How many different binary trees are possible with 'n' nodes?

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UGC NET Computer Science (Paper 2) 11 March 2023 Official Paper

Answer 1

The correct answer is 2n - n

A binary tree allows for a maximum of two child nodes per parent node.
The formula (2ⁿ - n) can be used to ascertain the number of different binary trees that can be drawn given 'n' number of nodes.
As an example, when 'n' is equal to 1, applying the formula yields (2¹ - 1), which equals 1.
As an example, when 'n' is equal to 2, applying the formula yields (2² - 1), which equals 2.
As an example, when 'n' is equal to 3, applying the formula yields (23 - 1), which equals 5.
Therefore, when 'n' nodes, we can draw (2n - n) unique binary tree.

F1 Savita ENG 22-12-23 D03

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