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 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, $0 < i < N$ , bool(invoke(comp, invoke(proj, a[ $⌊ \frac{i - 1}{2} ⌋$ ]), invoke(proj, a[i]))) is false.
(1.2)
*a may be removed by pop_heap, or a new element added by push_heap, in $O (log N)$ 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.

26.8.8.2 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 = {});

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]

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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 = {});

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) and Cpp17MoveAssignable (Table 33) 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

2 log (last - first)

comparisons and twice as many projections.

26.8.8.4 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 = {});

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) and Cpp17MoveAssignable (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]

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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 = {});

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) and Cpp17MoveAssignable (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

2 N log N

comparisons, where

N = last - first

, and twice as many projections.

26.8.8.6 is_heap [is.heap]

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template<class RandomAccessIterator>
  constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last);

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);

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);

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);

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 = {});

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 = {});

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.