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 {