AVL_V_6
Binary Search Tree shown below is an AVL Tree.

Question

BlackTom AI · Accepted Answer

Question restatement: The prompt shows a Binary Search Tree labeled as AVL_V_6 and asks whether, in the depicted diagram, it is an AVL Tree. The answer options are: True, False.

Option 1: True. Why this would be correct: An AVL Tree is a self-balancing binary search tree where every node has a balance factor of -1, 0, or +1, meaning the heights of the left and right subtrees differ by at most 1. If the diagram indeed assigns heights to subtrees such that for every node the difference between the heights of its left and right subtrees is at most 1, then the tree satisfies the AVL criterion. In practice this means checking each node (conceptually) to verify that no node has a left-heavy or right-heavy height difference exceeding 1. If the tree in the image has a stable, shallow profile and no node with a width of imbalance, then it qualifies as AVL.

Option 2: False. Why this would be incorrect: This would be the right choice only if there exists at least one node in the diagram whose left and right subtrees differ in height by more than 1, violating the AVL balance requirement. Common mistakes include overlooking a subtle height difference, miscounting subtree heights, or confusing the balance factor with the node degrees. If any node exhibits a bf of 2 or -2 (i.e., height difference 2 or more), the tree fails the AVL property and cannot be classified as AVL.

Contextual note: Since the image itself is not visible in this text format, the general rule remains: verify balance by checking that every node has height differences of at most 1. If the depicted tree satisfies that condition throughout, it is AVL; if any node violates it, it is not. The phrasing of the options intends to test understanding of the exact AVL condition rather than superficial attributes like overall shape.

In summary, the statement being true hinges on the uniform 1-or-less height difference across all nodes; if that holds in the diagram, True is correct; if it does not hold anywhere, False would be correct.

AVL_V_6 Binary Search Tree shown below is an AVL Tree.

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类似问题

AVL_BLRT_6 Refer to the AVL Tree shown in image below. Given that the node with the value 60 has just been inserted, after identifying which node becomes unbalanced first, describe the necessary rotation(s) to restore the tree's balance.

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AVL_BF_7 Refer to the AVL Tree shown in image below. Balance factor for Node 6 is ____.

AVL_BLRT_11 Refer to the AVL Tree shown in image below. Given that the node with the value 21 has just been inserted, after identifying which node becomes unbalanced first, describe the necessary rotation(s) to restore the tree's balance.

AVL_IDOff_6 Refer to the AVL Tree shown in image below. Considering that the node with the value 60 has been just inserted, After inserting the node with the value 60, which node first becomes unbalanced?

AVL_V_5 The following is a valid AVL Tree.

AVL_BF_4 Refer to the AVL Tree shown in image below. Balance factor of 25 is ___.

Which statement about an AVL tree is correct?

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