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What is the expected number of leaves in a randomized binary search tree?

(a) n + 1

(b) (n + 1)/3

(c) (n + 1)/2

(d) n + 3

This question is from Binary Trees in portion Binary Trees of Data Structures & Algorithms I

This question was addressed to me by my college professor while I was bunking the class.

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The correct answer is (b) (n + 1)/3

To explain: In a random mathematical model, the expected value of number of leaves in a randomized binary search tree is found to be exactly (n + 1)/3 using probability.

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