Problem Statement

The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.

The Ackermann function is usually defined as follows:

Its arguments are never negative and it always terminates.

Write a function which returns the value of

A ( m , n )

{\displaystyle A(m,n)}

. Arbitrary precision is preferred (since the function grows so quickly), but not required.

Let's start with the solution:

function ackermann m,n
    switch
        Case m = 0
            return n + 1
        Case (m > 0 And n = 0)
            return ackermann((m - 1), 1)
        Case (m > 0 And n > 0)
            return ackermann((m - 1), ackermann(m, (n - 1)))
    end switch
end ackermann