A heap is a binary tree-based data structure that satisfies the heap property: in a max heap, the parent node is always larger than its children, and in a min heap, the parent is smaller.

A heap is a specialized tree-based data structure that satisfies the heap property, which dictates that in a max heap, every parent node is greater than or equal to its children, and in a min heap, every parent node is less than or equal to its children. Heaps are used primarily in priority queues, where you need to efficiently access the highest (or lowest) priority element. The heap structure ensures that the maximum (in a max heap) or minimum (in a min heap) element is always at the root, allowing for constant time access. However, inserting and removing elements requires maintaining the heap property, which is done in O(log n) time. Heaps can be implemented as binary trees, but they are often stored as arrays for simplicity, with the parent and child relationships easily derived using array indices. One of the most famous applications of heaps is Heap Sort, a comparison-based sorting algorithm that builds a max heap from the data and then repeatedly removes the largest element from the heap. Heaps are also essential in algorithms like Dijkstra’s shortest path and Prim’s minimum spanning tree. Understanding heaps is critical for optimizing tasks that require priority-based processing.