Question

Using a compiler of your own choice, write a program to compute each of the following functions (The last one is called the Ackermann function):

(a) h(n) = h(n−1)+2h(n−2)+10;n ≥ 3;h(2) = 8;h(1) = 4;

Answer 1

A Python program is provided to compute the recursive function h(n) specified in the question. It defines h(1) and h(2) explicitly and uses recursion to calculate h(n) for n ≥ 3.

Step-by-step explanation:

The program to compute the specified recursive function, h(n), can be written in various programming languages. Since the choice of compiler is left to us, we'll use Python for its readability and dynamic typing. Below is a Python function to compute h(n):

def h(n):
if n == 1:
return 4
elif n == 2:
return 8
else:
return h(n-1) + 2*h(n-2) + 10

To calculate the value of h(n) for n ≥ 3, we simply call the h function with the desired value of n. For example, h(3) would compute the result based on the given recurrence relation. This program utilizes the concept of recursion to solve the problem. Notice that the base cases, h(1) and h(2), are explicitly defined as per the problem statement: h(1) = 4 and h(2) = 8, respectively.

The Ackermann function, mentioned in the question, is unrelated to the provided Python code example and is known for its ability to grow very rapidly with small inputs. It can be implemented in Python as well but is not shown here.