java AVL tree a). What are the conditions that must exist in a binary tree for calling the left and the right rotation? b). What is the smallest height that a tree of 1000 nodes can be? What is the bi...

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java AVL tree a). What are the conditions that must exist in a binary tree for calling the left and the right rotation? b). What is the smallest height that a tree of 1000 nodes can be? What is the bi...

java AVL tree

a). What are the conditions that must exist in a binary tree for calling the left and the right rotation?

b). What is the smallest height that a tree of 1000 nodes can be? What is the biggest?

Please be very specific, thank you.

engineering Computer-Science

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Answer 1

Answer #1

a)

The “balance factor” of a node in the AVL Tree determines whether or not it gets rotated. Keep track of the balance factor for each node in the tree and you'll be able to determine when you need to rotate easily.

The balance factor of a node “V” is calculated by subtracting the height of the right subtree of V from the height of the left subtree of V.

If the balance factor of any node is greater than 1 or less than -1, then a rotation needs to be performed. There are four rotation types: left, right, left-right, and right-left.

b)

If there are n nodes in AVL tree, minimum height of AVL tree is floor(log₂n). Hence, the minimum height with 1000 nodes is: 9
If there are n nodes in AVL tree, maximum height can’t exceed 1.44*log₂n. Hence, the maximum height is: 1.44 * log₂1000 = 14

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Answer 2

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java AVL tree a). What are the conditions that must exist in a binary tree for calling the left and the right rotation? b). What is the smallest height that a tree of 1000 nodes can be? What is the bi...

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