25 Algorithms library [algorithms]

25.7 Sorting and related operations [alg.sorting]

25.7.7 Heap operations [alg.heap.operations]

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:
  • With N = b - a, for all i, , bool(invoke(comp, invoke(proj, a[]), invoke(​proj, a[i]))) is false.
  • *a may be removed by pop_­heap, or a new element added by push_­heap, in time.
These properties make heaps useful as priority queues.
make_­heap converts a range into a heap and sort_­heap turns a heap into a sorted sequence.

25.7.7.1 push_­heap [push.heap]

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<RandomAccessIterator I, Sentinel<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<RandomAccessRange R, class Comp = ranges::less, class Proj = identity> requires Sortable<iterator_t<R>, Comp, Proj> constexpr safe_iterator_t<R> 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.
Requires: The range [first, last - 1) shall be a valid heap with respect to comp and proj.
For the overloads in namespace std, the type of *first shall meet the Cpp17MoveConstructible requirements (Table 26) and the Cpp17MoveAssignable requirements (Table 28).
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 comparisons and twice as many projections.

25.7.7.2 pop_­heap [pop.heap]

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<RandomAccessIterator I, Sentinel<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<RandomAccessRange R, class Comp = ranges::less, class Proj = identity> requires Sortable<iterator_t<R>, Comp, Proj> constexpr safe_iterator_t<R> 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.
Requires: The range [first, last) shall be a valid non-empty heap with respect to comp and proj.
For the overloads in namespace std, RandomAccessIterator shall meet the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first shall meet the Cpp17MoveConstructible (Table 26) and Cpp17MoveAssignable (Table 28) requirements.
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.
Returns: last for the overloads in namespace ranges.
Complexity: At most comparisons and twice as many projections.

25.7.7.3 make_­heap [make.heap]

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<RandomAccessIterator I, Sentinel<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<RandomAccessRange R, class Comp = ranges::less, class Proj = identity> requires Sortable<iterator_t<R>, Comp, Proj> constexpr safe_iterator_t<R> 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.
Requires: For the overloads in namespace std, the type of *first shall meet the Cpp17MoveConstructible (Table 26) and Cpp17MoveAssignable (Table 28) 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 comparisons and twice as many projections.

25.7.7.4 sort_­heap [sort.heap]

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<RandomAccessIterator I, Sentinel<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<RandomAccessRange R, class Comp = ranges::less, class Proj = identity> requires Sortable<iterator_t<R>, Comp, Proj> constexpr safe_iterator_t<R> 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.
Requires: The range [first, last) shall be a valid heap with respect to comp and proj.
For the overloads in namespace std, RandomAccessIterator shall meet the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first shall meet the Cpp17MoveConstructible (Table 26) and Cpp17MoveAssignable (Table 28) 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 comparisons, where , and twice as many projections.

25.7.7.5 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<ExecutionPolicy>(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<ExecutionPolicy>(exec), first, last, comp) == last;
template<RandomAccessIterator I, Sentinel<I> S, class Proj = identity, IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<RandomAccessRange R, class Proj = identity, IndirectStrictWeakOrder<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<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<RandomAccessIterator I, Sentinel<I> S, class Proj = identity, IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less> constexpr I ranges::is_heap_until(I first, S last, Comp comp = {}, Proj proj = {}); template<RandomAccessRange R, class Proj = identity, IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr safe_iterator_t<R> ranges::is_heap_until(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.