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1 // boost heap: pairing heap
2 //
3 // Copyright (C) 2010 Tim Blechmann
4 //
5 // Distributed under the Boost Software License, Version 1.0. (See
6 // accompanying file LICENSE_1_0.txt or copy at
7 // http://www.boost.org/LICENSE_1_0.txt)
8 
9 #ifndef BOOST_HEAP_PAIRING_HEAP_HPP
10 #define BOOST_HEAP_PAIRING_HEAP_HPP
11 
12 #include <algorithm>
13 #include <utility>
14 #include <vector>
15 
16 #include <boost/assert.hpp>
17 
18 #include <boost/heap/detail/heap_comparison.hpp>
19 #include <boost/heap/detail/heap_node.hpp>
20 #include <boost/heap/policies.hpp>
21 #include <boost/heap/detail/stable_heap.hpp>
22 #include <boost/heap/detail/tree_iterator.hpp>
23 #include <boost/type_traits/integral_constant.hpp>
24 
25 #ifdef BOOST_HAS_PRAGMA_ONCE
26 #pragma once
27 #endif
28 
29 
30 #ifndef BOOST_DOXYGEN_INVOKED
31 #ifdef BOOST_HEAP_SANITYCHECKS
32 #define BOOST_HEAP_ASSERT BOOST_ASSERT
33 #else
34 #define BOOST_HEAP_ASSERT(expression)
35 #endif
36 #endif
37 
38 namespace boost  {
39 namespace heap   {
40 namespace detail {
41 
42 typedef parameter::parameters<boost::parameter::optional<tag::allocator>,
43                               boost::parameter::optional<tag::compare>,
44                               boost::parameter::optional<tag::stable>,
45                               boost::parameter::optional<tag::constant_time_size>,
46                               boost::parameter::optional<tag::stability_counter_type>
47                              > pairing_heap_signature;
48 
49 template <typename T, typename Parspec>
50 struct make_pairing_heap_base
51 {
52     static const bool constant_time_size = parameter::binding<Parspec,
53                                                               tag::constant_time_size,
54                                                               boost::true_type
55                                                              >::type::value;
56     typedef typename detail::make_heap_base<T, Parspec, constant_time_size>::type base_type;
57     typedef typename detail::make_heap_base<T, Parspec, constant_time_size>::allocator_argument allocator_argument;
58     typedef typename detail::make_heap_base<T, Parspec, constant_time_size>::compare_argument compare_argument;
59 
60     typedef heap_node<typename base_type::internal_type, false> node_type;
61 
62     typedef typename boost::allocator_rebind<allocator_argument, node_type>::type allocator_type;
63 
64     struct type:
65         base_type,
66         allocator_type
67     {
typeboost::heap::detail::make_pairing_heap_base::type68         type(compare_argument const & arg):
69             base_type(arg)
70         {}
71 
72 #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
typeboost::heap::detail::make_pairing_heap_base::type73         type(type const & rhs):
74             base_type(rhs), allocator_type(rhs)
75         {}
76 
typeboost::heap::detail::make_pairing_heap_base::type77         type(type && rhs):
78             base_type(std::move(static_cast<base_type&>(rhs))),
79             allocator_type(std::move(static_cast<allocator_type&>(rhs)))
80         {}
81 
operator =boost::heap::detail::make_pairing_heap_base::type82         type & operator=(type && rhs)
83         {
84             base_type::operator=(std::move(static_cast<base_type&>(rhs)));
85             allocator_type::operator=(std::move(static_cast<allocator_type&>(rhs)));
86             return *this;
87         }
88 
operator =boost::heap::detail::make_pairing_heap_base::type89         type & operator=(type const & rhs)
90         {
91             base_type::operator=(static_cast<base_type const &>(rhs));
92             allocator_type::operator=(static_cast<const allocator_type&>(rhs));
93             return *this;
94         }
95 #endif
96     };
97 };
98 
99 }
100 
101 /**
102  * \class pairing_heap
103  * \brief pairing heap
104  *
105  * Pairing heaps are self-adjusting binary heaps. Although design and implementation are rather simple,
106  * the complexity analysis is yet unsolved. For details, consult:
107  *
108  * Pettie, Seth (2005), "Towards a final analysis of pairing heaps",
109  * Proc. 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 174-183
110  *
111  * The template parameter T is the type to be managed by the container.
112  * The user can specify additional options and if no options are provided default options are used.
113  *
114  * The container supports the following options:
115  * - \c boost::heap::compare<>, defaults to \c compare<std::less<T> >
116  * - \c boost::heap::stable<>, defaults to \c stable<false>
117  * - \c boost::heap::stability_counter_type<>, defaults to \c stability_counter_type<boost::uintmax_t>
118  * - \c boost::heap::allocator<>, defaults to \c allocator<std::allocator<T> >
119  * - \c boost::heap::constant_time_size<>, defaults to \c constant_time_size<true>
120  *
121  *
122  */
123 #ifdef BOOST_DOXYGEN_INVOKED
124 template<class T, class ...Options>
125 #else
126 template <typename T,
127           class A0 = boost::parameter::void_,
128           class A1 = boost::parameter::void_,
129           class A2 = boost::parameter::void_,
130           class A3 = boost::parameter::void_,
131           class A4 = boost::parameter::void_
132          >
133 #endif
134 class pairing_heap:
135     private detail::make_pairing_heap_base<T,
136                                            typename detail::pairing_heap_signature::bind<A0, A1, A2, A3, A4>::type
137                                           >::type
138 {
139     typedef typename detail::pairing_heap_signature::bind<A0, A1, A2, A3, A4>::type bound_args;
140     typedef detail::make_pairing_heap_base<T, bound_args> base_maker;
141     typedef typename base_maker::type super_t;
142 
143     typedef typename super_t::internal_type internal_type;
144     typedef typename super_t::size_holder_type size_holder;
145     typedef typename base_maker::allocator_argument allocator_argument;
146 
147 private:
148     template <typename Heap1, typename Heap2>
149     friend struct heap_merge_emulate;
150 
151 #ifndef BOOST_DOXYGEN_INVOKED
152     struct implementation_defined:
153         detail::extract_allocator_types<typename base_maker::allocator_argument>
154     {
155         typedef T value_type;
156         typedef typename detail::extract_allocator_types<typename base_maker::allocator_argument>::size_type size_type;
157         typedef typename detail::extract_allocator_types<typename base_maker::allocator_argument>::reference reference;
158 
159         typedef typename base_maker::compare_argument value_compare;
160         typedef typename base_maker::allocator_type allocator_type;
161 
162         typedef typename boost::allocator_pointer<allocator_type>::type node_pointer;
163         typedef typename boost::allocator_const_pointer<allocator_type>::type const_node_pointer;
164 
165         typedef detail::heap_node_list node_list_type;
166         typedef typename node_list_type::iterator node_list_iterator;
167         typedef typename node_list_type::const_iterator node_list_const_iterator;
168 
169         typedef typename base_maker::node_type node;
170 
171         typedef detail::value_extractor<value_type, internal_type, super_t> value_extractor;
172         typedef typename super_t::internal_compare internal_compare;
173         typedef detail::node_handle<node_pointer, super_t, reference> handle_type;
174 
175         typedef detail::tree_iterator<node,
176                                       const value_type,
177                                       allocator_type,
178                                       value_extractor,
179                                       detail::pointer_to_reference<node>,
180                                       false,
181                                       false,
182                                       value_compare
183                                      > iterator;
184 
185         typedef iterator const_iterator;
186 
187         typedef detail::tree_iterator<node,
188                                       const value_type,
189                                       allocator_type,
190                                       value_extractor,
191                                       detail::pointer_to_reference<node>,
192                                       false,
193                                       true,
194                                       value_compare
195                                      > ordered_iterator;
196     };
197 
198     typedef typename implementation_defined::node node;
199     typedef typename implementation_defined::node_pointer node_pointer;
200     typedef typename implementation_defined::node_list_type node_list_type;
201     typedef typename implementation_defined::node_list_iterator node_list_iterator;
202     typedef typename implementation_defined::node_list_const_iterator node_list_const_iterator;
203     typedef typename implementation_defined::internal_compare internal_compare;
204 
205     typedef boost::intrusive::list<detail::heap_node_base<true>,
206                                    boost::intrusive::constant_time_size<false>
207                                   > node_child_list;
208 #endif
209 
210 public:
211     typedef T value_type;
212 
213     typedef typename implementation_defined::size_type size_type;
214     typedef typename implementation_defined::difference_type difference_type;
215     typedef typename implementation_defined::value_compare value_compare;
216     typedef typename implementation_defined::allocator_type allocator_type;
217     typedef typename implementation_defined::reference reference;
218     typedef typename implementation_defined::const_reference const_reference;
219     typedef typename implementation_defined::pointer pointer;
220     typedef typename implementation_defined::const_pointer const_pointer;
221     /// \copydoc boost::heap::priority_queue::iterator
222     typedef typename implementation_defined::iterator iterator;
223     typedef typename implementation_defined::const_iterator const_iterator;
224     typedef typename implementation_defined::ordered_iterator ordered_iterator;
225 
226     typedef typename implementation_defined::handle_type handle_type;
227 
228     static const bool constant_time_size = super_t::constant_time_size;
229     static const bool has_ordered_iterators = true;
230     static const bool is_mergable = true;
231     static const bool is_stable = detail::extract_stable<bound_args>::value;
232     static const bool has_reserve = false;
233 
234     /// \copydoc boost::heap::priority_queue::priority_queue(value_compare const &)
pairing_heap(value_compare const & cmp=value_compare ())235     explicit pairing_heap(value_compare const & cmp = value_compare()):
236         super_t(cmp), root(NULL)
237     {}
238 
239     /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue const &)
pairing_heap(pairing_heap const & rhs)240     pairing_heap(pairing_heap const & rhs):
241         super_t(rhs), root(NULL)
242     {
243         if (rhs.empty())
244             return;
245 
246         clone_tree(rhs);
247         size_holder::set_size(rhs.get_size());
248     }
249 
250 #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
251     /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue &&)
pairing_heap(pairing_heap && rhs)252     pairing_heap(pairing_heap && rhs):
253         super_t(std::move(rhs)), root(rhs.root)
254     {
255         rhs.root = NULL;
256     }
257 
258     /// \copydoc boost::heap::priority_queue::operator=(priority_queue &&)
operator =(pairing_heap && rhs)259     pairing_heap & operator=(pairing_heap && rhs)
260     {
261         super_t::operator=(std::move(rhs));
262         root = rhs.root;
263         rhs.root = NULL;
264         return *this;
265     }
266 #endif
267 
268     /// \copydoc boost::heap::priority_queue::operator=(priority_queue const & rhs)
operator =(pairing_heap const & rhs)269     pairing_heap & operator=(pairing_heap const & rhs)
270     {
271         clear();
272         size_holder::set_size(rhs.get_size());
273         static_cast<super_t&>(*this) = rhs;
274 
275         clone_tree(rhs);
276         return *this;
277     }
278 
~pairing_heap(void)279     ~pairing_heap(void)
280     {
281         while (!empty())
282             pop();
283     }
284 
285     /// \copydoc boost::heap::priority_queue::empty
empty(void) const286     bool empty(void) const
287     {
288         return root == NULL;
289     }
290 
291     /// \copydoc boost::heap::binomial_heap::size
size(void) const292     size_type size(void) const
293     {
294         if (constant_time_size)
295             return size_holder::get_size();
296 
297         if (root == NULL)
298             return 0;
299         else
300             return detail::count_nodes(root);
301     }
302 
303     /// \copydoc boost::heap::priority_queue::max_size
max_size(void) const304     size_type max_size(void) const
305     {
306         const allocator_type& alloc = *this;
307         return boost::allocator_max_size(alloc);
308     }
309 
310     /// \copydoc boost::heap::priority_queue::clear
clear(void)311     void clear(void)
312     {
313         if (empty())
314             return;
315 
316         root->template clear_subtree<allocator_type>(*this);
317         root->~node();
318         allocator_type& alloc = *this;
319         alloc.deallocate(root, 1);
320         root = NULL;
321         size_holder::set_size(0);
322     }
323 
324     /// \copydoc boost::heap::priority_queue::get_allocator
get_allocator(void) const325     allocator_type get_allocator(void) const
326     {
327         return *this;
328     }
329 
330     /// \copydoc boost::heap::priority_queue::swap
swap(pairing_heap & rhs)331     void swap(pairing_heap & rhs)
332     {
333         super_t::swap(rhs);
334         std::swap(root, rhs.root);
335     }
336 
337 
338     /// \copydoc boost::heap::priority_queue::top
top(void) const339     const_reference top(void) const
340     {
341         BOOST_ASSERT(!empty());
342 
343         return super_t::get_value(root->value);
344     }
345 
346     /**
347      * \b Effects: Adds a new element to the priority queue. Returns handle to element
348      *
349      * \cond
350      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
351      * \endcond
352      *
353      * \b Complexity: 2**2*log(log(N)) (amortized).
354      *
355      * */
push(value_type const & v)356     handle_type push(value_type const & v)
357     {
358         size_holder::increment();
359 
360         allocator_type& alloc = *this;
361         node_pointer n = alloc.allocate(1);
362         new(n) node(super_t::make_node(v));
363         merge_node(n);
364         return handle_type(n);
365     }
366 
367 #if !defined(BOOST_NO_CXX11_RVALUE_REFERENCES) && !defined(BOOST_NO_CXX11_VARIADIC_TEMPLATES)
368     /**
369      * \b Effects: Adds a new element to the priority queue. The element is directly constructed in-place. Returns handle to element.
370      *
371      * \cond
372      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
373      * \endcond
374      *
375      * \b Complexity: 2**2*log(log(N)) (amortized).
376      *
377      * */
378     template <class... Args>
emplace(Args &&...args)379     handle_type emplace(Args&&... args)
380     {
381         size_holder::increment();
382 
383         allocator_type& alloc = *this;
384         node_pointer n = alloc.allocate(1);
385         new(n) node(super_t::make_node(std::forward<Args>(args)...));
386         merge_node(n);
387         return handle_type(n);
388     }
389 #endif
390 
391     /**
392      * \b Effects: Removes the top element from the priority queue.
393      *
394      * \b Complexity: Logarithmic (amortized).
395      *
396      * */
pop(void)397     void pop(void)
398     {
399         BOOST_ASSERT(!empty());
400 
401         erase(handle_type(root));
402     }
403 
404     /**
405      * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
406      *
407      * \cond
408      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
409      * \endcond
410      *
411      * \b Complexity: 2**2*log(log(N)) (amortized).
412      *
413      * */
update(handle_type handle,const_reference v)414     void update (handle_type handle, const_reference v)
415     {
416         handle.node_->value = super_t::make_node(v);
417         update(handle);
418     }
419 
420     /**
421      * \b Effects: Updates the heap after the element handled by \c handle has been changed.
422      *
423      * \cond
424      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
425      * \endcond
426      *
427      * \b Complexity: 2**2*log(log(N)) (amortized).
428      *
429      * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined!
430      * */
update(handle_type handle)431     void update (handle_type handle)
432     {
433         node_pointer n = handle.node_;
434 
435         n->unlink();
436         if (!n->children.empty())
437             n = merge_nodes(n, merge_node_list(n->children));
438 
439         if (n != root)
440             merge_node(n);
441     }
442 
443      /**
444      * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
445      *
446      * \cond
447      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
448      * \endcond
449      *
450      * \b Complexity: 2**2*log(log(N)) (amortized).
451      *
452      * \b Note: The new value is expected to be greater than the current one
453      * */
increase(handle_type handle,const_reference v)454     void increase (handle_type handle, const_reference v)
455     {
456         update(handle, v);
457     }
458 
459     /**
460      * \b Effects: Updates the heap after the element handled by \c handle has been changed.
461      *
462      * \cond
463      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
464      * \endcond
465      *
466      * \b Complexity: 2**2*log(log(N)) (amortized).
467      *
468      * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined!
469      * */
increase(handle_type handle)470     void increase (handle_type handle)
471     {
472         update(handle);
473     }
474 
475     /**
476      * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
477      *
478      * \cond
479      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
480      * \endcond
481      *
482      * \b Complexity: 2**2*log(log(N)) (amortized).
483      *
484      * \b Note: The new value is expected to be less than the current one
485      * */
decrease(handle_type handle,const_reference v)486     void decrease (handle_type handle, const_reference v)
487     {
488         update(handle, v);
489     }
490 
491     /**
492      * \b Effects: Updates the heap after the element handled by \c handle has been changed.
493      *
494      * \cond
495      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
496      * \endcond
497      *
498      * \b Complexity: 2**2*log(log(N)) (amortized).
499      *
500      * \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!
501      * */
decrease(handle_type handle)502     void decrease (handle_type handle)
503     {
504         update(handle);
505     }
506 
507     /**
508      * \b Effects: Removes the element handled by \c handle from the priority_queue.
509      *
510      * \cond
511      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
512      * \endcond
513      *
514      * \b Complexity: 2**2*log(log(N)) (amortized).
515      * */
erase(handle_type handle)516     void erase(handle_type handle)
517     {
518         node_pointer n = handle.node_;
519         if (n != root) {
520             n->unlink();
521             if (!n->children.empty())
522                 merge_node(merge_node_list(n->children));
523         } else {
524             if (!n->children.empty())
525                 root = merge_node_list(n->children);
526             else
527                 root = NULL;
528         }
529 
530         size_holder::decrement();
531         n->~node();
532         allocator_type& alloc = *this;
533         alloc.deallocate(n, 1);
534     }
535 
536     /// \copydoc boost::heap::priority_queue::begin
begin(void) const537     iterator begin(void) const
538     {
539         return iterator(root, super_t::value_comp());
540     }
541 
542     /// \copydoc boost::heap::priority_queue::end
end(void) const543     iterator end(void) const
544     {
545         return iterator(super_t::value_comp());
546     }
547 
548     /// \copydoc boost::heap::fibonacci_heap::ordered_begin
ordered_begin(void) const549     ordered_iterator ordered_begin(void) const
550     {
551         return ordered_iterator(root, super_t::value_comp());
552     }
553 
554     /// \copydoc boost::heap::fibonacci_heap::ordered_begin
ordered_end(void) const555     ordered_iterator ordered_end(void) const
556     {
557         return ordered_iterator(NULL, super_t::value_comp());
558     }
559 
560 
561     /// \copydoc boost::heap::d_ary_heap_mutable::s_handle_from_iterator
s_handle_from_iterator(iterator const & it)562     static handle_type s_handle_from_iterator(iterator const & it)
563     {
564         node * ptr = const_cast<node *>(it.get_node());
565         return handle_type(ptr);
566     }
567 
568     /**
569      * \b Effects: Merge all elements from rhs into this
570      *
571      * \cond
572      * \b Complexity: \f$2^2log(log(N))\f$ (amortized).
573      * \endcond
574      *
575      * \b Complexity: 2**2*log(log(N)) (amortized).
576      *
577      * */
merge(pairing_heap & rhs)578     void merge(pairing_heap & rhs)
579     {
580         if (rhs.empty())
581             return;
582 
583         merge_node(rhs.root);
584 
585         size_holder::add(rhs.get_size());
586         rhs.set_size(0);
587         rhs.root = NULL;
588 
589         super_t::set_stability_count((std::max)(super_t::get_stability_count(),
590                                      rhs.get_stability_count()));
591         rhs.set_stability_count(0);
592     }
593 
594     /// \copydoc boost::heap::priority_queue::value_comp
value_comp(void) const595     value_compare const & value_comp(void) const
596     {
597         return super_t::value_comp();
598     }
599 
600     /// \copydoc boost::heap::priority_queue::operator<(HeapType const & rhs) const
601     template <typename HeapType>
operator <(HeapType const & rhs) const602     bool operator<(HeapType const & rhs) const
603     {
604         return detail::heap_compare(*this, rhs);
605     }
606 
607     /// \copydoc boost::heap::priority_queue::operator>(HeapType const & rhs) const
608     template <typename HeapType>
operator >(HeapType const & rhs) const609     bool operator>(HeapType const & rhs) const
610     {
611         return detail::heap_compare(rhs, *this);
612     }
613 
614     /// \copydoc boost::heap::priority_queue::operator>=(HeapType const & rhs) const
615     template <typename HeapType>
operator >=(HeapType const & rhs) const616     bool operator>=(HeapType const & rhs) const
617     {
618         return !operator<(rhs);
619     }
620 
621     /// \copydoc boost::heap::priority_queue::operator<=(HeapType const & rhs) const
622     template <typename HeapType>
operator <=(HeapType const & rhs) const623     bool operator<=(HeapType const & rhs) const
624     {
625         return !operator>(rhs);
626     }
627 
628     /// \copydoc boost::heap::priority_queue::operator==(HeapType const & rhs) const
629     template <typename HeapType>
operator ==(HeapType const & rhs) const630     bool operator==(HeapType const & rhs) const
631     {
632         return detail::heap_equality(*this, rhs);
633     }
634 
635     /// \copydoc boost::heap::priority_queue::operator!=(HeapType const & rhs) const
636     template <typename HeapType>
operator !=(HeapType const & rhs) const637     bool operator!=(HeapType const & rhs) const
638     {
639         return !(*this == rhs);
640     }
641 
642 private:
643 #if !defined(BOOST_DOXYGEN_INVOKED)
clone_tree(pairing_heap const & rhs)644     void clone_tree(pairing_heap const & rhs)
645     {
646         BOOST_HEAP_ASSERT(root == NULL);
647         if (rhs.empty())
648             return;
649 
650         root = allocator_type::allocate(1);
651 
652         new(root) node(static_cast<node const &>(*rhs.root), static_cast<allocator_type&>(*this));
653     }
654 
merge_node(node_pointer other)655     void merge_node(node_pointer other)
656     {
657         BOOST_HEAP_ASSERT(other);
658         if (root != NULL)
659             root = merge_nodes(root, other);
660         else
661             root = other;
662     }
663 
merge_node_list(node_child_list & children)664     node_pointer merge_node_list(node_child_list & children)
665     {
666         BOOST_HEAP_ASSERT(!children.empty());
667         node_pointer merged = merge_first_pair(children);
668         if (children.empty())
669             return merged;
670 
671         node_child_list node_list;
672         node_list.push_back(*merged);
673 
674         do {
675             node_pointer next_merged = merge_first_pair(children);
676             node_list.push_back(*next_merged);
677         } while (!children.empty());
678 
679         return merge_node_list(node_list);
680     }
681 
merge_first_pair(node_child_list & children)682     node_pointer merge_first_pair(node_child_list & children)
683     {
684         BOOST_HEAP_ASSERT(!children.empty());
685         node_pointer first_child = static_cast<node_pointer>(&children.front());
686         children.pop_front();
687         if (children.empty())
688             return first_child;
689 
690         node_pointer second_child = static_cast<node_pointer>(&children.front());
691         children.pop_front();
692 
693         return merge_nodes(first_child, second_child);
694     }
695 
merge_nodes(node_pointer node1,node_pointer node2)696     node_pointer merge_nodes(node_pointer node1, node_pointer node2)
697     {
698         if (super_t::operator()(node1->value, node2->value))
699             std::swap(node1, node2);
700 
701         node2->unlink();
702         node1->children.push_front(*node2);
703         return node1;
704     }
705 
706     node_pointer root;
707 #endif
708 };
709 
710 
711 } /* namespace heap */
712 } /* namespace boost */
713 
714 #undef BOOST_HEAP_ASSERT
715 #endif /* BOOST_HEAP_PAIRING_HEAP_HPP */
716