25 Algorithms library [algorithms]

25.5 Sorting and related operations [alg.sorting]

25.5.6 Heap operations [alg.heap.operations]

A heap is a particular organization of elements in a range between two random access iterators [a, b) such that:

  • With N = b - a, for all i, 0 < i < N, comp(a[$\left \lfloor{\frac{i - 1}{2}}\right \rfloor$], a[i]) is false.

  • *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.

25.5.6.1 push_heap [push.heap]

template<class RandomAccessIterator> void push_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> void push_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

Requires: The range [first, last - 1) shall be a valid heap. The type of *first shall satisfy the MoveConstructible requirements (Table [tab:moveconstructible]) and the MoveAssignable requirements (Table [tab:moveassignable]).

Effects: Places the value in the location last - 1 into the resulting heap [first, last).

Complexity: At most log(last - first) comparisons.

25.5.6.2 pop_heap [pop.heap]

template<class RandomAccessIterator> void pop_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> void pop_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

Requires: The range [first, last) shall be a valid non-empty heap. RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [tab:moveconstructible]) and of MoveAssignable (Table [tab:moveassignable]).

Effects: Swaps the value in the location first with the value in the location last - 1 and makes [first, last - 1) into a heap.

Complexity: At most 2 log(last - first) comparisons.

25.5.6.3 make_heap [make.heap]

template<class RandomAccessIterator> void make_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> void make_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

Requires: The type of *first shall satisfy the MoveConstructible requirements (Table [tab:moveconstructible]) and the MoveAssignable requirements (Table [tab:moveassignable]).

Effects: Constructs a heap out of the range [first, last).

Complexity: At most 3(last - first) comparisons.

25.5.6.4 sort_heap [sort.heap]

template<class RandomAccessIterator> void sort_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> void sort_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

Requires: The range [first, last) shall be a valid heap. RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [tab:moveconstructible]) and of MoveAssignable (Table [tab:moveassignable]).

Effects: Sorts elements in the heap [first, last).

Complexity: At most N log(N) comparisons, where N = last - first.

25.5.6.5 is_heap [is.heap]

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

Returns: is_heap_until(first, last) == last

template<class ExecutionPolicy, class RandomAccessIterator> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last);

Returns: is_heap_until(std::forward<ExecutionPolicy>(exec), first, last) == last

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

Returns: 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);

Returns: is_heap_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last

template<class RandomAccessIterator> 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> 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);

Returns: If (last - first) < 2, returns last. Otherwise, returns the last iterator i in [first, last] for which the range [first, i) is a heap.

Complexity: Linear.