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 to 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).**