The height of a node in a binary tree is the number of edges on the longest path from that node to a leaf, and the height of the tree is the height of its root; this admits a direct recursive characterization, height(node) = 1 + max(height(left), height(right)), because the tallest path through a node must descend into one of its subtrees. The recursion terminates on the empty subtree, whose height is defined as −1 rather than 0, so that the non-existent edge to a null child cancels and a leaf correctly evaluates to height 0 — the base value is not arbitrary but is forced by the edge-counting definition. The procedure visits every node exactly once, giving Θ(n) time, and belongs to tree data structures where height is the quantity that bounds the cost of search, insertion, and deletion.
The height of a node in a binary tree is the number of edges on the longest path from that node to a leaf, and the height of the tree is the height of its root; this admits a direct recursive charact…