When executing a sequence of Unions, a node of rank r must have at least 2^r descendants.

Category: QuestionsWhen executing a sequence of Unions, a node of rank r must have at least 2^r descendants.
Editor">Editor Staff asked 4 weeks ago

When executing a sequence of Unions, a node of rank r must have at least 2^r descendants.
 
(a) true
 
(b) false
 
My question comes from Trees in section Trees of Data Structures & Algorithms I
 
I have been asked this question in an interview for job.

1 Answers
Editor">Editor Staff answered 4 weeks ago

Correct choice is (a) true
 
The best explanation: By the induction hypothesis, each tree has at least 2^r – 1 descendants, giving a total of 2^r and establishing the lemma.