Editing Heap (data structure) (section)

==Operations==
The common operations involving heaps are:
;Basic
* ''find-max'' (or ''find-min''): find a maximum item of a max-heap, or a minimum item of a min-heap, respectively (a.k.a. ''[[Peek (data type operation)|peek]]'')
* ''insert'': adding a new key to the heap (a.k.a., ''push''<ref>The Python Standard Library, 8.4. heapq — Heap queue algorithm, [https://docs.python.org/3/library/heapq.html#heapq.heappush heapq.heappush]</ref>)
* ''extract-max'' (or ''extract-min''): returns the node of maximum value from a max heap [or minimum value from a min heap] after removing it from the heap (a.k.a., ''pop''<ref>The Python Standard Library, 8.4. heapq — Heap queue algorithm, [https://docs.python.org/3/library/heapq.html#heapq.heappop heapq.heappop]</ref>)
* ''delete-max'' (or ''delete-min''): removing the root node of a max heap (or min heap), respectively
* ''replace'': pop root and push a new key. This is more efficient than a pop followed by a push, since it only needs to balance once, not twice, and is appropriate for fixed-size heaps.<ref>The Python Standard Library, 8.4. heapq — Heap queue algorithm, [https://docs.python.org/3/library/heapq.html#heapq.heapreplace heapq.heapreplace]</ref>

;Creation
* ''create-heap'': create an empty heap
* ''heapify'': create a heap out of given array of elements
* ''merge'' (''union''): joining two heaps to form a valid new heap containing all the elements of both, preserving the original heaps.
* ''meld'': joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps.

;Inspection
* ''size'': return the number of items in the heap.
* ''is-empty'': return true if the heap is empty, false otherwise.

;Internal
* ''increase-key'' or ''decrease-key'': updating a key within a max- or min-heap, respectively
* ''delete'': delete an arbitrary node (followed by moving last node and sifting to maintain heap)
* ''sift-up'': move a node up in the tree, as long as needed; used to restore heap condition after insertion. Called "sift" because node moves up the tree until it reaches the correct level, as in a [[sieve]].
* ''sift-down'': move a node down in the tree, similar to sift-up; used to restore heap condition after deletion or replacement.