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Constructing Unique Binary Search Trees

Q: Via Quora

Given the set of keys {6, 7, 1, 4, 2}, how many unique binary search trees of height 2 are possible? Draw the trees. Assume that the height of the root-node is zero.

A:

There are 6 unique Binary Search Trees (BST) of height 2 that can be constructed from the key set $\{ 6, 7, 1, 4, 2 \}$ when all keys are used. Furthermore, there are 36 total BSTs of height 2 that can be constructed from said key set.

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ZPL Commands

Command	Format	Description
^A	^Afo,h,w,d:f.x	Use Scalable/Bitmapped Font
^A@	^A@o,h,w,d:f.x	Use Font Name to Call Font
^B0	^B0a,b,c,d,e,f,g	Aztec Bar Code Parameters
^B1	^B1o,e,h,f,g	Code 11 Bar Code
^B2	^B2o,h,f,g,e,j	Interleaved 2 of 5 Bar Code
^B3	^B3o,e,h,f,g	Code 39 Bar Code