deletions | additions       diff --git a/section_Challenegs_in_Bushy_Trees__.tex b/section_Challenegs_in_Bushy_Trees__.tex  index ba023db..9c2f32c 100644  --- a/section_Challenegs_in_Bushy_Trees__.tex  +++ b/section_Challenegs_in_Bushy_Trees__.tex 
...
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$}; \\  $\displaystyle \sum_{i=1}^{N} \frac{1}{n}$ \text{if $N \ne 0$}  2 \text{if $ N = 1$}.\end{cases}$$  Therefore the number of possible permutations are $S(N)*N!$. Unlike left-deep tree case, estimating the cost for all the possible bushy trees is computationally infeasible for moderately large N. Therefore it is required to come with a heuristic to select set of permutations for cost computations.Some heuristics considered are