Calculating the factorial of a number in Delphi: Recursive and iterative methods

The factorial function can be defined in both recursive and iterative ways. Take a look at the following definitions borrowed from Wikipedia.

Recursive definition:

Iterative definition:

For both the above definitions we have that:

The purpose here is not the mathematical stuff, but two provide the implementation of such definitions in Delphi (Object Pascal).

First, I bring you one recursive implementation of the factorial function. Notice how the function calls itself, which is what the recursion really is:

function Factorial(aNumber: Integer): Integer;
begin
  if aNumber < 0 then
    raise Exception.Create('The factorial function is not
  defined for negative integers.');

  Result:= 1;
  if aNumber > 0 then
    Result:= Factorial(aNumber-1) * aNumber;
end;

Second, I present you one iterative implementation of the factorial function. You can easily see the iteration performed in the “for” loop below:

function Factorial(aNumber: Integer): Integer;
var
  i: Integer;
begin
  if aNumber < 0 then
    raise Exception.Create('The factorial function is not
  defined for negative integers.');

  Result:= 1;
  for i:=1 to aNumber do
    Result:= Result * i;
end;

Big-O considerations:
The recursive factorial function implemented before has a linear growth O(n), not O (n!). In addition, the iterative factorial function is also linear O(n).
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