].prio; } - /// \brief Returns the priority of \c item. + /// \brief The priority of the given item. /// - /// It returns the priority of \c item. - /// \pre \c item must be in the heap. + /// This function returns the priority of the given item. + /// \param item The item. + /// \pre \e item must be in the heap. const Prio& operator[](const Item& item) const { - return container[iimap[item]].prio; + return _data[_iim[item]].prio; } - /// \brief Deletes the item with minimum priority relative to \c Compare. + /// \brief Remove the item having minimum priority. /// - /// This method deletes the item with minimum priority relative to \c - /// Compare from the heap. + /// This function removes the item having minimum priority. /// \pre The heap must be non-empty. void pop() { - container[minimum].in=false; + _data[_min].in=false; int head_child=-1; - if ( container[minimum].child!=-1 ) { - int child=container[minimum].child; + if ( _data[_min].child!=-1 ) { + int child=_data[_min].child; int neighb; int prev=-1; while( child!=-1 ) { - neighb=container[child].right_neighbor; - container[child].parent=-1; - container[child].right_neighbor=prev; + neighb=_data[child].right_neighbor; + _data[child].parent=-1; + _data[child].right_neighbor=prev; head_child=child; prev=child; child=neighb; @@ -214,142 +220,144 @@ } // The first case is that there are only one root. - if ( -1==container[head].right_neighbor ) { - head=head_child; + if ( -1==_data[_head].right_neighbor ) { + _head=head_child; } // The case where there are more roots. else { - if( head!=minimum ) { unlace(minimum); } - else { head=container[head].right_neighbor; } + if( _head!=_min ) { unlace(_min); } + else { _head=_data[_head].right_neighbor; } merge(head_child); } - minimum=find_min(); - --num_items; + _min=findMin(); + --_num_items; } - /// \brief Deletes \c item from the heap. + /// \brief Remove the given item from the heap. /// - /// This method deletes \c item from the heap, if \c item was already - /// stored in the heap. It is quite inefficient in Binomial heaps. + /// This function removes the given item from the heap if it is + /// already stored. + /// \param item The item to delete. + /// \pre \e item must be in the heap. void erase (const Item& item) { - int i=iimap[item]; - if ( i >= 0 && container[i].in ) { - decrease( item, container[minimum].prio-1 ); + int i=_iim[item]; + if ( i >= 0 && _data[i].in ) { + decrease( item, _data[_min].prio-1 ); pop(); } } - /// \brief Decreases the priority of \c item to \c value. + /// \brief Decrease the priority of an item to the given value. /// - /// This method decreases the priority of \c item to \c value. - /// \pre \c item must be stored in the heap with priority at least \c - /// value relative to \c Compare. + /// This function decreases the priority of an item to the given value. + /// \param item The item. + /// \param value The priority. + /// \pre \e item must be stored in the heap with priority at least \e value. void decrease (Item item, const Prio& value) { - int i=iimap[item]; + int i=_iim[item]; - if( comp( value,container[i].prio ) ) { - container[i].prio=value; + if( _comp( value,_data[i].prio ) ) { + _data[i].prio=value; - int p_loc=container[i].parent, loc=i; + int p_loc=_data[i].parent, loc=i; int parent, child, neighb; - while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) { + while( -1!=p_loc && _comp(_data[loc].prio,_data[p_loc].prio) ) { // parent set for other loc_child - child=container[loc].child; + child=_data[loc].child; while( -1!=child ) { - container[child].parent=p_loc; - child=container[child].right_neighbor; + _data[child].parent=p_loc; + child=_data[child].right_neighbor; } // parent set for other p_loc_child - child=container[p_loc].child; + child=_data[p_loc].child; while( -1!=child ) { - container[child].parent=loc; - child=container[child].right_neighbor; + _data[child].parent=loc; + child=_data[child].right_neighbor; } - child=container[p_loc].child; - container[p_loc].child=container[loc].child; + child=_data[p_loc].child; + _data[p_loc].child=_data[loc].child; if( child==loc ) child=p_loc; - container[loc].child=child; + _data[loc].child=child; // left_neighb set for p_loc - if( container[loc].child!=p_loc ) { - while( container[child].right_neighbor!=loc ) - child=container[child].right_neighbor; - container[child].right_neighbor=p_loc; + if( _data[loc].child!=p_loc ) { + while( _data[child].right_neighbor!=loc ) + child=_data[child].right_neighbor; + _data[child].right_neighbor=p_loc; } // left_neighb set for loc - parent=container[p_loc].parent; - if( -1!=parent ) child=container[parent].child; - else child=head; + parent=_data[p_loc].parent; + if( -1!=parent ) child=_data[parent].child; + else child=_head; if( child!=p_loc ) { - while( container[child].right_neighbor!=p_loc ) - child=container[child].right_neighbor; - container[child].right_neighbor=loc; + while( _data[child].right_neighbor!=p_loc ) + child=_data[child].right_neighbor; + _data[child].right_neighbor=loc; } - neighb=container[p_loc].right_neighbor; - container[p_loc].right_neighbor=container[loc].right_neighbor; - container[loc].right_neighbor=neighb; + neighb=_data[p_loc].right_neighbor; + _data[p_loc].right_neighbor=_data[loc].right_neighbor; + _data[loc].right_neighbor=neighb; - container[p_loc].parent=loc; - container[loc].parent=parent; + _data[p_loc].parent=loc; + _data[loc].parent=parent; - if( -1!=parent && container[parent].child==p_loc ) - container[parent].child=loc; + if( -1!=parent && _data[parent].child==p_loc ) + _data[parent].child=loc; /*if new parent will be the first root*/ - if( head==p_loc ) - head=loc; + if( _head==p_loc ) + _head=loc; - p_loc=container[loc].parent; + p_loc=_data[loc].parent; } } - if( comp(value,container[minimum].prio) ) { - minimum=i; + if( _comp(value,_data[_min].prio) ) { + _min=i; } } - /// \brief Increases the priority of \c item to \c value. + /// \brief Increase the priority of an item to the given value. /// - /// This method sets the priority of \c item to \c value. Though - /// there is no precondition on the priority of \c item, this - /// method should be used only if it is indeed necessary to increase - /// (relative to \c Compare) the priority of \c item, because this - /// method is inefficient. + /// This function increases the priority of an item to the given value. + /// \param item The item. + /// \param value The priority. + /// \pre \e item must be stored in the heap with priority at most \e value. void increase (Item item, const Prio& value) { erase(item); push(item, value); } - - /// \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 item The item. State state(const Item &item) const { - int i=iimap[item]; + int i=_iim[item]; if( i>=0 ) { - if ( container[i].in ) i=0; + if ( _data[i].in ) i=0; else i=-2; } return State(i); } - /// \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) { @@ -359,7 +367,7 @@ if (state(i) == IN_HEAP) { erase(i); } - iimap[i] = st; + _iim[i] = st; break; case IN_HEAP: break; @@ -367,20 +375,20 @@ } private: - int find_min() { + int findMin() { int min_loc=-1, min_val; - int x=head; + int x=_head; if( x!=-1 ) { - min_val=container[x].prio; + min_val=_data[x].prio; min_loc=x; - x=container[x].right_neighbor; + x=_data[x].right_neighbor; while( x!=-1 ) { - if( comp( container[x].prio,min_val ) ) { - min_val=container[x].prio; + if( _comp( _data[x].prio,min_val ) ) { + min_val=_data[x].prio; min_loc=x; } - x=container[x].right_neighbor; + x=_data[x].right_neighbor; } } return min_loc; @@ -389,29 +397,29 @@ void merge(int a) { interleave(a); - int x=head; + int x=_head; if( -1!=x ) { - int x_prev=-1, x_next=container[x].right_neighbor; + int x_prev=-1, x_next=_data[x].right_neighbor; while( -1!=x_next ) { - if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) { + if( _data[x].degree!=_data[x_next].degree || ( -1!=_data[x_next].right_neighbor && _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { x_prev=x; x=x_next; } else { - if( comp(container[x].prio,container[x_next].prio) ) { - container[x].right_neighbor=container[x_next].right_neighbor; + if( _comp(_data[x].prio,_data[x_next].prio) ) { + _data[x].right_neighbor=_data[x_next].right_neighbor; fuse(x_next,x); } else { - if( -1==x_prev ) { head=x_next; } + if( -1==x_prev ) { _head=x_next; } else { - container[x_prev].right_neighbor=x_next; + _data[x_prev].right_neighbor=x_next; } fuse(x,x_next); x=x_next; } } - x_next=container[x].right_neighbor; + x_next=_data[x].right_neighbor; } } } @@ -419,68 +427,68 @@ void interleave(int a) { int other=-1, head_other=-1; - while( -1!=a || -1!=head ) { + while( -1!=a || -1!=_head ) { if( -1==a ) { if( -1==head_other ) { - head_other=head; + head_other=_head; } else { - container[other].right_neighbor=head; + _data[other].right_neighbor=_head; } - head=-1; + _head=-1; } - else if( -1==head ) { + else if( -1==_head ) { if( -1==head_other ) { head_other=a; } else { - container[other].right_neighbor=a; + _data[other].right_neighbor=a; } a=-1; } else { - if( container[a].degree #include #include #include namespace lemon { - ///\ingroup auxdat + /// \ingroup heaps /// - ///\brief A 4ary Heap implementation. + ///\brief Fourary heap data structure. /// - ///This class implements the \e 4ary \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. \c Compare specifies the ordering of the priorities. In a heap - ///one can change the priority of an item, add or erase an item, etc. + /// This class implements the \e fourary \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". /// - ///\param _Prio Type of the priority of the items. - ///\param _ItemIntMap A read and writable Item int map, used internally - ///to handle the cross references. - ///\param _Compare A class for the ordering of the priorities. The - ///default is \c std::less<_Prio>. + /// The fourary heap is a specialization of the \ref KaryHeap "K-ary heap" + /// for K=4. It is similar to the \ref BinHeap "binary heap", + /// but its nodes have at most four children, instead of two. /// - ///\sa FibHeap - ///\sa Dijkstra - ///\author Dorian Batha + /// \tparam PR Type of the priorities of the items. + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam CMP A functor class for comparing the priorities. + /// The default is \c std::less. + /// + ///\sa BinHeap + ///\sa KaryHeap +#ifdef DOXYGEN + template +#else + template > +#endif + class FouraryHeap { + public: + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef PR Prio; + /// Type of the items stored in the heap. + typedef typename ItemIntMap::Key Item; + /// Type of the item-priority pairs. + typedef std::pair Pair; + /// Functor type for comparing the priorities. + typedef CMP Compare; - template > - - class FouraryHeap { - - public: - ///\e - typedef _ItemIntMap ItemIntMap; - ///\e - typedef _Prio Prio; - ///\e - typedef typename ItemIntMap::Key Item; - ///\e - typedef std::pair Pair; - ///\e - typedef _Compare Compare; - - /// \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: - std::vector data; - Compare comp; - ItemIntMap &iim; + std::vector _data; + Compare _comp; + ItemIntMap &_iim; public: - /// \brief The constructor. + /// \brief Constructor. /// - /// The constructor. - /// \param _iim 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. - explicit FouraryHeap(ItemIntMap &_iim) : iim(_iim) {} + /// 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. + explicit FouraryHeap(ItemIntMap &map) : _iim(map) {} - /// \brief The constructor. + /// \brief Constructor. /// - /// The constructor. - /// \param _iim 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. + /// 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 comp The function object used for comparing the priorities. + FouraryHeap(ItemIntMap &map, const Compare &comp) + : _iim(map), _comp(comp) {} + + /// \brief The number of items stored in the heap. /// - /// \param _comp The comparator function object. - FouraryHeap(ItemIntMap &_iim, const Compare &_comp) - : iim(_iim), comp(_comp) {} + /// This function returns the number of items stored in the heap. + int size() const { return _data.size(); } - /// The number of items stored in the heap. + /// \brief Check if the heap is empty. /// - /// \brief Returns the number of items stored in the heap. - int size() const { return data.size(); } + /// This function returns \c true if the heap is empty. + bool empty() const { return _data.empty(); } - /// \brief Checks if the heap stores no items. + /// \brief Make the heap empty. /// - /// Returns \c true if and only if the heap stores no items. - bool empty() const { return data.empty(); } - - /// \brief Make empty this heap. - /// - /// Make empty this heap. It does not change the cross reference map. - /// If you want to reuse 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() { data.clear(); } + /// 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. + void clear() { _data.clear(); } private: static int parent(int i) { return (i-1)/4; } static int firstChild(int i) { return 4*i+1; } bool less(const Pair &p1, const Pair &p2) const { - return comp(p1.second, p2.second); + return _comp(p1.second, p2.second); } - int find_min(const int child, const int length) { + int findMin(const int child, const int length) { int min=child; if( child+30 && less(p,data[par]) ) { - move(data[par],hole); + while( hole>0 && less(p,_data[par]) ) { + move(_data[par],hole); hole = par; par = parent(hole); } move(p, hole); } - void bubble_down(int hole, Pair p, int length) { + void bubbleDown(int hole, Pair p, int length) { int child = firstChild(hole); while( child1 ) { - child = find_min(child,length); - if( !less(data[child], p) ) + child = findMin(child,length); + if( !less(_data[child], p) ) goto ok; - move(data[child], hole); + move(_data[child], hole); hole = child; child = firstChild(hole); } @@ -180,142 +179,143 @@ } void move(const Pair &p, int i) { - data[i] = p; - iim.set(p.first, i); + _data[i] = p; + _iim.set(p.first, i); } public: - /// \brief Insert a pair of item and priority into the heap. /// - /// Adds \c p.first to the heap with priority \c p.second. + /// This function inserts \c p.first to the heap with priority + /// \c p.second. /// \param p The pair to insert. + /// \pre \c p.first must not be stored in the heap. void push(const Pair &p) { - int n = data.size(); - data.resize(n+1); - bubble_up(n, p); + int n = _data.size(); + _data.resize(n+1); + bubbleUp(n, p); } - /// \brief Insert an item into the heap with the given heap. + /// \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. void push(const Item &i, const Prio &p) { push(Pair(i,p)); } - /// \brief Returns the item with minimum priority relative to \c Compare. + /// \brief Return the item having minimum priority. /// - /// This method returns the item with minimum priority relative to \c - /// Compare. - /// \pre The heap must be nonempty. - Item top() const { return data[0].first; } + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { return _data[0].first; } - /// \brief Returns the minimum priority relative to \c Compare. + /// \brief The minimum priority. /// - /// It returns the minimum priority relative to \c Compare. - /// \pre The heap must be nonempty. - Prio prio() const { return data[0].second; } + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { return _data[0].second; } - /// \brief Deletes the item with minimum priority relative to \c Compare. + /// \brief Remove the item having minimum priority. /// - /// This method deletes the item with minimum priority relative to \c - /// Compare from the heap. + /// This function removes the item having minimum priority. /// \pre The heap must be non-empty. void pop() { - int n = data.size()-1; - iim.set(data[0].first, POST_HEAP); - if (n>0) bubble_down(0, data[n], n); - data.pop_back(); + int n = _data.size()-1; + _iim.set(_data[0].first, POST_HEAP); + if (n>0) bubbleDown(0, _data[n], n); + _data.pop_back(); } - /// \brief Deletes \c i from the heap. + /// \brief Remove the given item from the heap. /// - /// This method deletes item \c i from the heap. - /// \param i The item to erase. - /// \pre The item should be in the heap. + /// 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 h = iim[i]; - int n = data.size()-1; - iim.set(data[h].first, POST_HEAP); + int h = _iim[i]; + int n = _data.size()-1; + _iim.set(_data[h].first, POST_HEAP); if( h=0) s=0; 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) { @@ -323,24 +323,25 @@ case POST_HEAP: case PRE_HEAP: if (state(i) == IN_HEAP) erase(i); - iim[i] = st; + _iim[i] = st; break; case IN_HEAP: break; } } - /// \brief Replaces an item in the heap. + /// \brief Replace an item in the heap. /// - /// The \c i item is replaced with \c j item. The \c i item should - /// be in the heap, while the \c j should be out of the heap. The - /// \c i item will out of the heap and \c j will be in the heap - /// with the same prioriority as prevoiusly the \c i item. + /// This function replaces item \c i with item \c j. + /// Item \c i must be in the heap, while \c j must be out of the heap. + /// After calling this method, item \c i will be out of the + /// heap and \c j will be in the heap with the same prioriority + /// as item \c i had before. void replace(const Item& i, const Item& j) { - int idx = iim[i]; - iim.set(i, iim[j]); - iim.set(j, idx); - data[idx].first = j; + int idx = _iim[i]; + _iim.set(i, _iim[j]); + _iim.set(j, idx); + _data[idx].first = j; } }; // class FouraryHeap diff --git a/lemon/kary_heap.h b/lemon/kary_heap.h --- a/lemon/kary_heap.h +++ b/lemon/kary_heap.h @@ -1,8 +1,8 @@ -/* -*- C++ -*- +/* -*- mode: C++; indent-tabs-mode: nil; -*- * - * This file is a part of LEMON, a generic C++ optimization library + * This file is a part of LEMON, a generic C++ optimization library. * - * Copyright (C) 2003-2008 + * Copyright (C) 2003-2009 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). * @@ -19,152 +19,151 @@ #ifndef LEMON_KARY_HEAP_H #define LEMON_KARY_HEAP_H -///\ingroup auxdat +///\ingroup heaps ///\file -///\brief Kary Heap implementation. +///\brief Fourary heap implementation. -#include #include #include #include namespace lemon { - ///\ingroup auxdat + /// \ingroup heaps /// - ///\brief A Kary Heap implementation. + ///\brief K-ary heap data structure. /// - ///This class implements the \e Kary \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. \c Compare specifies the ordering of the priorities. In a heap - ///one can change the priority of an item, add or erase an item, etc. + /// This class implements the \e K-ary \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". /// - ///\param _Prio Type of the priority of the items. - ///\param _ItemIntMap A read and writable Item int map, used internally - ///to handle the cross references. - ///\param _Compare A class for the ordering of the priorities. The - ///default is \c std::less<_Prio>. + /// The \ref KaryHeap "K-ary heap" is a generalization of the + /// \ref BinHeap "binary heap" structure, its nodes have at most + /// \c K children, instead of two. + /// \ref BinHeap and \ref FouraryHeap are specialized implementations + /// of this structure for K=2 and K=4, respectively. /// - ///\sa FibHeap - ///\sa Dijkstra - ///\author Dorian Batha + /// \tparam PR Type of the priorities of the items. + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam CMP A functor class for comparing the priorities. + /// The default is \c std::less. + /// + ///\sa BinHeap + ///\sa FouraryHeap +#ifdef DOXYGEN + template +#else + template > +#endif + class KaryHeap { + public: + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef PR Prio; + /// Type of the items stored in the heap. + typedef typename ItemIntMap::Key Item; + /// Type of the item-priority pairs. + typedef std::pair Pair; + /// Functor type for comparing the priorities. + typedef CMP Compare; - template > - - class KaryHeap { - - public: - ///\e - typedef _ItemIntMap ItemIntMap; - ///\e - typedef _Prio Prio; - ///\e - typedef typename ItemIntMap::Key Item; - ///\e - typedef std::pair Pair; - ///\e - typedef _Compare Compare; - ///\e - - /// \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: - std::vector data; - Compare comp; - ItemIntMap &iim; - int K; + std::vector _data; + Compare _comp; + ItemIntMap &_iim; + int _K; public: - /// \brief The constructor. + /// \brief Constructor. /// - /// The constructor. - /// \param _iim 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. - explicit KaryHeap(ItemIntMap &_iim, const int &_K=32) : iim(_iim), K(_K) {} + /// 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. + explicit KaryHeap(ItemIntMap &map, int K=32) : _iim(map), _K(K) {} - /// \brief The constructor. + /// \brief Constructor. /// - /// The constructor. - /// \param _iim 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. + /// 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 comp The function object used for comparing the priorities. + KaryHeap(ItemIntMap &map, const Compare &comp, int K=32) + : _iim(map), _comp(comp), _K(K) {} + + /// \brief The number of items stored in the heap. /// - /// \param _comp The comparator function object. - KaryHeap(ItemIntMap &_iim, const Compare &_comp, const int &_K=32) - : iim(_iim), comp(_comp), K(_K) {} + /// This function returns the number of items stored in the heap. + int size() const { return _data.size(); } + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _data.empty(); } - /// The number of items stored in the heap. + /// \brief Make the heap empty. /// - /// \brief Returns the number of items stored in the heap. - int size() const { return data.size(); } - - /// \brief Checks if the heap stores no items. - /// - /// Returns \c true if and only if the heap stores no items. - bool empty() const { return data.empty(); } - - /// \brief Make empty this heap. - /// - /// Make empty this heap. It does not change the cross reference map. - /// If you want to reuse 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() { data.clear(); } + /// 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. + void clear() { _data.clear(); } private: - int parent(int i) { return (i-1)/K; } - int first_child(int i) { return K*i+1; } + int parent(int i) { return (i-1)/_K; } + int firstChild(int i) { return _K*i+1; } bool less(const Pair &p1, const Pair &p2) const { - return comp(p1.second, p2.second); + return _comp(p1.second, p2.second); } - int find_min(const int child, const int length) { + int findMin(const int child, const int length) { int min=child, i=1; - while( i0 && less(p,data[par]) ) { - move(data[par],hole); + while( hole>0 && less(p,_data[par]) ) { + move(_data[par],hole); hole = par; par = parent(hole); } move(p, hole); } - void bubble_down(int hole, Pair p, int length) { + void bubbleDown(int hole, Pair p, int length) { if( length>1 ) { - int child = first_child(hole); + int child = firstChild(hole); while( child0) bubble_down(0, data[n], n); - data.pop_back(); + int n = _data.size()-1; + _iim.set(_data[0].first, POST_HEAP); + if (n>0) bubbleDown(0, _data[n], n); + _data.pop_back(); } - /// \brief Deletes \c i from the heap. + /// \brief Remove the given item from the heap. /// - /// This method deletes item \c i from the heap. - /// \param i The item to erase. - /// \pre The item should be in the heap. + /// 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 h = iim[i]; - int n = data.size()-1; - iim.set(data[h].first, POST_HEAP); + int h = _iim[i]; + int n = _data.size()-1; + _iim.set(_data[h].first, POST_HEAP); if( h=0) s=0; 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) { switch (st) { - case POST_HEAP: - case PRE_HEAP: - if (state(i) == IN_HEAP) erase(i); - iim[i] = st; - break; - case IN_HEAP: - break; + case POST_HEAP: + case PRE_HEAP: + if (state(i) == IN_HEAP) erase(i); + _iim[i] = st; + break; + case IN_HEAP: + break; } } - /// \brief Replaces an item in the heap. + /// \brief Replace an item in the heap. /// - /// The \c i item is replaced with \c j item. The \c i item should - /// be in the heap, while the \c j should be out of the heap. The - /// \c i item will out of the heap and \c j will be in the heap - /// with the same prioriority as prevoiusly the \c i item. + /// This function replaces item \c i with item \c j. + /// Item \c i must be in the heap, while \c j must be out of the heap. + /// After calling this method, item \c i will be out of the + /// heap and \c j will be in the heap with the same prioriority + /// as item \c i had before. void replace(const Item& i, const Item& j) { - int idx=iim[i]; - iim.set(i, iim[j]); - iim.set(j, idx); - data[idx].first=j; + int idx=_iim[i]; + _iim.set(i, _iim[j]); + _iim.set(j, idx); + _data[idx].first=j; } }; // class KaryHeap diff --git a/lemon/pairing_heap.h b/lemon/pairing_heap.h --- a/lemon/pairing_heap.h +++ b/lemon/pairing_heap.h @@ -1,8 +1,8 @@ -/* -*- C++ -*- +/* -*- mode: C++; indent-tabs-mode: nil; -*- * - * This file is a part of LEMON, a generic C++ optimization library + * This file is a part of LEMON, a generic C++ optimization library. * - * Copyright (C) 2003-2008 + * Copyright (C) 2003-2009 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). * @@ -20,217 +20,223 @@ #define LEMON_PAIRING_HEAP_H ///\file -///\ingroup auxdat -///\brief Pairing Heap implementation. +///\ingroup heaps +///\brief Pairing heap implementation. #include +#include #include #include namespace lemon { - /// \ingroup auxdat + /// \ingroup heaps /// ///\brief Pairing Heap. /// - ///This class implements the \e Pairing \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. \c Compare specifies the ordering of the priorities. In a heap - ///one can change the priority of an item, add or erase an item, etc. + /// This class implements the \e pairing \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". /// - ///The methods \ref increase and \ref erase are not efficient in a Pairing - ///heap. In case of many calls to these operations, it is better to use a - ///\ref BinHeap "binary heap". + /// The methods \ref increase() and \ref erase() are not efficient + /// in a pairing heap. In case of many calls of these operations, + /// it is better to use other heap structure, e.g. \ref BinHeap + /// "binary heap". /// - ///\param _Prio Type of the priority of the items. - ///\param _ItemIntMap A read and writable Item int map, used internally - ///to handle the cross references. - ///\param _Compare A class for the ordering of the priorities. The - ///default is \c std::less<_Prio>. - /// - ///\sa BinHeap - ///\sa Dijkstra - ///\author Dorian Batha - + /// \tparam PR Type of the priorities of the items. + /// \tparam IM A read-writable item map with \c int values, used + /// internally to handle the cross references. + /// \tparam CMP A functor class for comparing the priorities. + /// The default is \c std::less. #ifdef DOXYGEN - template + template #else - template > + template > #endif class PairingHeap { public: - typedef _ItemIntMap ItemIntMap; - typedef _Prio Prio; + /// Type of the item-int map. + typedef IM ItemIntMap; + /// Type of the priorities. + typedef PR Prio; + /// Type of the items stored in the heap. typedef typename ItemIntMap::Key Item; - typedef std::pair Pair; - typedef _Compare Compare; + /// Functor type for comparing the priorities. + typedef CMP Compare; + + /// \brief Type to represent the states of the items. + /// + /// 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 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, ///< = 0. + PRE_HEAP = -1, ///< = -1. + POST_HEAP = -2 ///< = -2. + }; private: class store; - std::vector container; - int minimum; - ItemIntMap &iimap; - Compare comp; - int num_items; + std::vector _data; + int _min; + ItemIntMap &_iim; + Compare _comp; + int _num_items; public: - ///Status of the nodes - enum State { - ///The node is in the heap - IN_HEAP = 0, - ///The node has never been in the heap - PRE_HEAP = -1, - ///The node was in the heap but it got out of it - POST_HEAP = -2 - }; + /// \brief Constructor. + /// + /// 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. + explicit PairingHeap(ItemIntMap &map) + : _min(0), _iim(map), _num_items(0) {} - /// \brief The constructor + /// \brief Constructor. /// - /// \c _iimap should be given to the constructor, since it is - /// used internally to handle the cross references. - explicit PairingHeap(ItemIntMap &_iimap) - : minimum(0), iimap(_iimap), num_items(0) {} - - /// \brief The constructor - /// - /// \c _iimap should be given to the constructor, since it is used - /// internally to handle the cross references. \c _comp is an - /// object for ordering of the priorities. - PairingHeap(ItemIntMap &_iimap, const Compare &_comp) - : minimum(0), iimap(_iimap), comp(_comp), num_items(0) {} + /// 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 comp The function object used for comparing the priorities. + PairingHeap(ItemIntMap &map, const Compare &comp) + : _min(0), _iim(map), _comp(comp), _num_items(0) {} /// \brief The number of items stored in the heap. /// - /// Returns the number of items stored in the heap. - int size() const { return num_items; } + /// This function returns the number of items stored in the heap. + int size() const { return _num_items; } - /// \brief Checks if the heap stores no items. + /// \brief Check if the heap is empty. /// - /// Returns \c true if and only if the heap stores no items. - bool empty() const { return num_items==0; } + /// This function returns \c true if the heap is empty. + bool empty() const { return _num_items==0; } - /// \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. + /// 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. void clear() { - container.clear(); - minimum = 0; - num_items = 0; + _data.clear(); + _min = 0; + _num_items = 0; } - /// \brief \c item gets to the heap with priority \c value independently - /// if \c item 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 item, \c value) if \c item is not - /// stored in the heap and it calls \ref decrease(\c item, \c value) or - /// \ref increase(\c item, \c value) otherwise. + /// 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 item The item. + /// \param value The priority. void set (const Item& item, const Prio& value) { - int i=iimap[item]; - if ( i>=0 && container[i].in ) { - if ( comp(value, container[i].prio) ) decrease(item, value); - if ( comp(container[i].prio, value) ) increase(item, value); + int i=_iim[item]; + if ( i>=0 && _data[i].in ) { + if ( _comp(value, _data[i].prio) ) decrease(item, value); + if ( _comp(_data[i].prio, value) ) increase(item, value); } else push(item, value); } - /// \brief Adds \c item to the heap with priority \c value. + /// \brief Insert an item into the heap with the given priority. /// - /// Adds \c item to the heap with priority \c value. - /// \pre \c item must not be stored in the heap. + /// This function inserts the given item into the heap with the + /// given priority. + /// \param item The item to insert. + /// \param value The priority of the item. + /// \pre \e item must not be stored in the heap. void push (const Item& item, const Prio& value) { - int i=iimap[item]; + int i=_iim[item]; if( i<0 ) { - int s=container.size(); - iimap.set(item, s); + int s=_data.size(); + _iim.set(item, s); store st; st.name=item; - container.push_back(st); + _data.push_back(st); i=s; } else { - container[i].parent=container[i].child=-1; - container[i].left_child=false; - container[i].degree=0; - container[i].in=true; + _data[i].parent=_data[i].child=-1; + _data[i].left_child=false; + _data[i].degree=0; + _data[i].in=true; } - container[i].prio=value; + _data[i].prio=value; - if ( num_items!=0 ) { - if ( comp( value, container[minimum].prio) ) { - fuse(i,minimum); - minimum=i; + if ( _num_items!=0 ) { + if ( _comp( value, _data[_min].prio) ) { + fuse(i,_min); + _min=i; } - else fuse(minimum,i); + else fuse(_min,i); } - else minimum=i; + else _min=i; - ++num_items; + ++_num_items; } - /// \brief Returns the item with minimum priority relative to \c Compare. + /// \brief Return the item having minimum priority. /// - /// This method returns the item with minimum priority relative to \c - /// Compare. - /// \pre The heap must be nonempty. - Item top() const { return container[minimum].name; } + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { return _data[_min].name; } - /// \brief Returns the minimum priority relative to \c Compare. + /// \brief The minimum priority. /// - /// It returns the minimum priority relative to \c Compare. - /// \pre The heap must be nonempty. - const Prio& prio() const { return container[minimum].prio; } + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + const Prio& prio() const { return _data[_min].prio; } - /// \brief Returns the priority of \c item. + /// \brief The priority of the given item. /// - /// It returns the priority of \c item. - /// \pre \c item must be in the heap. + /// This function returns the priority of the given item. + /// \param item The item. + /// \pre \e item must be in the heap. const Prio& operator[](const Item& item) const { - return container[iimap[item]].prio; + return _data[_iim[item]].prio; } - /// \brief Deletes the item with minimum priority relative to \c Compare. + /// \brief Remove the item having minimum priority. /// - /// This method deletes the item with minimum priority relative to \c - /// Compare from the heap. + /// This function removes the item having minimum priority. /// \pre The heap must be non-empty. void pop() { - int TreeArray[num_items]; + int TreeArray[_num_items]; int i=0, num_child=0, child_right = 0; - container[minimum].in=false; + _data[_min].in=false; - if( -1!=container[minimum].child ) { - i=container[minimum].child; + if( -1!=_data[_min].child ) { + i=_data[_min].child; TreeArray[num_child] = i; - container[i].parent = -1; - container[minimum].child = -1; + _data[i].parent = -1; + _data[_min].child = -1; ++num_child; int ch=-1; - while( container[i].child!=-1 ) { - ch=container[i].child; - if( container[ch].left_child && i==container[ch].parent ) { + while( _data[i].child!=-1 ) { + ch=_data[i].child; + if( _data[ch].left_child && i==_data[ch].parent ) { i=ch; //break; } else { - if( container[ch].left_child ) { - child_right=container[ch].parent; - container[ch].parent = i; - --container[i].degree; + if( _data[ch].left_child ) { + child_right=_data[ch].parent; + _data[ch].parent = i; + --_data[i].degree; } else { child_right=ch; - container[i].child=-1; - container[i].degree=0; + _data[i].child=-1; + _data[i].degree=0; } - container[child_right].parent = -1; + _data[child_right].parent = -1; TreeArray[num_child] = child_right; i = child_right; ++num_child; @@ -239,8 +245,8 @@ int other; for( i=0; i=2) { - if ( comp(container[TreeArray[i]].prio, - container[TreeArray[i-2]].prio) ) { + if ( _comp(_data[TreeArray[i]].prio, + _data[TreeArray[i-2]].prio) ) { other=TreeArray[i]; TreeArray[i]=TreeArray[i-2]; TreeArray[i-2]=other; @@ -259,88 +265,91 @@ fuse( TreeArray[i-2], TreeArray[i] ); i-=2; } - minimum = TreeArray[0]; + _min = TreeArray[0]; } if ( 0==num_child ) { - minimum = container[minimum].child; + _min = _data[_min].child; } - if (minimum >= 0) container[minimum].left_child = false; + if (_min >= 0) _data[_min].left_child = false; - --num_items; + --_num_items; } - /// \brief Deletes \c item from the heap. + /// \brief Remove the given item from the heap. /// - /// This method deletes \c item from the heap, if \c item was already - /// stored in the heap. It is quite inefficient in Pairing heaps. + /// This function removes the given item from the heap if it is + /// already stored. + /// \param item The item to delete. + /// \pre \e item must be in the heap. void erase (const Item& item) { - int i=iimap[item]; - if ( i>=0 && container[i].in ) { - decrease( item, container[minimum].prio-1 ); + int i=_iim[item]; + if ( i>=0 && _data[i].in ) { + decrease( item, _data[_min].prio-1 ); pop(); } } - /// \brief Decreases the priority of \c item to \c value. + /// \brief Decrease the priority of an item to the given value. /// - /// This method decreases the priority of \c item to \c value. - /// \pre \c item must be stored in the heap with priority at least \c - /// value relative to \c Compare. + /// This function decreases the priority of an item to the given value. + /// \param item The item. + /// \param value The priority. + /// \pre \e item must be stored in the heap with priority at least \e value. void decrease (Item item, const Prio& value) { - int i=iimap[item]; - container[i].prio=value; - int p=container[i].parent; + int i=_iim[item]; + _data[i].prio=value; + int p=_data[i].parent; - if( container[i].left_child && i!=container[p].child ) { - p=container[p].parent; + if( _data[i].left_child && i!=_data[p].child ) { + p=_data[p].parent; } - if ( p!=-1 && comp(value,container[p].prio) ) { + if ( p!=-1 && _comp(value,_data[p].prio) ) { cut(i,p); - if ( comp(container[minimum].prio,value) ) { - fuse(minimum,i); + if ( _comp(_data[_min].prio,value) ) { + fuse(_min,i); } else { - fuse(i,minimum); - minimum=i; + fuse(i,_min); + _min=i; } } } - /// \brief Increases the priority of \c item to \c value. + /// \brief Increase the priority of an item to the given value. /// - /// This method sets the priority of \c item to \c value. Though - /// there is no precondition on the priority of \c item, this - /// method should be used only if it is indeed necessary to increase - /// (relative to \c Compare) the priority of \c item, because this - /// method is inefficient. + /// This function increases the priority of an item to the given value. + /// \param item The item. + /// \param value The priority. + /// \pre \e item must be stored in the heap with priority at most \e value. void increase (Item item, const Prio& value) { erase(item); push(item,value); } - /// \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 item The item. State state(const Item &item) const { - int i=iimap[item]; + int i=_iim[item]; if( i>=0 ) { - if( container[i].in ) i=0; + if( _data[i].in ) i=0; else i=-2; } return State(i); } - /// \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) { @@ -348,7 +357,7 @@ case POST_HEAP: case PRE_HEAP: if (state(i) == IN_HEAP) erase(i); - iimap[i]=st; + _iim[i]=st; break; case IN_HEAP: break; @@ -359,95 +368,95 @@ void cut(int a, int b) { int child_a; - switch (container[a].degree) { + switch (_data[a].degree) { case 2: - child_a = container[container[a].child].parent; - if( container[a].left_child ) { - container[child_a].left_child=true; - container[b].child=child_a; - container[child_a].parent=container[a].parent; + child_a = _data[_data[a].child].parent; + if( _data[a].left_child ) { + _data[child_a].left_child=true; + _data[b].child=child_a; + _data[child_a].parent=_data[a].parent; } else { - container[child_a].left_child=false; - container[child_a].parent=b; - if( a!=container[b].child ) - container[container[b].child].parent=child_a; + _data[child_a].left_child=false; + _data[child_a].parent=b; + if( a!=_data[b].child ) + _data[_data[b].child].parent=child_a; else - container[b].child=child_a; + _data[b].child=child_a; } - --container[a].degree; - container[container[a].child].parent=a; + --_data[a].degree; + _data[_data[a].child].parent=a; break; case 1: - child_a = container[a].child; - if( !container[child_a].left_child ) { - --container[a].degree; - if( container[a].left_child ) { - container[child_a].left_child=true; - container[child_a].parent=container[a].parent; - container[b].child=child_a; + child_a = _data[a].child; + if( !_data[child_a].left_child ) { + --_data[a].degree; + if( _data[a].left_child ) { + _data[child_a].left_child=true; + _data[child_a].parent=_data[a].parent; + _data[b].child=child_a; } else { - container[child_a].left_child=false; - container[child_a].parent=b; - if( a!=container[b].child ) - container[container[b].child].parent=child_a; + _data[child_a].left_child=false; + _data[child_a].parent=b; + if( a!=_data[b].child ) + _data[_data[b].child].parent=child_a; else - container[b].child=child_a; + _data[b].child=child_a; } - container[a].child=-1; + _data[a].child=-1; } else { - --container[b].degree; - if( container[a].left_child ) { - container[b].child = - (1==container[b].degree) ? container[a].parent : -1; + --_data[b].degree; + if( _data[a].left_child ) { + _data[b].child = + (1==_data[b].degree) ? _data[a].parent : -1; } else { - if (1==container[b].degree) - container[container[b].child].parent=b; + if (1==_data[b].degree) + _data[_data[b].child].parent=b; else - container[b].child=-1; + _data[b].child=-1; } } break; case 0: - --container[b].degree; - if( container[a].left_child ) { - container[b].child = - (0!=container[b].degree) ? container[a].parent : -1; + --_data[b].degree; + if( _data[a].left_child ) { + _data[b].child = + (0!=_data[b].degree) ? _data[a].parent : -1; } else { - if( 0!=container[b].degree ) - container[container[b].child].parent=b; + if( 0!=_data[b].degree ) + _data[_data[b].child].parent=b; else - container[b].child=-1; + _data[b].child=-1; } break; } - container[a].parent=-1; - container[a].left_child=false; + _data[a].parent=-1; + _data[a].left_child=false; } void fuse(int a, int b) { - int child_a = container[a].child; - int child_b = container[b].child; - container[a].child=b; - container[b].parent=a; - container[b].left_child=true; + int child_a = _data[a].child; + int child_b = _data[b].child; + _data[a].child=b; + _data[b].parent=a; + _data[b].left_child=true; if( -1!=child_a ) { - container[b].child=child_a; - container[child_a].parent=b; - container[child_a].left_child=false; - ++container[b].degree; + _data[b].child=child_a; + _data[child_a].parent=b; + _data[child_a].left_child=false; + ++_data[b].degree; if( -1!=child_b ) { - container[b].child=child_b; - container[child_b].parent=child_a; + _data[b].child=child_b; + _data[child_b].parent=child_a; } } - else { ++container[a].degree; } + else { ++_data[a].degree; } } class store {