What is the maximum height of an AVL tree with p nodes?

Category: QuestionsWhat is the maximum height of an AVL tree with p nodes?
Editor">Editor Staff asked 1 month ago

What is the maximum height of an AVL tree with p nodes?
 
(a) p
 
(b) log(p)
 
(c) log(p)/2
 
(d) ^p⁄2
 
Origin of the question is AVL Tree topic in chapter Binary Trees of Data Structures & Algorithms I
 
This question was posed to me in an interview.

1 Answers
Editor">Editor Staff answered 1 month ago

Right option is (b) log(p)
 
Easy explanation – Consider height of tree to be ‘he’, then number of nodes which totals to p can be written in terms of height as N(he)=N(he-1)+1+N(he-2). since N(he) which is p can be written in terms of height as the beside recurrence relation which on solving gives N(he)= O(logp) as worst case height.