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AVL Tree rotations: (a) Given the following AVL tree, if node 83 is deleted, how many rotations are needed to obtain an AVL tree again?

AVL Tree rotations: (a) Given the following AVL tree, if node 83 is deleted, how many rotations are needed to obtain an AVL tree again? Draw the tree after each rotation. (b) An AVL tree may become unbalanced when a node is deleted. In general, how many sub-trees will be re-balanced in the worst case when an item is deleted from an AVL tree? Explain your answer. (c) An AVL tree may become unbalanced when a node is inserted. In general, what is the maximum number of rotations that must be performed to rebalance the tree due to an insertion? Explain your answer.

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95 25 48 83 96 12 55 98 46 95 25 48 83 96 12 55 98 46

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