newaverage.fsx

(*
    The accounts of the "Fat to Fit Club (FFC)" association are supervised by John as a volunteered accountant. 
    The association is funded through financial donations from generous benefactors. 
    John has a list of the first n donations: [14, 30, 5, 7, 9, 11, 15] 
    He wants to know how much the next benefactor should give to the association so that the average of the first n + 1 donations 
    should reach an average of 30. After doing the math he found 149. He thinks that he made a mistake. Could you help him?

    if dons = [14, 30, 5, 7, 9, 11, 15] then new_avg(dons, 30) --> 149
    The function new_avg(arr, navg) should return the expected donation (rounded up to the next integer) that will permit to reach the average navg.
    Should the last donation be a non positive number (<= 0) John wants us to throw an error 
    (return Nothing in Haskell, return None in F# and Ocaml, return -1 in C) so that he clearly sees that his expectations are not great enough.

    Notes:
    all donations are numbers, arr can be empty.
    See examples below to see which error is to be thrown.

    new_avg([14, 30, 5, 7, 9, 11, 15], 92) should return 645
    new_avg([14, 30, 5, 7, 9, 11, 15], 2) should raise an error (ValueError or invalid_argument)

    taken from: https://www.codewars.com/kata/569b5cec755dd3534d00000f/train/fsharp
*)

let newavg (xs: list<float>) (navg: float) =
    match (navg * (float(xs.Length) + 1.0)) - (xs |> Seq.sum) with
    |x when x <= 0.0 -> None
    |x -> Some(int(ceil(x)))

let a = newavg [14.0;30.0;5.0;7.0;9.0;11.0;15.0] 30.0 

// (sum + x) / count = avg
// avg * count = sum + x
// (avg * count) - sum = x