What is the maximum height of a balanced AVL tree with 15 nodes?a)5b)3c)6d)4
Question
What is the maximum height of a balanced AVL tree with 15 nodes?a)5b)3c)6d)4
Solution
The height of an AVL tree with N nodes is calculated by the formula H = log2(N+1). This gives the minimum height. However, the question asks for the maximum height.
The maximum height of an AVL tree with N nodes is approximately 1.44 * log2(N+2) - 0.328.
If we substitute N = 15 into the formula, we get:
Hmax = 1.44 * log2(15+2) - 0.328 = 4.56
Since the height of a tree must be an integer, we round this up to the nearest whole number, which is 5.
So, the maximum height of a balanced AVL tree with 15 nodes is 5 (option a).
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