24 KiB
[alg.heap.operations]
26 Algorithms library [algorithms]
26.8 Sorting and related operations [alg.sorting]
26.8.8 Heap operations [alg.heap.operations]
26.8.8.1 General [alg.heap.operations.general]
A random access range [a, b) is aheap with respect to comp and proj for a comparator and projection comp and proj if its elements are organized such that:
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With N = b - a, for all i, 0<i<N, bool(invoke(comp, invoke(proj, a[âiâ12â]), invoke(proj, a[i]))) is false.
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*a may be removed by pop_heap, or a new element added by push_heap, in O(logN) time.
These properties make heaps useful as priority queues.
make_heap converts a range into a heap andsort_heap turns a heap into a sorted sequence.
26.8.8.2 push_heap [push.heap]
`template constexpr void push_heap(RandomAccessIterator first, RandomAccessIterator last);
template<class RandomAccessIterator, class Compare> constexpr void push_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
template<random_access_iterator I, sentinel_for S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::push_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_access_range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t, Comp, Proj> constexpr borrowed_iterator_t ranges::push_heap(R&& r, Comp comp = {}, Proj proj = {}); `
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
Preconditions: The range [first, last - 1) is a valid heap with respect to comp and proj.
For the overloads in namespace std,RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible requirements (Table 31) and the Cpp17MoveAssignable requirements (Table 33).
Effects: Places the value in the location last - 1 into the resulting heap [first, last).
Returns: last for the overloads in namespace ranges.
Complexity: At most log(last - first) comparisons and twice as many projections.
26.8.8.3 pop_heap [pop.heap]
`template constexpr void pop_heap(RandomAccessIterator first, RandomAccessIterator last);
template<class RandomAccessIterator, class Compare> constexpr void pop_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
template<random_access_iterator I, sentinel_for S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::pop_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_access_range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t, Comp, Proj> constexpr borrowed_iterator_t ranges::pop_heap(R&& r, Comp comp = {}, Proj proj = {}); `
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
Preconditions: The range [first, last) is a valid non-empty heap with respect to comp and proj.
For the overloads in namespace std,RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) andCpp17MoveAssignable (Table 33) requirements.
Effects: Swaps the value in the location first with the value in the locationlast - 1 and makes [first, last - 1) into a heap with respect to comp and proj.
Returns: last for the overloads in namespace ranges.
Complexity: At most 2log(last - first) comparisons and twice as many projections.
26.8.8.4 make_heap [make.heap]
`template constexpr void make_heap(RandomAccessIterator first, RandomAccessIterator last);
template<class RandomAccessIterator, class Compare> constexpr void make_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
template<random_access_iterator I, sentinel_for S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::make_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_access_range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t, Comp, Proj> constexpr borrowed_iterator_t ranges::make_heap(R&& r, Comp comp = {}, Proj proj = {}); `
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
Preconditions: For the overloads in namespace std,RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) andCpp17MoveAssignable (Table 33) requirements.
Effects: Constructs a heap with respect to comp and proj out of the range [first, last).
Returns: last for the overloads in namespace ranges.
Complexity: At most 3(last - first) comparisons and twice as many projections.
26.8.8.5 sort_heap [sort.heap]
`template constexpr void sort_heap(RandomAccessIterator first, RandomAccessIterator last);
template<class RandomAccessIterator, class Compare> constexpr void sort_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
template<random_access_iterator I, sentinel_for S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::sort_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_access_range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t, Comp, Proj> constexpr borrowed_iterator_t ranges::sort_heap(R&& r, Comp comp = {}, Proj proj = {}); `
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
Preconditions: The range [first, last) is a valid heap with respect to comp and proj.
For the overloads in namespace std,RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 31) andCpp17MoveAssignable (Table 33) requirements.
Effects: Sorts elements in the heap [first, last) with respect to comp and proj.
Returns: last for the overloads in namespace ranges.
Complexity: At most 2NlogN comparisons, where N=last - first, and twice as many projections.
26.8.8.6 is_heap [is.heap]
template<class RandomAccessIterator> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last);
Effects: Equivalent to: return is_heap_until(first, last) == last;
template<class ExecutionPolicy, class RandomAccessIterator> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last);
Effects: Equivalent to:return is_heap_until(std::forward(exec), first, last) == last;
template<class RandomAccessIterator, class Compare> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
Effects: Equivalent to: return is_heap_until(first, last, comp) == last;
template<class ExecutionPolicy, class RandomAccessIterator, class Compare> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
Effects: Equivalent to:return is_heap_until(std::forward(exec), first, last, comp) == last;
template<[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_access_iterator [iterator.concept.random.access]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_for [iterator.concept.sentinel]")<I> S, class Proj = identity, [indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<I, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<[random_access_range](range.refinements#concept:random_access_range "25.4.6 Other range refinements [range.refinements]") R, class Proj = identity, [indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(R&& r, Comp comp = {}, Proj proj = {});
Effects: Equivalent to:return ranges::is_heap_until(first, last, comp, proj) == last;
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_access_iterator [iterator.concept.random.access]") I, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_sentinel_for [iterator.concept.sizedsentinel]")<I> S, class Proj = identity, [indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<I, Proj>> Comp = ranges::less> bool ranges::is_heap(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {}); template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R, class Proj = identity, [indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<iterator_t<R>, Proj>> Comp = ranges::less> bool ranges::is_heap(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {});
Effects: Equivalent to:return ranges::is_heap_until(std::forward(exec), first, last, comp, proj) == last;
`template constexpr RandomAccessIterator is_heap_until(RandomAccessIterator first, RandomAccessIterator last); template<class ExecutionPolicy, class RandomAccessIterator> RandomAccessIterator is_heap_until(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last);
template<class RandomAccessIterator, class Compare> constexpr RandomAccessIterator is_heap_until(RandomAccessIterator first, RandomAccessIterator last, Compare comp); template<class ExecutionPolicy, class RandomAccessIterator, class Compare> RandomAccessIterator is_heap_until(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
template<random_access_iterator I, sentinel_for S, class Proj = identity, indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less> constexpr I ranges::is_heap_until(I first, S last, Comp comp = {}, Proj proj = {}); template<random_access_range R, class Proj = identity, indirect_strict_weak_order<projected<iterator_t, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t ranges::is_heap_until(R&& r, Comp comp = {}, Proj proj = {});
template<execution-policy Ep, random_access_iterator I, sized_sentinel_for S, class Proj = identity, indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less> I ranges::is_heap_until(Ep&& exec, I first, S last, Comp comp = {}, Proj proj = {}); template<execution-policy Ep, sized-random-access-range R, class Proj = identity, indirect_strict_weak_order<projected<iterator_t, Proj>> Comp = ranges::less> borrowed_iterator_t ranges::is_heap_until(Ep&& exec, R&& r, Comp comp = {}, Proj proj = {}); `
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
Returns: The last iterator i in [first, last] for which the range [first, i) is a heap with respect to comp and proj.
Complexity: Linear.