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

Question

BlackTom AI · Accepted Answer

When evaluating the balance factor in an AVL tree, we recall that the balance factor (BF) of a node is defined as BF = height(left subtree) − height(right subtree). With this in mind, we examine the node labeled 25 in the given AVL tree image.
Option -1: This indicates the right subtree of node 25 is one level taller than the left subtree. Since the provided answer lists -1 as the correct value, this aligns with the tree's structure where the right side has height by one.
Option 0: A BF of 0 would mean that the heights of the left and right subtrees are equal. If the image shows any imbalance leaning to one side, this would not be correct.
Option -2: A BF of -2 would mean the right subtree is two levels taller than the left, which is a stricter imbalance than typically allowed in a single insertion before rotations in an AVL tree. The image likely does not exhibit such a large disparity.
Option 1: A BF of 1 would mean the left subtree is taller by one. This contradicts the -1 given as the correct answer, so this would be incorrect for the depicted node.
Option 2: A BF of 2 would imply a significant left-right height difference with the left subtree notably taller by two levels, which again would contradict the visual balance shown for node 25.
In summary, the balance factor being -1 indicates the right subtree is one level taller than the left, which matches the structural cues from the tree image for node 25. The other values imply equal or greater imbalances that are not consistent with the depicted configuration.

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

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