Which of the following trees are height balanced? A. Binary Search Tree B. AVL…

Answer: AVL Tree and Red-Black Tree are height balanced.

• AVL Tree — strictly height-balanced: for every node, the heights of the left and right subtrees differ by at most 1. This guarantees the tree height is O(log n) and ensures logarithmic-time operations.

• Red-Black Tree — height-balanced in a relaxed sense: color and black-height properties ensure the tree height is bounded by O(log n) (specifically height ≤ 2·log2(n+1)), so it provides logarithmic-time operations as well.

• Binary Search Tree — not necessarily height-balanced: without rebalancing, it can become skewed (e.g., inserting sorted keys) and have height O(n), causing degraded performance.

• B-Tree — balanced in the multi-way-tree sense: all leaves are at the same depth, which is important for external storage. However, the phrase "height-balanced" in this question refers to binary-tree left/right subtree height constraints, so B-Tree is not counted among the binary height-balanced trees asked for here.

Therefore the correct choice is the one that selects AVL Tree and Red-Black Tree.