Question

8. Ackermann's Function Ackermann's Function is a recursive mathematical algorithm that can be used to test how well a system optimizes its performance of recursion. Design a function ackermann (m, n), which solves Ackermann's function. Use the following logic in your function: If m 0 then return n + 1 If n = 0 then return ackermann(m – 1, 1) Otherwise, return ackermann(m – 1, ackermann(m, n - 1)) Once you've designed your function, test it by calling it with small values for m and n.

Code in python please!

Answer 1

Recursion:

The recursive function calls to itself and a terminate or base condition is specified which breaks the infinite execution of the recursive call. When the function call to itself then it works like a continue statement and the control goes to the starting of the function with updated argument value.

The stack data structure is used in recursion for storing the intermediate value when each function call is made.

In a recursive function, two cases are mentioned:

1. Base condition
2. Recursive call

Base condition:

A terminate condition or base condition is specified which breaks the infinite execution of the recursive call.

Recursive Call:

The function will call to itself and this is known as a recursive call.

The required function is given below:

def ackermann(m,n):
if m==0:
return n+1
elif n == 0:
return ackermann(m-1,1)
else:
return ackermann(m-1, ackermann(m,n-1))

The screenshot of the above source code is given below:

def ackermann(m, n): if m=0: return n+1 elif n == 0: return ackermann(m-1,1) else: return ackermann(m-1, ackermann(m,n-1))

The complete program source code including above method for testing is given below:

def ackermann(m,n):
if m==0:
return n+1
elif n == 0:
return ackermann(m-1,1)
else:
return ackermann(m-1, ackermann(m,n-1))

#function calling and display result
print(ackermann(2,4))

The screenshot of the above source code is given below:

def ackermann(m, n): if m=0: return n+1 elif n == 0: return ackermann(m-1,1) else: return ackermann(m-1, ackermann(m,n-1)) #function calling and display result print(ackermann(2,4))

OUTPUT:

11