Question-3 There are n number of students in a class.Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2 n a) Write a recursive function to solve this problem...

Question-3

There are

n

number of students in a class.Assume a teacher enters and wants to shake hand according to an algorithm:

Algorithm (X) à  2ⁿ

a)    Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion.

b)      Consider this Algorithm-Z , Taking list of integer as input

List Of Integer: X(Integer: number)

     List Of Integer: Y

     Integer: i = 2

     While (i<>

While (number Mod i == 0)

                                     Y.Add(i)

number = number / i

End While

i = i + 1

End While

If (number > 1) Then Y.Add(number)

     Return Y

End X

(i)                Explain what Algorithm Z is doing?

(ii)              Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexity