How can building a heap be O(n) time complexity?

Question

Can someone help explain how can building a heap be O(n) complexity?

Inserting an item into a heap is O(log n), and the insert is repeated n/2 times (t

Answer 1

Proof of O(n)

The proof isn't fancy, and quite straightforward, I only proved the case for a full binary tree, the result can be generalized for a complete binary tree.