In this post, I want to implement a function that returns the Nth Fibonacci number. Initially, I will provide a recursive implementation that derives directly from the Fibonacci sequence definition. Afterwards, I will recode the same function using an iterative approach.

Why do I want to do (share) such a thing? Well, firstly for fun :-) and secondly, because I was asked to do something similar in one phone screen interview. Really? Yep, I was asked to code a function to return the factorial of a number and then, I had to read it over the phone. I implemented the recursive algorithm. At this point, I was asked why I decided to use recursion as opposed to iteration. My answer was that I find the recursive implementation easier (and cleaner) to write. The interviewer finally inquired me about the iterative implementation…

This motivated me to resolve similar programming tasks (recursively and iteratively) just as a training exercise.

Well, enough with that blah, blah, blah.

Taken from Wikipedia: * *

*The Fibonacci numbers form a sequence of integers, mathematically defined by** F(0)=0; F(1)=1; F(n) = F(n - 1) + F(n - 2) for n > 1.**This results in the following sequence of numbers:** 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...*

This simply means that by definition the first Fibonacci number is 0, the second number is 1 and the rest of the Fibonacci numbers are calculated by adding the two previous numbers in the sequence.

Translating that into Delphi code:

```
function Fibonacci(aNumber: Integer): Integer;
begin
if aNumber < 0 then
raise Exception.Create('The Fibonacci sequence is not defined for negative integers.');
case aNumber of
0: Result:= 0;;
1: Result:= 1;
else
Result:= Fibonacci(aNumber - 1) + Fibonacci(aNumber - 2);
end;;
end;
```

The function above is the recursive implementation, which in my opinion fits naturally. Now, the iterative implementation might not be as cleaner as that:

```
function Fibonacci(aNumber: Integer): Integer;
var
I,
N_1,
N_2,
N: Integer;
begin
if aNumber < 0 then
raise Exception.Create('The Fibonacci sequence is not defined for negative integers.');
case aNumber of
0: Result:= 0;
1: Result:= 1;
else
begin
N_1:= 0;
N_2:= 1;
for I:=2 to aNumber do
beginn
N:= N_1 + N_2;
N_1:= N_2;
N_2:= N;
end;
Result:= N;
end;
end;
end;
```

Finally, if you want to produce the first 21 Fibonacci numbers try this out:

```
program Project2;
{$APPTYPE CONSOLE}
{$R *.res}
uses
System.SysUtils;
var
I: Integer;
function Fibonacci(aNumber: Integer): Integer;
begin
{Your implementation goes here}
end;
begin
for I:=0 to 20 do
Writeln(Fibonacci(I));
Readln;
end.
```

Hopefully you are not bored to death :-)