Validating that a binary tree satisfies the binary search tree property requires checking a global, not merely local, ordering constraint: every key in a node's left subtree must be lesser (or lesser-or-equal, if duplicates are permitted) and every key in its right subtree greater, recursively at every node. The naive formulation applies this definition literally by scanning each node's entire subtrees for a bound violation, which re-reads each node once per ancestor and costs O(n^2); the efficient formulation carries a permissible open interval down the recursion, initialized to (-infinity, +infinity) at the root and narrowed on descent — the upper bound becomes the parent's key when going left, the lower bound becomes the parent's key when going right — so each node is examined once against a constant-time range test, giving O(n). An equivalent alternative exploits the theorem that inorder traversal of a binary search tree yields keys in ascending order, so tracking the previously visited key and requiring strict increase validates the tree in a single traversal. This belongs to the data structures and algorithms subfield of computer science, specifically tree invariant verification.
Validating that a binary tree satisfies the binary search tree property requires checking a global, not merely local, ordering constraint: every key in a node's left subtree must be lesser (or lesser…