For Binary trees: There’s no need to consider tree node values, I am only interested in different tree topologies with ‘N’ nodes.
For Binary Search Tree: We have to consider tree node values.
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For Binary trees: There’s no need to consider tree node values, I am only interested in different tree topologies with ‘N’ nodes.
For Binary Search Tree: We have to consider tree node values.
I recommend this article by my colleague Nick Parlante (from back when he was still at Stanford). The count of structurally different binary trees (problem 12) has a simple recursive solution (which in closed form ends up being the Catalan formula which @codeka’s answer already mentioned).
I’m not sure how the number of structurally different binary search trees (BSTs for short) would differ from that of “plain” binary trees — except that, if by “consider tree node values” you mean that each node may be e.g. any number compatible with the BST condition, then the number of different (but not all structurally different!-) BSTs is infinite. I doubt you mean that, so, please clarify what you do mean with an example!