With ‘ N ‘ no of nodes, how many different Binary and Binary Search Trees possible?

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  1. Total no of Binary Trees are = enter image description![enter image description here

  2. Summing over i gives the total number of binary search trees with n nodes.
    enter image description here

The base case is t(0) = 1 and t(1) = 1, i.e. there is one empty BST and there is one BST with one node.
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So, In general you can compute total no of Binary Search Trees using above formula.
I was asked a question in Google interview related on this formula.
Question was how many total no of Binary Search Trees are possible with 6 vertices.
So Answer is t(6) = 132

I think that I gave you some idea…

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