Extend your python program below to include the recursive methods, as described in part A , B ad C.

class BST:

def __init__(self,data):

self.root = data

self.left = None

self.right = None

def insert(self,data):

if self.root == None:

self.root = BST(data)

elif data > self.root:

if self.right == None:

self.right = BST(data)

else:

self.right.insert(data)

elif data < self.root:

if self.left == None:

self.left = BST(data)

else:

self.left.insert(data)

def inordertraversal(self):

if self.left != None:

self.left.inordertraversal()

print (self.root),

if self.right != None:

self.right.inordertraversal()

t = BST(9)

t.insert(8)

t.insert(3)

t.insert(6)

t.insert(12)

t.insert(10)

t.insert(11)

t.inordertraversal()

(a) numberOfNodes Accepts a BST node r and returns an integer value of the

number of nodes in the BST whose root is r.

(b) treeHeight Accepts a BST node r and returns and integer value of the height

of the BST whose root is r.

(c) numberOfLeaves Accepts a BST node r and returns an integer value of the

number of leaves in the BST whose root is r.

Comment: You may choose to submit pseudocode only for Question 9. Include it

along with your Part A. Each algorithm will require very few lines of code. Do not

use extra local (or global) variables, they are unnecessary. Think: \if at the base

case, return base case solution" else eturn something involving a recursive call".