// Learn more about F# at http://fsharp.net
// See the 'F# Tutorial' project for more help.
open System.Collections.Generic

let inline  left (x, y) = (x + 1, y)
let inline down (x, y) = (x, y + 1)
let max = 30
let (|Left|Down|Both|End|) (x, y) =
                  if (x < max && y >= max) then Left
                  else if (x >= max && y < max) then Down
                  else if (x < max && y < max) then Both
                  else End

let cache = Dictionary<_,_>()

let addToCache x res =
    cache.Add(x,res)
    res

let rec compute2 x =
    match cache.TryGetValue(x) with
    | true,r -> r
    | _ ->
            match x with
            | End ->  1L
            | Left -> compute2 (left x) |> addToCache x
            | Down -> compute2 (down x) |> addToCache x
            | Both -> compute2 (left x) + compute2 (down x) |> addToCache x


[<EntryPoint>]
let main argv =
  //  let processing = compute (1, 1) 0L (fun x -> x)
    //printfn "%A" processing
    let processing = compute2 (1, 1)
    printfn "%A" processing
    0 // return an integer exit code