boost/heap/pairing_heap.hpp
// boost heap: pairing heap // // Copyright (C) 2010 Tim Blechmann // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_HEAP_PAIRING_HEAP_HPP #define BOOST_HEAP_PAIRING_HEAP_HPP #include <algorithm> #include <utility> #include <vector> #include <boost/assert.hpp> #include <boost/heap/detail/heap_comparison.hpp> #include <boost/heap/detail/heap_node.hpp> #include <boost/heap/policies.hpp> #include <boost/heap/detail/stable_heap.hpp> #include <boost/heap/detail/tree_iterator.hpp> #ifdef BOOST_HAS_PRAGMA_ONCE #pragma once #endif #ifndef BOOST_DOXYGEN_INVOKED #ifdef BOOST_HEAP_SANITYCHECKS #define BOOST_HEAP_ASSERT BOOST_ASSERT #else #define BOOST_HEAP_ASSERT(expression) #endif #endif namespace boost { namespace heap { namespace detail { typedef parameter::parameters<boost::parameter::optional<tag::allocator>, boost::parameter::optional<tag::compare>, boost::parameter::optional<tag::stable>, boost::parameter::optional<tag::constant_time_size>, boost::parameter::optional<tag::stability_counter_type> > pairing_heap_signature; template <typename T, typename Parspec> struct make_pairing_heap_base { static const bool constant_time_size = parameter::binding<Parspec, tag::constant_time_size, boost::mpl::true_ >::type::value; typedef typename detail::make_heap_base<T, Parspec, constant_time_size>::type base_type; typedef typename detail::make_heap_base<T, Parspec, constant_time_size>::allocator_argument allocator_argument; typedef typename detail::make_heap_base<T, Parspec, constant_time_size>::compare_argument compare_argument; typedef heap_node<typename base_type::internal_type, false> node_type; typedef typename allocator_argument::template rebind<node_type>::other allocator_type; struct type: base_type, allocator_type { type(compare_argument const & arg): base_type(arg) {} #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES type(type const & rhs): base_type(rhs), allocator_type(rhs) {} type(type && rhs): base_type(std::move(static_cast<base_type&>(rhs))), allocator_type(std::move(static_cast<allocator_type&>(rhs))) {} type & operator=(type && rhs) { base_type::operator=(std::move(static_cast<base_type&>(rhs))); allocator_type::operator=(std::move(static_cast<allocator_type&>(rhs))); return *this; } type & operator=(type const & rhs) { base_type::operator=(static_cast<base_type const &>(rhs)); allocator_type::operator=(static_cast<const allocator_type&>(rhs)); return *this; } #endif }; }; } /** * \class pairing_heap * \brief pairing heap * * Pairing heaps are self-adjusting binary heaps. Although design and implementation are rather simple, * the complexity analysis is yet unsolved. For details, consult: * * Pettie, Seth (2005), "Towards a final analysis of pairing heaps", * Proc. 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 174-183 * * The template parameter T is the type to be managed by the container. * The user can specify additional options and if no options are provided default options are used. * * The container supports the following options: * - \c boost::heap::compare<>, defaults to \c compare<std::less<T> > * - \c boost::heap::stable<>, defaults to \c stable<false> * - \c boost::heap::stability_counter_type<>, defaults to \c stability_counter_type<boost::uintmax_t> * - \c boost::heap::allocator<>, defaults to \c allocator<std::allocator<T> > * - \c boost::heap::constant_time_size<>, defaults to \c constant_time_size<true> * * */ #ifdef BOOST_DOXYGEN_INVOKED template<class T, class ...Options> #else template <typename T, class A0 = boost::parameter::void_, class A1 = boost::parameter::void_, class A2 = boost::parameter::void_, class A3 = boost::parameter::void_, class A4 = boost::parameter::void_ > #endif class pairing_heap: private detail::make_pairing_heap_base<T, typename detail::pairing_heap_signature::bind<A0, A1, A2, A3, A4>::type >::type { typedef typename detail::pairing_heap_signature::bind<A0, A1, A2, A3, A4>::type bound_args; typedef detail::make_pairing_heap_base<T, bound_args> base_maker; typedef typename base_maker::type super_t; typedef typename super_t::internal_type internal_type; typedef typename super_t::size_holder_type size_holder; typedef typename base_maker::allocator_argument allocator_argument; private: template <typename Heap1, typename Heap2> friend struct heap_merge_emulate; #ifndef BOOST_DOXYGEN_INVOKED struct implementation_defined: detail::extract_allocator_types<typename base_maker::allocator_argument> { typedef T value_type; typedef typename detail::extract_allocator_types<typename base_maker::allocator_argument>::size_type size_type; typedef typename detail::extract_allocator_types<typename base_maker::allocator_argument>::reference reference; typedef typename base_maker::compare_argument value_compare; typedef typename base_maker::allocator_type allocator_type; typedef typename allocator_type::pointer node_pointer; typedef typename allocator_type::const_pointer const_node_pointer; typedef detail::heap_node_list node_list_type; typedef typename node_list_type::iterator node_list_iterator; typedef typename node_list_type::const_iterator node_list_const_iterator; typedef typename base_maker::node_type node; typedef detail::value_extractor<value_type, internal_type, super_t> value_extractor; typedef typename super_t::internal_compare internal_compare; typedef detail::node_handle<node_pointer, super_t, reference> handle_type; typedef detail::tree_iterator<node, const value_type, allocator_type, value_extractor, detail::pointer_to_reference<node>, false, false, value_compare > iterator; typedef iterator const_iterator; typedef detail::tree_iterator<node, const value_type, allocator_type, value_extractor, detail::pointer_to_reference<node>, false, true, value_compare > ordered_iterator; }; typedef typename implementation_defined::node node; typedef typename implementation_defined::node_pointer node_pointer; typedef typename implementation_defined::node_list_type node_list_type; typedef typename implementation_defined::node_list_iterator node_list_iterator; typedef typename implementation_defined::node_list_const_iterator node_list_const_iterator; typedef typename implementation_defined::internal_compare internal_compare; typedef boost::intrusive::list<detail::heap_node_base<true>, boost::intrusive::constant_time_size<false> > node_child_list; #endif public: typedef T value_type; typedef typename implementation_defined::size_type size_type; typedef typename implementation_defined::difference_type difference_type; typedef typename implementation_defined::value_compare value_compare; typedef typename implementation_defined::allocator_type allocator_type; typedef typename implementation_defined::reference reference; typedef typename implementation_defined::const_reference const_reference; typedef typename implementation_defined::pointer pointer; typedef typename implementation_defined::const_pointer const_pointer; /// \copydoc boost::heap::priority_queue::iterator typedef typename implementation_defined::iterator iterator; typedef typename implementation_defined::const_iterator const_iterator; typedef typename implementation_defined::ordered_iterator ordered_iterator; typedef typename implementation_defined::handle_type handle_type; static const bool constant_time_size = super_t::constant_time_size; static const bool has_ordered_iterators = true; static const bool is_mergable = true; static const bool is_stable = detail::extract_stable<bound_args>::value; static const bool has_reserve = false; /// \copydoc boost::heap::priority_queue::priority_queue(value_compare const &) explicit pairing_heap(value_compare const & cmp = value_compare()): super_t(cmp), root(NULL) {} /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue const &) pairing_heap(pairing_heap const & rhs): super_t(rhs), root(NULL) { if (rhs.empty()) return; clone_tree(rhs); size_holder::set_size(rhs.get_size()); } #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue &&) pairing_heap(pairing_heap && rhs): super_t(std::move(rhs)), root(rhs.root) { rhs.root = NULL; } /// \copydoc boost::heap::priority_queue::operator=(priority_queue &&) pairing_heap & operator=(pairing_heap && rhs) { super_t::operator=(std::move(rhs)); root = rhs.root; rhs.root = NULL; return *this; } #endif /// \copydoc boost::heap::priority_queue::operator=(priority_queue const & rhs) pairing_heap & operator=(pairing_heap const & rhs) { clear(); size_holder::set_size(rhs.get_size()); static_cast<super_t&>(*this) = rhs; clone_tree(rhs); return *this; } ~pairing_heap(void) { while (!empty()) pop(); } /// \copydoc boost::heap::priority_queue::empty bool empty(void) const { return root == NULL; } /// \copydoc boost::heap::binomial_heap::size size_type size(void) const { if (constant_time_size) return size_holder::get_size(); if (root == NULL) return 0; else return detail::count_nodes(root); } /// \copydoc boost::heap::priority_queue::max_size size_type max_size(void) const { return allocator_type::max_size(); } /// \copydoc boost::heap::priority_queue::clear void clear(void) { if (empty()) return; root->template clear_subtree<allocator_type>(*this); root->~node(); allocator_type::deallocate(root, 1); root = NULL; size_holder::set_size(0); } /// \copydoc boost::heap::priority_queue::get_allocator allocator_type get_allocator(void) const { return *this; } /// \copydoc boost::heap::priority_queue::swap void swap(pairing_heap & rhs) { super_t::swap(rhs); std::swap(root, rhs.root); } /// \copydoc boost::heap::priority_queue::top const_reference top(void) const { BOOST_ASSERT(!empty()); return super_t::get_value(root->value); } /** * \b Effects: Adds a new element to the priority queue. Returns handle to element * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * */ handle_type push(value_type const & v) { size_holder::increment(); node_pointer n = allocator_type::allocate(1); new(n) node(super_t::make_node(v)); merge_node(n); return handle_type(n); } #if !defined(BOOST_NO_CXX11_RVALUE_REFERENCES) && !defined(BOOST_NO_CXX11_VARIADIC_TEMPLATES) /** * \b Effects: Adds a new element to the priority queue. The element is directly constructed in-place. Returns handle to element. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * */ template <class... Args> handle_type emplace(Args&&... args) { size_holder::increment(); node_pointer n = allocator_type::allocate(1); new(n) node(super_t::make_node(std::forward<Args>(args)...)); merge_node(n); return handle_type(n); } #endif /** * \b Effects: Removes the top element from the priority queue. * * \b Complexity: Logarithmic (amortized). * * */ void pop(void) { BOOST_ASSERT(!empty()); erase(handle_type(root)); } /** * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * */ void update (handle_type handle, const_reference v) { handle.node_->value = super_t::make_node(v); update(handle); } /** * \b Effects: Updates the heap after the element handled by \c handle has been changed. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined! * */ void update (handle_type handle) { node_pointer n = handle.node_; n->unlink(); if (!n->children.empty()) n = merge_nodes(n, merge_node_list(n->children)); if (n != root) merge_node(n); } /** * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * \b Note: The new value is expected to be greater than the current one * */ void increase (handle_type handle, const_reference v) { update(handle, v); } /** * \b Effects: Updates the heap after the element handled by \c handle has been changed. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined! * */ void increase (handle_type handle) { update(handle); } /** * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * \b Note: The new value is expected to be less than the current one * */ void decrease (handle_type handle, const_reference v) { update(handle, v); } /** * \b Effects: Updates the heap after the element handled by \c handle has been changed. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * \b Note: The new value is expected to be less than the current one. If this is not called, after a handle has been updated, the behavior of the data structure is undefined! * */ void decrease (handle_type handle) { update(handle); } /** * \b Effects: Removes the element handled by \c handle from the priority_queue. * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * */ void erase(handle_type handle) { node_pointer n = handle.node_; if (n != root) { n->unlink(); if (!n->children.empty()) merge_node(merge_node_list(n->children)); } else { if (!n->children.empty()) root = merge_node_list(n->children); else root = NULL; } size_holder::decrement(); n->~node(); allocator_type::deallocate(n, 1); } /// \copydoc boost::heap::priority_queue::begin iterator begin(void) const { return iterator(root, super_t::value_comp()); } /// \copydoc boost::heap::priority_queue::end iterator end(void) const { return iterator(super_t::value_comp()); } /// \copydoc boost::heap::fibonacci_heap::ordered_begin ordered_iterator ordered_begin(void) const { return ordered_iterator(root, super_t::value_comp()); } /// \copydoc boost::heap::fibonacci_heap::ordered_begin ordered_iterator ordered_end(void) const { return ordered_iterator(NULL, super_t::value_comp()); } /// \copydoc boost::heap::d_ary_heap_mutable::s_handle_from_iterator static handle_type s_handle_from_iterator(iterator const & it) { node * ptr = const_cast<node *>(it.get_node()); return handle_type(ptr); } /** * \b Effects: Merge all elements from rhs into this * * \cond * \b Complexity: \f$2^2log(log(N))\f$ (amortized). * \endcond * * \b Complexity: 2**2*log(log(N)) (amortized). * * */ void merge(pairing_heap & rhs) { if (rhs.empty()) return; merge_node(rhs.root); size_holder::add(rhs.get_size()); rhs.set_size(0); rhs.root = NULL; super_t::set_stability_count((std::max)(super_t::get_stability_count(), rhs.get_stability_count())); rhs.set_stability_count(0); } /// \copydoc boost::heap::priority_queue::value_comp value_compare const & value_comp(void) const { return super_t::value_comp(); } /// \copydoc boost::heap::priority_queue::operator<(HeapType const & rhs) const template <typename HeapType> bool operator<(HeapType const & rhs) const { return detail::heap_compare(*this, rhs); } /// \copydoc boost::heap::priority_queue::operator>(HeapType const & rhs) const template <typename HeapType> bool operator>(HeapType const & rhs) const { return detail::heap_compare(rhs, *this); } /// \copydoc boost::heap::priority_queue::operator>=(HeapType const & rhs) const template <typename HeapType> bool operator>=(HeapType const & rhs) const { return !operator<(rhs); } /// \copydoc boost::heap::priority_queue::operator<=(HeapType const & rhs) const template <typename HeapType> bool operator<=(HeapType const & rhs) const { return !operator>(rhs); } /// \copydoc boost::heap::priority_queue::operator==(HeapType const & rhs) const template <typename HeapType> bool operator==(HeapType const & rhs) const { return detail::heap_equality(*this, rhs); } /// \copydoc boost::heap::priority_queue::operator!=(HeapType const & rhs) const template <typename HeapType> bool operator!=(HeapType const & rhs) const { return !(*this == rhs); } private: #if !defined(BOOST_DOXYGEN_INVOKED) void clone_tree(pairing_heap const & rhs) { BOOST_HEAP_ASSERT(root == NULL); if (rhs.empty()) return; root = allocator_type::allocate(1); new(root) node(static_cast<node const &>(*rhs.root), static_cast<allocator_type&>(*this)); } void merge_node(node_pointer other) { BOOST_HEAP_ASSERT(other); if (root != NULL) root = merge_nodes(root, other); else root = other; } node_pointer merge_node_list(node_child_list & children) { BOOST_HEAP_ASSERT(!children.empty()); node_pointer merged = merge_first_pair(children); if (children.empty()) return merged; node_child_list node_list; node_list.push_back(*merged); do { node_pointer next_merged = merge_first_pair(children); node_list.push_back(*next_merged); } while (!children.empty()); return merge_node_list(node_list); } node_pointer merge_first_pair(node_child_list & children) { BOOST_HEAP_ASSERT(!children.empty()); node_pointer first_child = static_cast<node_pointer>(&children.front()); children.pop_front(); if (children.empty()) return first_child; node_pointer second_child = static_cast<node_pointer>(&children.front()); children.pop_front(); return merge_nodes(first_child, second_child); } node_pointer merge_nodes(node_pointer node1, node_pointer node2) { if (super_t::operator()(node1->value, node2->value)) std::swap(node1, node2); node2->unlink(); node1->children.push_front(*node2); return node1; } node_pointer root; #endif }; } /* namespace heap */ } /* namespace boost */ #undef BOOST_HEAP_ASSERT #endif /* BOOST_HEAP_PAIRING_HEAP_HPP */