What is the longest length path for a node x in random binary search tree for the insertion process?

Category: QuestionsWhat is the longest length path for a node x in random binary search tree for the insertion process?
Editor">Editor Staff asked 4 weeks ago

What is the longest length path for a node x in random binary search tree for the insertion process?
 
(a) log x
 
(b) x^2
 
(c) x!
 
(d) 4.311 log x
 
My enquiry is from Binary Trees in division Binary Trees of Data Structures & Algorithms I
 
I got this question during an interview.

1 Answers
Editor">Editor Staff answered 4 weeks ago

Right option is (d) 4.311 log x
 
Best explanation: Although it is difficult to find the length of the longest path in randomized binary search tree, but it has been found that the longest length is around 4.311 log x.