# 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 5 months 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.

Editor">Editor Staff answered 5 months 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.

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