Determine whether a binary tree is max heap

Question

I am writing a function to determine whether a given binary tree is a max heap. If the binary tree had only one node (the root), would it be considered a valid max heap?

Answer 1

To be considered a valid max-heap, a binary tree must satisfy two properties:

1. Shape property. The tree must be a complete binary tree. That is, every level except the last must be full. If the last is not full, it is left-filled.
2. Heap property. Every child node must be less than or equal to its parent.

A tree with a single node satisfies both properties, so it is a valid max-heap.