Which of the following statement(s) is/are TRUE for any binary search tree (BST) having $n$ distinct integers?

Let us analyze each statement for a binary search tree (BST) with $n$ distinct integers:

• Statement (A) is TRUE: In a degenerate or skewed BST (where each node has at most one child), the tree structure becomes linear like a linked list. The path from the root node to the deepest node contains $n$ nodes, which corresponds to an edge count (path length) of $n - 1$. Thus, the maximum path length from the root to any other node is $n - 1$.

• Statement (B) is TRUE: By definition of a BST, for any node $x$, all keys in its left subtree are strictly less than $x$'s key, and all keys in its right subtree are strictly greater. An inorder traversal visits the left subtree, the root, and then the right subtree, which recursively guarantees that elements are output in strictly ascending sorted order.

• Statement (C) is FALSE: Finding an element in a balanced BST takes $O(\log_2 n)$ time, but in the worst case (a skewed BST), the search time is $O(n)$.

• Statement (D) is FALSE: In a min-heap, the key of every node must be less than or equal to the keys of its children. However, in a BST, any non-empty left child has a key smaller than its parent, which violates the min-heap property.

Therefore, statements (A) and (B) are correct.