A heap is a specialized binary tree that satisfies the heap property. In a max-heap, the parent node is greater than its children, and in a min-heap, the parent node is smaller than its children.

A heap is a special type of binary tree that is used to implement priority queues and to facilitate efficient algorithms like heapsort. There are two main types of heaps: max-heaps and min-heaps. In a max-heap, every parent node has a value greater than or equal to its children, and the largest element is always at the root. In a min-heap, the opposite is true: every parent node is smaller than or equal to its children, with the smallest element at the root. The primary operations in a heap are 'insert' and 'extract' (or remove), both of which can be performed in O(log n) time because the height of the heap is proportional to the logarithm of the number of elements. Heaps are especially useful in scenarios where you need to efficiently access the maximum or minimum element, like in priority queues, where elements are served based on priority rather than order of arrival. Heaps also play a critical role in algorithms like heapsort, an efficient sorting algorithm that has a time complexity of O(n log n). The heap property ensures that insertion and deletion can be performed quickly, making heaps a good choice for applications where the dataset changes frequently and the need to find the largest or smallest element is frequent. Another important use case of heaps is in graph algorithms like Dijkstra's algorithm, where a min-heap is used to efficiently find the vertex with the smallest distance. Building a heap from an unsorted array can be done in O(n) time using a process called 'heapify,' which ensures that the heap property is maintained. Heaps are also used in memory management and scheduling algorithms where tasks or processes need to be handled based on priority. Understanding how heaps work is essential for optimizing performance in many applications, especially those involving priority-based operations.