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subtree and the height of the right subtree differ by at most 1. We also proved that the height of an AVL tree with n

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subtree and the height of the right subtree differ by at most 1. We also proved that the height of an AVL tree with n nodes is O(log n). Define a 2AVL tree as a tree where for every node the height of the left subtree and the height of the right subtree differ by at most 2. Prove that for 2AVL, trees also the height is O(log n). Hint: Let n(h) be the number of nodes of a 2AVL tree of height h. I Prove that by induction, since n(0) 1 and you know that n(h)>nth-1 tree condition. It's sufficient to prove that nh)2 )+ n(h-3) +1 due to t

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