AVL_V_5
The following is a valid AVL Tree.

Question

BlackTom AI · Accepted Answer

Analyzing whether the given AVL Tree diagram is valid requires applying the core AVL properties. 
Option 1: True. If the tree shown adheres to AVL rules, then every node must have a balance factor (difference between heights of left and right subtrees) of -1, 0, or +1, and the subtree heights must be maintained so no node’s subtrees differ by more than one level. In a correctly drawn AVL tree, after every insertion or rotation, the balance conditions are preserved at all nodes, ensuring logarithmic height and search efficiency. The statement being True would be consistent with a diagram that has all nodes with balance factors within the allowed range and no violations of AVL rotation constraints.
Option 2: False. This would be the correct choice only if some node in the diagram violated the AVL balance criteria, such as having a balance factor of -2 or +2, or if there were an incorrect height relationship between a node and its children that could not be resolved by a single rotation (or required an additional rotation). Without seeing the diagram, we cannot point to a specific violation, but any violation of the -1, 0, +1 balance factor rule would render the tree not an AVL.
To differentiate further: consider what would make a tree invalid. A node whose left subtree is two levels taller than its right subtree (or vice versa) would create a balance factor outside the allowed range. If such a condition were present in the diagram, the statement would be false. Conversely, if every node’s left and right subtrees differ in height by at most one level and the structure corresponds to a sequence of valid AVL rotations, the statement would be true. 
In practice, when presented with an AVL tree diagram, you would inspect each node’s height and compute the balance factor (left height minus right height) to verify it lies in {-1, 0, 1} for all nodes. If that holds across the entire tree, the diagram represents a valid AVL tree; if any node violates this, the diagram is not AVL. 
Note: If there are any ambiguities about subtree heights due to missing value labels, the cautious approach is to recount depths from the leaves upward to confirm balance factors and ensure no violations exist. If you can provide the specific node-by-node structure or heights, I can walk through the exact balance factors and rotations relevant to the diagram.

AVL_V_5 The following is a valid AVL Tree.

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AVL_V_6 Binary Search Tree shown below is an AVL Tree.

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Which statement about an AVL tree is correct?

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