module _101

open common
open System

let leGrange points x =
    points
    |> Seq.mapi (fun j (xj,y) -> 
        y * (
            points
            |> Seq.mapi (fun k (xk,_) -> 
                    if (j = k) then 1.0 else
                    (x - xk) / (xj - xk)
                )
            |> Seq.fold (*) 1.0
            )
        )
    |> Seq.sum

let rec polynomialGen p x =
    if p = 0 then 1L else
    let rest = polynomialGen (p-1) x
    let this = int64 (Math.Pow(float x, float p))
    if p % 2 = 0 then
        rest + this
    else
        rest - this

let poly10 = polynomialGen 10

let cube x =
    int64 (Math.Pow(float x,3.0))

let funTup f n = (n, f n)

let sumOfFITsOfBOPs =
    let leGrangeTermChecker f seqLimit =
        [1..seqLimit]
        |> Seq.map (fun n -> (float n, float (f n)))
        |> (fun points -> 
            let nth = points |> Seq.nth (seqLimit - 1) |> snd
            let pointsMinusLast = points |> Seq.take (seqLimit - 1)
            let nthLegrange = leGrange pointsMinusLast (float seqLimit)

            (int64 nth, int64 nthLegrange)
            )

    allIntegers |> Seq.skip 2
    |> Seq.map (leGrangeTermChecker poly10)
    |> Seq.take 11
    //|> Seq.takeWhile (fun (nth,nthLeGrange) ->  .Abs( nth - nthLeGrange) < 2)
    |> Seq.toArray
    //|> Array.map snd
    //|> Array.sum