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\section{Challenegs in Bushy Tree Implementation}  Moving from left-deep tree to a Bushy tree is a challenge as the number of possible structures in bushy trees are much larger. Left-deep trees have only one structure regardless of the number of attributes involved. Therefor the number of possible permutations are N! . But for bushy trees possible number of structures are given by   $$f(x) = \begin{cases}   0 & \text{if $0 < x \le 0.05$}; \\  0.1 & \text{if $0.05 < x \le 1$}; \\  0.2 & \text{if $1 < x \le 5$};\\  2^{\frac{x}{20}} & \text{if $5 < x \le 100$};.\end{cases} $$  $$S(N) = \begin{cases}   1 \text{if $ N = 1$}; \\