25 Algorithms library [algorithms]

25.8 Sorting and related operations [alg.sorting]

25.8.7 Heap operations [alg.heap.operations]

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A random access range [a, b) is a heap with respect to comp and proj for a comparator and projection comp and proj if its elements are organized such that:
  • (1.1)
    With N = b - a, for all i, , bool(invoke(comp, invoke(proj, a[]), invoke(​proj, a[i]))) is false.
  • (1.2)
    *a may be removed by pop_­heap, or a new element added by push_­heap, in time.
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These properties make heaps useful as priority queues.
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make_­heap converts a range into a heap and sort_­heap turns a heap into a sorted sequence.

25.8.7.1 push_­heap [push.heap]

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template<class RandomAccessIterator> 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<I> 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<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::push_heap(R&& r, Comp comp = {}, Proj proj = {});
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Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
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Preconditions: The range [first, last - 1) is a valid heap with respect to comp and proj.
For the overloads in namespace std, the type of *first meets the Cpp17MoveConstructible requirements (Table 28) and the Cpp17MoveAssignable requirements (Table 30).
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Effects: Places the value in the location last - 1 into the resulting heap [first, last).
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Returns: last for the overloads in namespace ranges.
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Complexity: At most comparisons and twice as many projections.

25.8.7.2 pop_­heap [pop.heap]

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template<class RandomAccessIterator> 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<I> 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<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::pop_heap(R&& r, Comp comp = {}, Proj proj = {});
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Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
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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 28) and Cpp17MoveAssignable (Table 30) requirements.
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Effects: Swaps the value in the location first with the value in the location last - 1 and makes [first, last - 1) into a heap with respect to comp and proj.
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Returns: last for the overloads in namespace ranges.
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Complexity: At most comparisons and twice as many projections.

25.8.7.3 make_­heap [make.heap]

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template<class RandomAccessIterator> 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<I> 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<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::make_heap(R&& r, Comp comp = {}, Proj proj = {});
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Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
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Preconditions: For the overloads in namespace std, the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
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Effects: Constructs a heap with respect to comp and proj out of the range [first, last).
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Returns: last for the overloads in namespace ranges.
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Complexity: At most comparisons and twice as many projections.

25.8.7.4 sort_­heap [sort.heap]

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template<class RandomAccessIterator> 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<I> 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<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::sort_heap(R&& r, Comp comp = {}, Proj proj = {});
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Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
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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 28) and Cpp17MoveAssignable (Table 30) requirements.
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Effects: Sorts elements in the heap [first, last) with respect to comp and proj.
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Returns: last for the overloads in namespace ranges.
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Complexity: At most comparisons, where , and twice as many projections.

25.8.7.5 is_­heap [is.heap]

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template<class RandomAccessIterator> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last);
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Effects: Equivalent to: return is_­heap_­until(first, last) == last;
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template<class ExecutionPolicy, class RandomAccessIterator> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last);
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Effects: Equivalent to: 
return is_heap_until(std::forward<ExecutionPolicy>(exec), first, last) == last;
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template<class RandomAccessIterator, class Compare> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
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Effects: Equivalent to: return is_­heap_­until(first, last, comp) == last;
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template<class ExecutionPolicy, class RandomAccessIterator, class Compare> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
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Effects: Equivalent to: 
return is_heap_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last;
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template<random_­access_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(R&& r, Comp comp = {}, Proj proj = {});
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Effects: Equivalent to: return ranges​::​is_­heap_­until(first, last, comp, proj) == last;
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template<class RandomAccessIterator> 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<I> 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<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::is_heap_until(R&& r, Comp comp = {}, Proj proj = {});
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Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
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Returns: The last iterator i in [first, last] for which the range [first, i) is a heap with respect to comp and proj.
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Complexity: Linear.