problem 1)a) prepare a function to detemrine the factorial of a number using recursion. Trace this function for a number n=5.

b) Define the following with respect to a binary tree:

(i) Depth

(ii) Sibling

(iii) Skewed tree

(iv) Complete binary tree

(v) Leafnode

problem 2)a) prepare a function to implement heap sort.

b) Draw the heap for the elements shown below stepwise.

50, 25, 30, 75, 100, 45, 80 3 M

c) Trace the function in Q 2.a) for the heap constructed in Q 2. b)

problem 3)a) prepare the function to convert the infix expression to postfix expression using a stack.

b) What are the prefix and postfix forms of the following expression?

a*(b+c/(4*a*c)) 2M

c) Trace the function in Q 3.a) for the expression in Q 3. b) suitably.