diff --git a/lemon/Makefile.am b/lemon/Makefile.am --- a/lemon/Makefile.am +++ b/lemon/Makefile.am @@ -59,6 +59,7 @@ lemon/assert.h \ lemon/bfs.h \ lemon/bin_heap.h \ + lemon/binom_heap.h \ lemon/bucket_heap.h \ lemon/cbc.h \ lemon/circulation.h \ @@ -78,12 +79,14 @@ 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 +1,506 @@ +/* -*- C++ -*- + * + * This file is a part of LEMON, a generic C++ optimization library + * + * Copyright (C) 2003-2008 + * 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 auxdat +///\brief Binomial Heap implementation. + +#include +#include +#include +#include + +namespace lemon { + + /// \ingroup auxdat + /// + ///\brief Binomial Heap. + /// + ///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. + /// + ///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". + /// + ///\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 + +#ifdef DOXYGEN + template +#else + template > +#endif + class BinomHeap { + public: + typedef _ItemIntMap ItemIntMap; + typedef _Prio Prio; + typedef typename ItemIntMap::Key Item; + typedef std::pair Pair; + typedef _Compare Compare; + + private: + class store; + + std::vector container; + int minimum, head; + ItemIntMap &iimap; + 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 The 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() {} + + /// \brief The number of items stored in the heap. + /// + /// Returns the number of items stored in the heap. + int size() const { return num_items; } + + /// \brief Checks if the heap stores no items. + /// + /// Returns \c true if and only if the heap stores no items. + bool empty() const { return num_items==0; } + + /// \brief Make empty this heap. + /// + /// Make empty this heap. It does not change the cross reference + /// map. If you want to reuse a heap what is not surely empty you + /// should first clear the heap and after that you should set the + /// cross reference map for each item to \c PRE_HEAP. + void clear() { + container.clear(); minimum=0; num_items=0; head=-1; + } + + /// \brief \c item gets to the heap with priority \c value independently + /// if \c item was already there. + /// + /// 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. + 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); + } else push(item, value); + } + + /// \brief Adds \c item to the heap with priority \c value. + /// + /// Adds \c item to the heap with priority \c value. + /// \pre \c item must not be stored in the heap. + void push (const Item& item, const Prio& value) { + int i=iimap[item]; + if ( i<0 ) { + int s=container.size(); + iimap.set( item,s ); + store st; + st.name=item; + container.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; + } + container[i].prio=value; + + if( 0==num_items ) { head=i; minimum=i; } + else { merge(i); } + + minimum = find_min(); + + ++num_items; + } + + /// \brief Returns the item with minimum priority relative to \c Compare. + /// + /// 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; } + + /// \brief Returns the minimum priority relative to \c Compare. + /// + /// It returns the minimum priority relative to \c Compare. + /// \pre The heap must be nonempty. + const Prio& prio() const { return container[minimum].prio; } + + /// \brief Returns the priority of \c item. + /// + /// It returns the priority of \c item. + /// \pre \c item must be in the heap. + const Prio& operator[](const Item& item) const { + return container[iimap[item]].prio; + } + + /// \brief Deletes the item with minimum priority relative to \c Compare. + /// + /// This method deletes the item with minimum priority relative to \c + /// Compare from the heap. + /// \pre The heap must be non-empty. + void pop() { + container[minimum].in=false; + + int head_child=-1; + if ( container[minimum].child!=-1 ) { + int child=container[minimum].child; + int neighb; + int prev=-1; + while( child!=-1 ) { + neighb=container[child].right_neighbor; + container[child].parent=-1; + container[child].right_neighbor=prev; + head_child=child; + prev=child; + child=neighb; + } + } + + // The first case is that there are only one root. + if ( -1==container[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; } + + merge(head_child); + } + minimum=find_min(); + --num_items; + } + + /// \brief Deletes \c 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. + void erase (const Item& item) { + int i=iimap[item]; + if ( i >= 0 && container[i].in ) { + decrease( item, container[minimum].prio-1 ); + pop(); + } + } + + /// \brief Decreases the priority of \c item to \c 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. + void decrease (Item item, const Prio& value) { + int i=iimap[item]; + + if( comp( value,container[i].prio ) ) { + container[i].prio=value; + + int p_loc=container[i].parent, loc=i; + int parent, child, neighb; + + while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) { + + // parent set for other loc_child + child=container[loc].child; + while( -1!=child ) { + container[child].parent=p_loc; + child=container[child].right_neighbor; + } + + // parent set for other p_loc_child + child=container[p_loc].child; + while( -1!=child ) { + container[child].parent=loc; + child=container[child].right_neighbor; + } + + child=container[p_loc].child; + container[p_loc].child=container[loc].child; + if( child==loc ) + child=p_loc; + container[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; + } + + // left_neighb set for loc + parent=container[p_loc].parent; + if( -1!=parent ) child=container[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; + } + + neighb=container[p_loc].right_neighbor; + container[p_loc].right_neighbor=container[loc].right_neighbor; + container[loc].right_neighbor=neighb; + + container[p_loc].parent=loc; + container[loc].parent=parent; + + if( -1!=parent && container[parent].child==p_loc ) + container[parent].child=loc; + + /*if new parent will be the first root*/ + if( head==p_loc ) + head=loc; + + p_loc=container[loc].parent; + } + } + if( comp(value,container[minimum].prio) ) { + minimum=i; + } + } + + /// \brief Increases the priority of \c item to \c 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. + 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. + /// + /// 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. + State state(const Item &item) const { + int i=iimap[item]; + if( i>=0 ) { + if ( container[i].in ) i=0; + else i=-2; + } + return State(i); + } + + /// \brief Sets the state of the \c 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. + /// \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); + } + iimap[i] = st; + break; + case IN_HEAP: + break; + } + } + + private: + int find_min() { + int min_loc=-1, min_val; + int x=head; + if( x!=-1 ) { + min_val=container[x].prio; + min_loc=x; + x=container[x].right_neighbor; + + while( x!=-1 ) { + if( comp( container[x].prio,min_val ) ) { + min_val=container[x].prio; + min_loc=x; + } + x=container[x].right_neighbor; + } + } + return min_loc; + } + + void merge(int a) { + interleave(a); + + int x=head; + if( -1!=x ) { + int x_prev=-1, x_next=container[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 ) ) { + 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; + fuse(x_next,x); + } + else { + if( -1==x_prev ) { head=x_next; } + else { + container[x_prev].right_neighbor=x_next; + } + fuse(x,x_next); + x=x_next; + } + } + x_next=container[x].right_neighbor; + } + } + } + + void interleave(int a) { + int other=-1, head_other=-1; + + while( -1!=a || -1!=head ) { + if( -1==a ) { + if( -1==head_other ) { + head_other=head; + } + else { + container[other].right_neighbor=head; + } + head=-1; + } + else if( -1==head ) { + if( -1==head_other ) { + head_other=a; + } + else { + container[other].right_neighbor=a; + } + a=-1; + } + else { + if( container[a].degree +#include +#include +#include + +namespace lemon { + + ///\ingroup auxdat + /// + ///\brief A 4ary Heap implementation. + /// + ///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. + /// + ///\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 FibHeap + ///\sa Dijkstra + ///\author Dorian Batha + + 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. + /// + /// 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 + /// 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... + enum State { + IN_HEAP = 0, + PRE_HEAP = -1, + POST_HEAP = -2 + }; + + private: + std::vector data; + Compare comp; + ItemIntMap &iim; + + public: + /// \brief The 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) {} + + /// \brief The 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. + /// + /// \param _comp The comparator function object. + FouraryHeap(ItemIntMap &_iim, const Compare &_comp) + : iim(_iim), comp(_comp) {} + + /// The number of items stored in the heap. + /// + /// \brief Returns the number of items stored in the heap. + int size() const { return data.size(); } + + /// \brief Checks if the heap stores no items. + /// + /// 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(); } + + 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); + } + + int find_min(const int child, const int length) { + int min=child; + if( child+30 && 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) { + int child = firstChild(hole); + while( child1 ) { + child = find_min(child,length); + if( !less(data[child], p) ) + goto ok; + move(data[child], hole); + hole = child; + child = firstChild(hole); + } + ok: + move(p, hole); + } + + void move(const Pair &p, int 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. + /// \param p The pair to insert. + void push(const Pair &p) { + int n = data.size(); + data.resize(n+1); + bubble_up(n, p); + } + + /// \brief Insert an item into the heap with the given heap. + /// + /// Adds \c i to the heap with priority \c p. + /// \param i The item to insert. + /// \param p The priority of the item. + void push(const Item &i, const Prio &p) { push(Pair(i,p)); } + + /// \brief Returns the item with minimum priority relative to \c Compare. + /// + /// 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; } + + /// \brief Returns the minimum priority relative to \c Compare. + /// + /// It returns the minimum priority relative to \c Compare. + /// \pre The heap must be nonempty. + Prio prio() const { return data[0].second; } + + /// \brief Deletes the item with minimum priority relative to \c Compare. + /// + /// This method deletes the item with minimum priority relative to \c + /// Compare from the heap. + /// \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(); + } + + /// \brief Deletes \c i 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. + 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 Sets the state of the \c 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. + /// \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 Replaces 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. + 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 +1,342 @@ +/* -*- C++ -*- + * + * This file is a part of LEMON, a generic C++ optimization library + * + * Copyright (C) 2003-2008 + * 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 auxdat +///\file +///\brief Kary Heap implementation. + +#include +#include +#include +#include + +namespace lemon { + + ///\ingroup auxdat + /// + ///\brief A Kary Heap implementation. + /// + ///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. + /// + ///\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 FibHeap + ///\sa Dijkstra + ///\author Dorian Batha + + 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. + /// + /// 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 + /// 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... + enum State { + IN_HEAP = 0, + PRE_HEAP = -1, + POST_HEAP = -2 + }; + + private: + std::vector data; + Compare comp; + ItemIntMap &iim; + int K; + + public: + /// \brief The 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) {} + + /// \brief The 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. + /// + /// \param _comp The comparator function object. + KaryHeap(ItemIntMap &_iim, const Compare &_comp, const int &_K=32) + : iim(_iim), comp(_comp), K(_K) {} + + + /// The number of items stored in the heap. + /// + /// \brief Returns the number of items stored in the heap. + int size() const { return data.size(); } + + /// \brief Checks if the heap stores no items. + /// + /// 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(); } + + private: + int parent(int i) { return (i-1)/K; } + int first_child(int i) { return K*i+1; } + + bool less(const Pair &p1, const Pair &p2) const { + return comp(p1.second, p2.second); + } + + int find_min(const int child, const int length) { + int min=child, i=1; + while( i0 && 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) { + if( length>1 ) { + int child = first_child(hole); + while( child0) bubble_down(0, data[n], n); + data.pop_back(); + } + + /// \brief Deletes \c i 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. + 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 Sets the state of the \c 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. + /// \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 Replaces 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. + 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 +1,469 @@ +/* -*- C++ -*- + * + * This file is a part of LEMON, a generic C++ optimization library + * + * Copyright (C) 2003-2008 + * 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 auxdat +///\brief Pairing Heap implementation. + +#include +#include +#include + +namespace lemon { + + /// \ingroup auxdat + /// + ///\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. + /// + ///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". + /// + ///\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 + +#ifdef DOXYGEN + template +#else + template > +#endif + class PairingHeap { + public: + typedef _ItemIntMap ItemIntMap; + typedef _Prio Prio; + typedef typename ItemIntMap::Key Item; + typedef std::pair Pair; + typedef _Compare Compare; + + private: + class store; + + std::vector container; + int minimum; + ItemIntMap &iimap; + 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 The 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) {} + + /// \brief The number of items stored in the heap. + /// + /// Returns the number of items stored in the heap. + int size() const { return num_items; } + + /// \brief Checks if the heap stores no items. + /// + /// Returns \c true if and only if the heap stores no items. + bool empty() const { return num_items==0; } + + /// \brief Make empty this heap. + /// + /// Make empty this heap. It does not change the cross reference + /// map. If you want to reuse a heap what is not surely empty you + /// should first clear the heap and after that you should set the + /// cross reference map for each item to \c PRE_HEAP. + void clear() { + container.clear(); + minimum = 0; + num_items = 0; + } + + /// \brief \c item gets to the heap with priority \c value independently + /// if \c item was already there. + /// + /// 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. + 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); + } else push(item, value); + } + + /// \brief Adds \c item to the heap with priority \c value. + /// + /// Adds \c item to the heap with priority \c value. + /// \pre \c item must not be stored in the heap. + void push (const Item& item, const Prio& value) { + int i=iimap[item]; + if( i<0 ) { + int s=container.size(); + iimap.set(item, s); + store st; + st.name=item; + container.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; + } + + container[i].prio=value; + + if ( num_items!=0 ) { + if ( comp( value, container[minimum].prio) ) { + fuse(i,minimum); + minimum=i; + } + else fuse(minimum,i); + } + else minimum=i; + + ++num_items; + } + + /// \brief Returns the item with minimum priority relative to \c Compare. + /// + /// 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; } + + /// \brief Returns the minimum priority relative to \c Compare. + /// + /// It returns the minimum priority relative to \c Compare. + /// \pre The heap must be nonempty. + const Prio& prio() const { return container[minimum].prio; } + + /// \brief Returns the priority of \c item. + /// + /// It returns the priority of \c item. + /// \pre \c item must be in the heap. + const Prio& operator[](const Item& item) const { + return container[iimap[item]].prio; + } + + /// \brief Deletes the item with minimum priority relative to \c Compare. + /// + /// This method deletes the item with minimum priority relative to \c + /// Compare from the heap. + /// \pre The heap must be non-empty. + void pop() { + int TreeArray[num_items]; + int i=0, num_child=0, child_right = 0; + container[minimum].in=false; + + if( -1!=container[minimum].child ) { + i=container[minimum].child; + TreeArray[num_child] = i; + container[i].parent = -1; + container[minimum].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 ) { + i=ch; + //break; + } else { + if( container[ch].left_child ) { + child_right=container[ch].parent; + container[ch].parent = i; + --container[i].degree; + } + else { + child_right=ch; + container[i].child=-1; + container[i].degree=0; + } + container[child_right].parent = -1; + TreeArray[num_child] = child_right; + i = child_right; + ++num_child; + } + } + + int other; + for( i=0; i=2) { + if ( comp(container[TreeArray[i]].prio, + container[TreeArray[i-2]].prio) ) { + other=TreeArray[i]; + TreeArray[i]=TreeArray[i-2]; + TreeArray[i-2]=other; + } + fuse( TreeArray[i-2], TreeArray[i] ); + i-=2; + } + minimum = TreeArray[0]; + } + + if ( 0==num_child ) { + minimum = container[minimum].child; + } + + --num_items; + } + + /// \brief Deletes \c 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. + void erase (const Item& item) { + int i=iimap[item]; + if ( i>=0 && container[i].in ) { + decrease( item, container[minimum].prio-1 ); + pop(); + } + } + + /// \brief Decreases the priority of \c item to \c 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. + void decrease (Item item, const Prio& value) { + int i=iimap[item]; + container[i].prio=value; + int p=container[i].parent; + + if( container[i].left_child && i!=container[p].child ) { + p=container[p].parent; + } + + if ( p!=-1 && comp(value,container[p].prio) ) { + cut(i,p); + if ( comp(container[minimum].prio,value) ) { + fuse(minimum,i); + } else { + fuse(i,minimum); + minimum=i; + } + } + } + + /// \brief Increases the priority of \c item to \c 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. + 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. + /// + /// 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. + State state(const Item &item) const { + int i=iimap[item]; + if( i>=0 ) { + if( container[i].in ) i=0; + else i=-2; + } + return State(i); + } + + /// \brief Sets the state of the \c 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. + /// \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); + iimap[i]=st; + break; + case IN_HEAP: + break; + } + } + + private: + + void cut(int a, int b) { + int child_a; + switch (container[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; + } + else { + container[child_a].left_child=false; + container[child_a].parent=b; + if( a!=container[b].child ) + container[container[b].child].parent=child_a; + else + container[b].child=child_a; + } + --container[a].degree; + container[container[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; + } + else { + container[child_a].left_child=false; + container[child_a].parent=b; + if( a!=container[b].child ) + container[container[b].child].parent=child_a; + else + container[b].child=child_a; + } + container[a].child=-1; + } + else { + --container[b].degree; + if( container[a].left_child ) { + container[b].child = + (1==container[b].degree) ? container[a].parent : -1; + } else { + if (1==container[b].degree) + container[container[b].child].parent=b; + else + container[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; + } else { + if( 0!=container[b].degree ) + container[container[b].child].parent=b; + else + container[b].child=-1; + } + break; + } + container[a].parent=-1; + container[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; + + if( -1!=child_a ) { + container[b].child=child_a; + container[child_a].parent=b; + container[child_a].left_child=false; + ++container[b].degree; + + if( -1!=child_b ) { + container[b].child=child_b; + container[child_b].parent=child_a; + } + } + else { ++container[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; }