Heap Operations Overview

Three core operations:

$1.$ Peek: return the root (min or max). Time: $O(1)$.

$2.$ Insert: add an element, maintain heap property. Time: $O(\log n)$.

$3.$ Extract: remove and return the root, maintain heap property. Time: $O(\log n)$. The $O(\log n)$ comes from the tree height. A complete binary tree with $n$ nodes has height $O(\log n)$.