What is a Heap? A Detailed Explanation of Basic Operations on Heaps in Data Structures

A heap is a special structure based on a complete binary tree, stored in an array, and satisfies the properties of a max heap (parent node value ≥ child node) or a min heap (parent node value ≤ child node). It can efficiently retrieve the maximum or minimum value and is widely used in algorithms. The array indices map parent-child relationships: left child is at 2i+1, right child at 2i+2, and parent is at (i-1)//2. A max heap has the largest root (e.g., [9,5,7,3,6,2,4]), while a min heap has the smallest root (e.g., [3,6,5,9,7,2,4]). Core operations include insertion (appending new element to the end and adjusting upward to satisfy heap property), deletion (swapping root with last element and adjusting downward), heap construction (adjusting from the last non-leaf node downward), and retrieving the root (directly accessing the root node). It is applied in priority queues, heap sort, and Top K problems. The efficient structure and operations of heaps are crucial for understanding algorithms, and beginners can start with array simulation to master them.