adilakhter

// Tail recursive computation of List's length 
let length list = 
    // Auxiliary function to compute length
    // It store intermediate result in acc.
    let rec lengthAux acc list = 
        match list with 
        | [] -> acc
        | _::tail -> lengthAux (acc+1) tail
    lengthAux 0 list  // invoking lengthAux with acc = 0

adilakhter

let rec (|%|) a n = 
  match a, n with 
  |_ when a < n -> a
  |_ when a>=n  -> (|%|) (a-n) n

//Resulting signature:  val ( |%| ) : int -> int -> int

adilakhter

let isprime n = 
    let rec isprimeAux i n = 
        i > n/2 || (n%i <> 0 && (isprimeAux (i+1) n))
    isprimeAux  2 n

//> output:
//
//val isprime : int -> bool
//
//> isprime 10;;

adilakhter

let names = ["alice"; "bob"; "carol"]
let name = List.tryFind (fun s -> length s < 4) names
match name with 
| Some n -> printfn "%s"  n
| None   -> printfn "They all have long names" 


// partial application 

let doubled = Seq.map (fun v -> v *2) values

adilakhter

let avg list = 
    let rec avgAux sum length list = 
      match list with 
      | []  -> sum/length 
      | x::xs -> avgAux (x+sum) (length + 1) xs
    avgAux 0 0 list  

adilakhter

let countElements list = 
  let rec countElementsAux sum length l=
    match l with 
    | []      -> (sum/length, 0) // computing average from sum and length accumulator 
    | x :: xs ->  
        let (avg,count) = countElementsAux (x+ sum) (length+1) xs 
        if  x < avg  then (avg,count) else (avg,count+1)
  let (avg, count) = countElementsAux 0 0 list       
  count

adilakhter

// Recursive solution 
let eulerProblem2Answer'' = 
    let maxF = 4000000
    let rec computeSum f1 f2 sum = 
        match f1 + f2 with 
        | n              -> computeSum f2 n sum 
        | n when n%2 = 0 -> if (n<maxF) then (computeSum f2 n (sum+n)) else sum
    computeSum 0 1 0

adilakhter

let eulerProblem2Answer = 
    (0,1) 
    |> Seq.unfold (fun (f1,f2) -> Some(f2, (f2, f1+f2)))  // Fibonacci Sequence
    |> Seq.takeWhile(fun x -> x < 4000000) // Taking upto Max Fibbonacci  
    |> Seq.filter (fun x -> x%2=0) // Filtering only even numbers 
    |> Seq.sum // computing sum

adilakhter

let eulerProblem2Answer' = 
    (0,1) 
    |> Seq.unfold (fun (f1,f2) -> Some(f2, (f2, f1+f2))) 
    |> Seq.takeWhile(fun x -> x < 4000000)
    |> Seq.sumBy (fun x -> if (x%2)=0 then x else 0) // using SumBy with a projection

adilakhter

let length list = 
    List.fold 
        (fun acc _ -> acc+1) 
        0 
        list