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In ________balance factor of a node is the difference between the left subtree and the right subtree.

Question

In ________ balance factor of a node is the difference between the left subtree and the right subtree.

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Solution

In an AVL tree, the balance factor of a node is the difference between the heights of the left subtree and the right subtree. This factor helps maintain the tree's balance through rotations during insertions and deletions. The balance factor is calculated as:

Balance Factor=Height(Left Subtree)Height(Right Subtree) \text{Balance Factor} = \text{Height(Left Subtree)} - \text{Height(Right Subtree)}

The balance factor for any node in an AVL tree can be -1, 0, or +1, indicating whether the left subtree is taller, both subtrees are of equal height, or the right subtree is taller, respectively. This property ensures that the tree remains approximately balanced, allowing for efficient search, insertion, and deletion operations.

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