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Define N(h) to be the minimum number of elements that can be stored in a Relaxed AVL tree. Prove that N(h) = Ω(k

h ) for some constant k > 1. Note that you do not have to find the largest k for which this holds.

Screen Shot 2019-09-30 at 11.43.54 PM.png

Screen Shot 2019-09-30 at 11.43.54 PM.png

In class, we saw that AVL trees satisfy the height—balance property, which means that
for every internal node, the left child subtree and the right child subtree have height
differing by at most 1. Consider a slight relaxation of the height—balance requirement,
where, for every internal node, the left child subtree and the right child subtree have
height which differs by at most 2. Let’s call these trees “Relaxed AVL trees”. Define N (h) to be the minimum number of elements that can be stored in a Relaxed
AVL tree. Prove that N (h) = 9(kh) for some constant k > 1. Note that you do not
have to find the largest k for which this holds.

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