Consider the following tree:

Is this an AVL tree?

Question

Consider the following tree:

Is this an AVL tree?

BlackTom AI · Accepted Answer

To assess whether this tree is AVL, we need to verify that it is a binary search tree where the height difference (balance factor) between left and right subtrees of every node is at most 1.
Option  True: This tree actually satisfies the AVL balance condition at every node. Starting from the bottom:
- Node 32, 51, 68, and 89 are leaves with height 1.
- Node 11 has left child 32 (height 1) and no right child, so its height is 2 and |left − right| = |1 − 0| = 1.
- Node 62 has left child 68 (height 1) and no right child, so its height is 2 and balance is |1 − 0| = 1.
- Node 55 has left child 51 (height 1) and right child 62 (height 2); its height is 3 and balance is |1 − 2| = 1.
- Node 42 has left child 11 (height 2) and right child 55 (height 3); its height is 4 and balance is |2 − 3| = 1.
- Node 70 is a leaf (height 1), so 72 has left height 1 and no right child, giving height 2 and balance 1.
- Node 76 has left child 72 (height 2) and right child 89 (height 1); its height is 3 and balance is |2 − 1| = 1.
- Finally, the root 67 has left subtree height 4 and right subtree height 3; its height is 5 and balance is |4 − 3| = 1.
Since every node’s left-right height difference is at most 1, the tree is AVL.
Option  False: This statement would be incorrect because the tree does meet the AVL balance criteria described above. The balance factors at each node do not exceed 1, so declaring it not to be AVL would be a misconception rather than a factual inaccuracy of the structure.
Option  True (revisited): Remember that AVL trees require both an empty or ordered BST structure and a height-balanced property; here, both conditions hold, reinforcing that the assertion in this question should be true.
Overall, the reasoning shows that the given tree adheres to AVL properties, so the claim labeled as False is incorrect for this specific diagram.

Consider the following tree: Is this an AVL tree?判断题

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