Explain the heapify operation and its time complexity.

Heapify maintains heap property by moving a node to its correct position. Heapify-down (sift-down) compares parent with children and swaps with larger (max-heap) or smaller (min-heap) child, repeating until valid. Single heapify is O(log n). Building a heap from array uses bottom-up heapify on all non-leaf nodes, achieving O(n) total time (not O(n log n)) because most nodes are near the bottom with small heights.