28 Algorithms library [algorithms]

28.7 Sorting and related operations [alg.sorting]

28.7.7 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[i12], a[i]) is false.

• *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 and sort_­heap() turns a heap into a sorted sequence.

28.7.7.1push_­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 and the MoveAssignable requirements.

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

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

28.7.7.2pop_­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. The type of *first shall satisfy the requirements of MoveConstructible and of 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 2log(last - first) comparisons.

28.7.7.3make_­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 and the MoveAssignable requirements.

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

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

28.7.7.4sort_­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. The type of *first shall satisfy the requirements of MoveConstructible and of MoveAssignable.

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

Complexity: At most NlogN comparisons, where N=last - first.

28.7.7.5is_­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.