1. Write the code for the method that calculates the number of unique shapes for a binary search tree with n nodes. Use the formula
where b_{n} is the number of possible shapes for a binary search tree with n nodes.
2. Write the code for the method that approximates the number of unique shapes for a binary search tree with n nodes. Use the formula
b_{n }= 4^{n} /n1.5√π
where is the number of possible shapes for a binary search tree with n nodes.