diff --git a/lemon/Makefile.am b/lemon/Makefile.am --- a/lemon/Makefile.am +++ b/lemon/Makefile.am @@ -60,6 +60,7 @@ lemon/bellman_ford.h \ lemon/bfs.h \ lemon/bin_heap.h \ + lemon/binom_heap.h \ lemon/bucket_heap.h \ lemon/cbc.h \ lemon/circulation.h \ @@ -79,12 +80,14 @@ lemon/error.h \ lemon/euler.h \ lemon/fib_heap.h \ + lemon/fourary_heap.h \ lemon/full_graph.h \ lemon/glpk.h \ lemon/gomory_hu.h \ lemon/graph_to_eps.h \ lemon/grid_graph.h \ lemon/hypercube_graph.h \ + lemon/kary_heap.h \ lemon/kruskal.h \ lemon/hao_orlin.h \ lemon/lgf_reader.h \ @@ -99,6 +102,7 @@ lemon/min_cost_arborescence.h \ lemon/nauty_reader.h \ lemon/network_simplex.h \ + lemon/pairing_heap.h \ lemon/path.h \ lemon/preflow.h \ lemon/radix_heap.h \ diff --git a/lemon/binom_heap.h b/lemon/binom_heap.h new file mode 100644 --- /dev/null +++ b/lemon/binom_heap.h @@ -0,0 +1,445 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_BINOM_HEAP_H +#define LEMON_BINOM_HEAP_H + +///\file +///\ingroup heaps +///\brief Binomial Heap implementation. + +#include +#include +#include +#include +#include + +namespace lemon { + + /// \ingroup heaps + /// + ///\brief Binomial heap data structure. + /// + /// 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 of these operations, + /// it is better to use other heap structure, e.g. \ref BinHeap + /// "binary heap". + /// + /// \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 +#else + template > +#endif + class BinomHeap { + 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; + /// 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 _data; + int _min, _head; + ItemIntMap &_iim; + Compare _comp; + int _num_items; + + public: + /// \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 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. + /// \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. + /// + /// This function returns the number of items stored in the heap. + int size() const { return _num_items; } + + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _num_items==0; } + + /// \brief Make the heap empty. + /// + /// 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(); _min=0; _num_items=0; _head=-1; + } + + /// \brief Set the priority of an item or insert it, if it is + /// not stored in the heap. + /// + /// 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=_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 Insert an item into the heap with the given priority. + /// + /// 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=_iim[item]; + if ( i<0 ) { + int s=_data.size(); + _iim.set( item,s ); + Store st; + st.name=item; + st.prio=value; + _data.push_back(st); + i=s; + } + else { + _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; + _data[i].degree=0; + _data[i].in=true; + _data[i].prio=value; + } + + if( 0==_num_items ) { + _head=i; + _min=i; + } else { + merge(i); + if( _comp(_data[i].prio, _data[_min].prio) ) _min=i; + } + ++_num_items; + } + + /// \brief Return the item having minimum priority. + /// + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { return _data[_min].name; } + + /// \brief The minimum priority. + /// + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + Prio prio() const { return _data[_min].prio; } + + /// \brief The priority of the given item. + /// + /// 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 _data[_iim[item]].prio; + } + + /// \brief Remove the item having minimum priority. + /// + /// This function removes the item having minimum priority. + /// \pre The heap must be non-empty. + void pop() { + _data[_min].in=false; + + int head_child=-1; + if ( _data[_min].child!=-1 ) { + int child=_data[_min].child; + int neighb; + while( child!=-1 ) { + neighb=_data[child].right_neighbor; + _data[child].parent=-1; + _data[child].right_neighbor=head_child; + head_child=child; + child=neighb; + } + } + + if ( _data[_head].right_neighbor==-1 ) { + // there was only one root + _head=head_child; + } + else { + // there were more roots + if( _head!=_min ) { unlace(_min); } + else { _head=_data[_head].right_neighbor; } + merge(head_child); + } + _min=findMin(); + --_num_items; + } + + /// \brief Remove the given item from the heap. + /// + /// 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=_iim[item]; + if ( i >= 0 && _data[i].in ) { + decrease( item, _data[_min].prio-1 ); + pop(); + } + } + + /// \brief Decrease the priority of an item to the given value. + /// + /// 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=_iim[item]; + int p=_data[i].parent; + _data[i].prio=value; + + while( p!=-1 && _comp(value, _data[p].prio) ) { + _data[i].name=_data[p].name; + _data[i].prio=_data[p].prio; + _data[p].name=item; + _data[p].prio=value; + _iim[_data[i].name]=i; + i=p; + p=_data[p].parent; + } + _iim[item]=i; + if ( _comp(value, _data[_min].prio) ) _min=i; + } + + /// \brief Increase the priority of an item to the given value. + /// + /// 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 Return the state of an item. + /// + /// 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=_iim[item]; + if( i>=0 ) { + if ( _data[i].in ) i=0; + else i=-2; + } + return State(i); + } + + /// \brief Set the state of an item in the heap. + /// + /// 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; + } + } + + private: + + // Find the minimum of the roots + int findMin() { + if( _head!=-1 ) { + int min_loc=_head, min_val=_data[_head].prio; + for( int x=_data[_head].right_neighbor; x!=-1; + x=_data[x].right_neighbor ) { + if( _comp( _data[x].prio,min_val ) ) { + min_val=_data[x].prio; + min_loc=x; + } + } + return min_loc; + } + else return -1; + } + + // Merge the heap with another heap starting at the given position + void merge(int a) { + if( _head==-1 || a==-1 ) return; + if( _data[a].right_neighbor==-1 && + _data[a].degree<=_data[_head].degree ) { + _data[a].right_neighbor=_head; + _head=a; + } else { + interleave(a); + } + if( _data[_head].right_neighbor==-1 ) return; + + int x=_head; + int x_prev=-1, x_next=_data[x].right_neighbor; + while( x_next!=-1 ) { + if( _data[x].degree!=_data[x_next].degree || + ( _data[x_next].right_neighbor!=-1 && + _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { + x_prev=x; + x=x_next; + } + else { + if( _comp(_data[x_next].prio,_data[x].prio) ) { + if( x_prev==-1 ) { + _head=x_next; + } else { + _data[x_prev].right_neighbor=x_next; + } + fuse(x,x_next); + x=x_next; + } + else { + _data[x].right_neighbor=_data[x_next].right_neighbor; + fuse(x_next,x); + } + } + x_next=_data[x].right_neighbor; + } + } + + // Interleave the elements of the given list into the list of the roots + void interleave(int a) { + int p=_head, q=a; + int curr=_data.size(); + _data.push_back(Store()); + + while( p!=-1 || q!=-1 ) { + if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) { + _data[curr].right_neighbor=p; + curr=p; + p=_data[p].right_neighbor; + } + else { + _data[curr].right_neighbor=q; + curr=q; + q=_data[q].right_neighbor; + } + } + + _head=_data.back().right_neighbor; + _data.pop_back(); + } + + // Lace node a under node b + void fuse(int a, int b) { + _data[a].parent=b; + _data[a].right_neighbor=_data[b].child; + _data[b].child=a; + + ++_data[b].degree; + } + + // Unlace node a (if it has siblings) + void unlace(int a) { + int neighb=_data[a].right_neighbor; + int other=_head; + + while( _data[other].right_neighbor!=a ) + other=_data[other].right_neighbor; + _data[other].right_neighbor=neighb; + } + + private: + + class Store { + friend class BinomHeap; + + Item name; + int parent; + int right_neighbor; + int child; + int degree; + bool in; + Prio prio; + + Store() : parent(-1), right_neighbor(-1), child(-1), degree(0), + in(true) {} + }; + }; + +} //namespace lemon + +#endif //LEMON_BINOM_HEAP_H + diff --git a/lemon/fourary_heap.h b/lemon/fourary_heap.h new file mode 100644 --- /dev/null +++ b/lemon/fourary_heap.h @@ -0,0 +1,342 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_FOURARY_HEAP_H +#define LEMON_FOURARY_HEAP_H + +///\ingroup heaps +///\file +///\brief Fourary heap implementation. + +#include +#include +#include + +namespace lemon { + + /// \ingroup heaps + /// + ///\brief Fourary heap data structure. + /// + /// This class implements the \e fourary \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". + /// + /// 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. + /// + /// \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; + + /// \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: + std::vector _data; + Compare _comp; + ItemIntMap &_iim; + + public: + /// \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 FouraryHeap(ItemIntMap &map) : _iim(map) {} + + /// \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. + /// \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. + /// + /// 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(); } + + /// \brief Make the heap empty. + /// + /// 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); + } + + void bubbleUp(int hole, Pair p) { + int par = parent(hole); + while( hole>0 && less(p,_data[par]) ) { + move(_data[par],hole); + hole = par; + par = parent(hole); + } + move(p, hole); + } + + void bubbleDown(int hole, Pair p, int length) { + if( length>1 ) { + int child = firstChild(hole); + while( child+30) bubbleDown(0, _data[n], n); + _data.pop_back(); + } + + /// \brief Remove the given item from 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); + if( h=0) s=0; + return State(s); + } + + /// \brief Set the state of an item in the heap. + /// + /// 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; + } + } + + /// \brief Replace an item in the heap. + /// + /// 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; + } + + }; // class FouraryHeap + +} // namespace lemon + +#endif // LEMON_FOURARY_HEAP_H diff --git a/lemon/kary_heap.h b/lemon/kary_heap.h new file mode 100644 --- /dev/null +++ b/lemon/kary_heap.h @@ -0,0 +1,352 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_KARY_HEAP_H +#define LEMON_KARY_HEAP_H + +///\ingroup heaps +///\file +///\brief Fourary heap implementation. + +#include +#include +#include + +namespace lemon { + + /// \ingroup heaps + /// + ///\brief K-ary heap data structure. + /// + /// This class implements the \e K-ary \e heap data structure. + /// It fully conforms to the \ref concepts::Heap "heap concept". + /// + /// 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. + /// + /// \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 K The degree of the heap, each node have at most \e K + /// children. The default is 16. Powers of two are suggested to use + /// so that the multiplications and divisions needed to traverse the + /// nodes of the heap could be performed faster. + /// \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; + + /// \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: + std::vector _data; + Compare _comp; + ItemIntMap &_iim; + + public: + /// \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 KaryHeap(ItemIntMap &map) : _iim(map) {} + + /// \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. + /// \param comp The function object used for comparing the priorities. + KaryHeap(ItemIntMap &map, const Compare &comp) + : _iim(map), _comp(comp) {} + + /// \brief The number of items stored in the heap. + /// + /// 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(); } + + /// \brief Make the heap empty. + /// + /// 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 firstChild(int i) { return K*i+1; } + + bool less(const Pair &p1, const Pair &p2) const { + return _comp(p1.second, p2.second); + } + + void bubbleUp(int hole, Pair p) { + int par = parent(hole); + while( hole>0 && less(p,_data[par]) ) { + move(_data[par],hole); + hole = par; + par = parent(hole); + } + move(p, hole); + } + + void bubbleDown(int hole, Pair p, int length) { + if( length>1 ) { + int child = firstChild(hole); + while( child+K<=length ) { + int min=child; + for (int i=1; i0) bubbleDown(0, _data[n], n); + _data.pop_back(); + } + + /// \brief Remove the given item from 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); + if( h=0) s=0; + return State(s); + } + + /// \brief Set the state of an item in the heap. + /// + /// 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; + } + } + + /// \brief Replace an item in the heap. + /// + /// 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; + } + + }; // class KaryHeap + +} // namespace lemon + +#endif // LEMON_KARY_HEAP_H diff --git a/lemon/pairing_heap.h b/lemon/pairing_heap.h new file mode 100644 --- /dev/null +++ b/lemon/pairing_heap.h @@ -0,0 +1,474 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_PAIRING_HEAP_H +#define LEMON_PAIRING_HEAP_H + +///\file +///\ingroup heaps +///\brief Pairing heap implementation. + +#include +#include +#include +#include + +namespace lemon { + + /// \ingroup heaps + /// + ///\brief Pairing Heap. + /// + /// 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 of these operations, + /// it is better to use other heap structure, e.g. \ref BinHeap + /// "binary heap". + /// + /// \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 +#else + template > +#endif + class PairingHeap { + 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; + /// 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 _data; + int _min; + ItemIntMap &_iim; + Compare _comp; + int _num_items; + + public: + /// \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 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. + /// \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. + /// + /// This function returns the number of items stored in the heap. + int size() const { return _num_items; } + + /// \brief Check if the heap is empty. + /// + /// This function returns \c true if the heap is empty. + bool empty() const { return _num_items==0; } + + /// \brief Make the heap empty. + /// + /// 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(); + _min = 0; + _num_items = 0; + } + + /// \brief Set the priority of an item or insert it, if it is + /// not stored in the heap. + /// + /// 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=_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 Insert an item into the heap with the given priority. + /// + /// 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=_iim[item]; + if( i<0 ) { + int s=_data.size(); + _iim.set(item, s); + store st; + st.name=item; + _data.push_back(st); + i=s; + } else { + _data[i].parent=_data[i].child=-1; + _data[i].left_child=false; + _data[i].degree=0; + _data[i].in=true; + } + + _data[i].prio=value; + + if ( _num_items!=0 ) { + if ( _comp( value, _data[_min].prio) ) { + fuse(i,_min); + _min=i; + } + else fuse(_min,i); + } + else _min=i; + + ++_num_items; + } + + /// \brief Return the item having minimum priority. + /// + /// This function returns the item having minimum priority. + /// \pre The heap must be non-empty. + Item top() const { return _data[_min].name; } + + /// \brief The minimum priority. + /// + /// This function returns the minimum priority. + /// \pre The heap must be non-empty. + const Prio& prio() const { return _data[_min].prio; } + + /// \brief The priority of the given item. + /// + /// 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 _data[_iim[item]].prio; + } + + /// \brief Remove the item having minimum priority. + /// + /// This function removes the item having minimum priority. + /// \pre The heap must be non-empty. + void pop() { + std::vector trees; + int i=0, child_right = 0; + _data[_min].in=false; + + if( -1!=_data[_min].child ) { + i=_data[_min].child; + trees.push_back(i); + _data[i].parent = -1; + _data[_min].child = -1; + + int ch=-1; + while( _data[i].child!=-1 ) { + ch=_data[i].child; + if( _data[ch].left_child && i==_data[ch].parent ) { + break; + } else { + if( _data[ch].left_child ) { + child_right=_data[ch].parent; + _data[ch].parent = i; + --_data[i].degree; + } + else { + child_right=ch; + _data[i].child=-1; + _data[i].degree=0; + } + _data[child_right].parent = -1; + trees.push_back(child_right); + i = child_right; + } + } + + int num_child = trees.size(); + int other; + for( i=0; i=2) { + if ( _comp(_data[trees[i]].prio, _data[trees[i-2]].prio) ) { + other=trees[i]; + trees[i]=trees[i-2]; + trees[i-2]=other; + } + fuse( trees[i-2], trees[i] ); + i-=2; + } + _min = trees[0]; + } + else { + _min = _data[_min].child; + } + + if (_min >= 0) _data[_min].left_child = false; + --_num_items; + } + + /// \brief Remove the given item from the heap. + /// + /// 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=_iim[item]; + if ( i>=0 && _data[i].in ) { + decrease( item, _data[_min].prio-1 ); + pop(); + } + } + + /// \brief Decrease the priority of an item to the given value. + /// + /// 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=_iim[item]; + _data[i].prio=value; + int p=_data[i].parent; + + if( _data[i].left_child && i!=_data[p].child ) { + p=_data[p].parent; + } + + if ( p!=-1 && _comp(value,_data[p].prio) ) { + cut(i,p); + if ( _comp(_data[_min].prio,value) ) { + fuse(_min,i); + } else { + fuse(i,_min); + _min=i; + } + } + } + + /// \brief Increase the priority of an item to the given value. + /// + /// 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 Return the state of an item. + /// + /// 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=_iim[item]; + if( i>=0 ) { + if( _data[i].in ) i=0; + else i=-2; + } + return State(i); + } + + /// \brief Set the state of an item in the heap. + /// + /// 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; + } + } + + private: + + void cut(int a, int b) { + int child_a; + switch (_data[a].degree) { + case 2: + 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 { + _data[child_a].left_child=false; + _data[child_a].parent=b; + if( a!=_data[b].child ) + _data[_data[b].child].parent=child_a; + else + _data[b].child=child_a; + } + --_data[a].degree; + _data[_data[a].child].parent=a; + break; + + case 1: + 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 { + _data[child_a].left_child=false; + _data[child_a].parent=b; + if( a!=_data[b].child ) + _data[_data[b].child].parent=child_a; + else + _data[b].child=child_a; + } + _data[a].child=-1; + } + else { + --_data[b].degree; + if( _data[a].left_child ) { + _data[b].child = + (1==_data[b].degree) ? _data[a].parent : -1; + } else { + if (1==_data[b].degree) + _data[_data[b].child].parent=b; + else + _data[b].child=-1; + } + } + break; + + case 0: + --_data[b].degree; + if( _data[a].left_child ) { + _data[b].child = + (0!=_data[b].degree) ? _data[a].parent : -1; + } else { + if( 0!=_data[b].degree ) + _data[_data[b].child].parent=b; + else + _data[b].child=-1; + } + break; + } + _data[a].parent=-1; + _data[a].left_child=false; + } + + void fuse(int a, int b) { + 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 ) { + _data[b].child=child_a; + _data[child_a].parent=b; + _data[child_a].left_child=false; + ++_data[b].degree; + + if( -1!=child_b ) { + _data[b].child=child_b; + _data[child_b].parent=child_a; + } + } + else { ++_data[a].degree; } + } + + class store { + friend class PairingHeap; + + Item name; + int parent; + int child; + bool left_child; + int degree; + bool in; + Prio prio; + + store() : parent(-1), child(-1), left_child(false), degree(0), in(true) {} + }; + }; + +} //namespace lemon + +#endif //LEMON_PAIRING_HEAP_H + diff --git a/test/heap_test.cc b/test/heap_test.cc --- a/test/heap_test.cc +++ b/test/heap_test.cc @@ -25,14 +25,17 @@ #include #include - #include #include #include #include +#include +#include #include +#include #include +#include #include #include "test_tools.h" @@ -89,18 +92,16 @@ template void heapSortTest() { RangeMap map(test_len, -1); - Heap heap(map); std::vector v(test_len); - for (int i = 0; i < test_len; ++i) { v[i] = test_seq[i]; heap.push(i, v[i]); } std::sort(v.begin(), v.end()); for (int i = 0; i < test_len; ++i) { - check(v[i] == heap.prio() ,"Wrong order in heap sort."); + check(v[i] == heap.prio(), "Wrong order in heap sort."); heap.pop(); } } @@ -112,7 +113,6 @@ Heap heap(map); std::vector v(test_len); - for (int i = 0; i < test_len; ++i) { v[i] = test_seq[i]; heap.push(i, v[i]); @@ -123,13 +123,11 @@ } std::sort(v.begin(), v.end()); for (int i = 0; i < test_len; ++i) { - check(v[i] == heap.prio() ,"Wrong order in heap increase test."); + check(v[i] == heap.prio(), "Wrong order in heap increase test."); heap.pop(); } } - - template void dijkstraHeapTest(const Digraph& digraph, const IntArcMap& length, Node source) { @@ -144,7 +142,7 @@ Node t = digraph.target(a); if (dijkstra.reached(s)) { check( dijkstra.dist(t) - dijkstra.dist(s) <= length[a], - "Error in a shortest path tree!"); + "Error in shortest path tree."); } } @@ -153,7 +151,7 @@ Arc a = dijkstra.predArc(n); Node s = digraph.source(a); check( dijkstra.dist(n) - dijkstra.dist(s) == length[a], - "Error in a shortest path tree!"); + "Error in shortest path tree."); } } @@ -175,6 +173,7 @@ node("source", source). run(); + // BinHeap { typedef BinHeap IntHeap; checkConcept, IntHeap>(); @@ -186,6 +185,31 @@ dijkstraHeapTest(digraph, length, source); } + // FouraryHeap + { + typedef FouraryHeap IntHeap; + checkConcept, IntHeap>(); + heapSortTest(); + heapIncreaseTest(); + + typedef FouraryHeap NodeHeap; + checkConcept, NodeHeap>(); + dijkstraHeapTest(digraph, length, source); + } + + // KaryHeap + { + typedef KaryHeap IntHeap; + checkConcept, IntHeap>(); + heapSortTest(); + heapIncreaseTest(); + + typedef KaryHeap NodeHeap; + checkConcept, NodeHeap>(); + dijkstraHeapTest(digraph, length, source); + } + + // FibHeap { typedef FibHeap IntHeap; checkConcept, IntHeap>(); @@ -197,6 +221,19 @@ dijkstraHeapTest(digraph, length, source); } + // PairingHeap + { + typedef PairingHeap IntHeap; + checkConcept, IntHeap>(); + heapSortTest(); + heapIncreaseTest(); + + typedef PairingHeap NodeHeap; + checkConcept, NodeHeap>(); + dijkstraHeapTest(digraph, length, source); + } + + // RadixHeap { typedef RadixHeap IntHeap; checkConcept, IntHeap>(); @@ -208,6 +245,19 @@ dijkstraHeapTest(digraph, length, source); } + // BinomHeap + { + typedef BinomHeap IntHeap; + checkConcept, IntHeap>(); + heapSortTest(); + heapIncreaseTest(); + + typedef BinomHeap NodeHeap; + checkConcept, NodeHeap>(); + dijkstraHeapTest(digraph, length, source); + } + + // BucketHeap, SimpleBucketHeap { typedef BucketHeap IntHeap; checkConcept, IntHeap>(); @@ -217,8 +267,10 @@ typedef BucketHeap NodeHeap; checkConcept, NodeHeap>(); dijkstraHeapTest(digraph, length, source); + + typedef SimpleBucketHeap SimpleIntHeap; + heapSortTest(); } - return 0; }