Which of the following tree data structures is not a balanced binary tree?

Solution

A “binary tree” restricts every node to at most two children. A “balanced binary tree” must satisfy both of these in turn: (1) it is a binary tree, AND (2) it enforces a height-balance invariant (a bounded balance factor, or a rotation/colouring rule) so that operations stay O(log n). Merely being self-balancing is not enough — the structure must first qualify as binary.

• Red-black tree: every node has at most two children, and colouring plus rotation rules bound the height — it satisfies both parts of the test.

• AVL tree: every node has at most two children, and a strict balance factor (height difference of left and right subtrees ≤ 1) is enforced via rotations — it also satisfies both parts.

• B-tree: it is self-balancing, but each node can hold multiple keys and link to more than two children — it is an m-ary search tree, not a binary tree. It fails the “binary” part of the test outright, regardless of how well it balances.

Cross-check: exactly one of the three named structures fails the two-part test, so a compound verdict of “more than one” or “none” cannot hold — the failure is singular and specific.

Conclusion: the B-tree is the structure that is not a balanced binary tree, because it is not a binary tree in the first place.