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 : Integer) : Integer;
begin
    if m = 0 then
        Result := n+1
    else if n = 0 then
        Result := Ackermann(m-1, 1)
    else Result := Ackermann(m-1, Ackermann(m, n-1));
end;