Generating Fibonacci series in F#

Question

I\'m just starting to learn F# using VS2010 and below is my first attempt at generating the Fibonacci series. What I\'m trying to do is to build a list of all numbers less

Answer 1

One more codata'ish way:

let rec fib = seq {
  yield! seq {0..1}
  yield! Seq.map (fun(a,b)->a+b) <| Seq.zip fib (Seq.skip 1 fib)
}
let a = fib |> Seq.take 10 |> Seq.toList

Answer 2

Here's a good article by .Net guru Scott Hanselman on generating fibonacci series in F#

let rec fib n = if n < 2 then 1 else fib (n-2) + fib(n-1)

http://www.hanselman.com/blog/TheWeeklySourceCode13FibonacciEdition.aspx

It also compares with other languages as a reference

Answer 3

Yes, mutable variables and while loops are usually a good sign that your code is not very functional. Also the fibonacci series, doesn't start with 1,2 - it starts with 0,1 or 1,1 depending on who you ask.

Here's how I'd do it:

let rec fabListHelper (a:int,b:int,n:int) =
  if a+b < n then
    a+b :: fabListHelper (b, a+b, n)
  else
    [];;

let fabList (n:int) = 0 :: 1 :: fabListHelper (0,1, n);;

(*> fabList 400;;
val it : int list = [0; 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377]*)

Answer 4

One with an array:

let fibonacci n = [|1..n|] |> Array.fold (fun (a,b) _ -> b, a + b) (0,1) |> fst

Answer 5

The great solution of Scott Hanselman does not report the 0 the fibonacci sequence starts with.

So here is a minor change to his solution to also report the 0. I used a small list from 0 to 10 to display the first 11 items of the sequence.

let nums=[0..10]
let rec fib n = if n < 1 then 0 else if n < 2 then 1 else fib (n-2) + fib(n-1)
let finres = List.map fib nums
printfn "%A" finres

I'm new and incompetent in relation to f# and still not totally fully understanding the need of it. But found this an interesting test.

Just for fun : If found a formula of Binet that calculates the n-th Fibonacci number. Unfortunately some floating point functions are needed to get the integer result back in the end : [Fibonacci formula of Binet][1]

http://i.stack.imgur.com/nMkxf.png

let fib2 n = (1.0 / sqrt(5.0)) * ( (((1.0 + sqrt(5.0)) /2.0)**n)  -  (((1.0 -  sqrt(5.0)) /2.0)**n) )
let fib2res = fib2 10.0
System.Console.WriteLine(fib2res)
let strLine = System.Console.ReadLine()

A quick and dirty translation to f# would be as shown above. I'm sure others can improve on this in matter of style and efficiency. The example calculates the 10th number. The result will be 55.