What is the probability of selecting a tree uniformly at random?

Category: QuestionsWhat is the probability of selecting a tree uniformly at random?
Editor">Editor Staff asked 4 weeks ago

What is the probability of selecting a tree uniformly at random?
 
(a) Equal to Catalan Number
 
(b) Less Than Catalan Number
 
(c) Greater than Catalan Number
 
(d) Reciprocal of Catalan Number
 
My question is based upon Binary Trees topic in division Binary Trees of Data Structures & Algorithms I
 
I have been asked this question during an interview for a job.

1 Answers
Editor">Editor Staff answered 4 weeks ago

The correct choice is (d) Reciprocal of Catalan Number
 
The best I can explain: Catalan number is a sequence of natural number that is used in counting problem. Hence it is found that the selecting off a tree uniformly at random is reciprocal of Catalan number.