What is the maximum height of a balanced AVL tree with 15 nodes?
Question
What is the maximum height of a balanced AVL tree with 15 nodes?
Solution
The height of an AVL tree with N nodes is calculated by the formula log(N+2) base 2, rounded down to the nearest integer, then subtracted by 1.
Let's calculate it step by step:
- Add 2 to the number of nodes: 15 + 2 = 17
- Take the base 2 logarithm of that number: log2(17) ≈ 4.09
- Round down to the nearest integer: 4
- Subtract 1: 4 - 1 = 3
So, the maximum height of a balanced AVL tree with 15 nodes is 3.
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