What is the maximum height of any AVL-tree with 7 nodes? Assume that the…

Answer: 3

Explanation: Compute the minimum number of nodes N(h) required for an AVL tree of height h using the recurrence N(h) = 1 + N(h-1) + N(h-2), with N(0) = 1 and N(1) = 2. Find the largest h such that N(h) ≤ 7.

• N(0) = 1 (single node)

• N(1) = 2

• N(2) = 1 + 2 + 1 = 4

• N(3) = 1 + 4 + 2 = 7

• N(4) = 1 + 7 + 4 = 12

Conclusion: Since N(3) = 7 ≤ 7 and N(4) = 12 > 7, the maximum height achievable with 7 nodes is 3.