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*Heap property: the key stored in each node is either greater than or equal to (≥) or less than or equal to (≤) the keys in the node's children, according to some [[total order]].
Heaps where the parent key is greater than or equal to (≥) the child keys are called ''max-heaps''; those where it is less than or equal to (≤) are called ''min-heaps''. Efficient (that is, [[logarithmic time]]) algorithms are known for the two operations needed to implement a priority queue on a binary heap: inserting an element, and removing the smallest or largest element from a min-heap or max-heap, respectively. Binary heaps are also commonly employed in the [[heapsort]] [[sorting algorithm]], which is an in-place algorithm because binary heaps can be implemented as an [[implicit data structure]], storing keys in an array and using their relative positions within that array to represent child–parent relationships.
==Heap operations==
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