open System

let beeTotal = 1000
let magicA = 150
let magicB = 100
let areaGen = beeTotal / (magicA + magicB)

let iterTotal = 1000
let areaShrink = 0.2

let rng = System.Random()

let shuffleR xs = xs |> List.sortBy (fun _ -> rng.Next())

type Func = float * float -> float

type Area = struct
    val x1: float
    val x2: float
    val y1: float
    val y2: float
    new(X1, Y1, X2, Y2) = {x1 = X1; x2 = X2; y1 = Y1; y2 = Y2;}
    member this.RandP () =
        let x = this.x1 + (this.x2 - this.x1) * rng.NextDouble()
        let y = this.y1 + (this.y2 - this.y1) * rng.NextDouble()
        (x, y)
    member this.Radius =
        let x1 = this.x1
        let x2 = this.x2
        let y1 = this.y1
        let y2 = this.y2
        sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)) / 2.
end

let areaBound (a: Area) (p: float * float) =
    let xmin = min a.x1 a.x2
    let xmax = max a.x1 a.x2
    let ymin = min a.y1 a.y2
    let ymax = max a.y1 a.y2
    let (x, y) = p
    min (max x xmin) xmax, min (max y ymin) ymax

let pArea r p =
    let x, y = p
    Area(x - r, y - r, x + r, y + r)

let initState (f: Func) (a: Area) =
    a, areaShrink * a.Radius,
    [for i = 1 to beeTotal do
        let coords = a.RandP()
        (f coords, coords)
    ] |> List.sort |> List.rev

let iterate (f: Func) (state: Area * float * (float * (float * float)) list) =
    let a, r, li = state
    let top = List.take magicA li
    let bottom = List.skip magicA li |> shuffleR |> List.take magicB
    let points =
        (top @ bottom)
        |> List.map ((fun (_, p) -> pArea r p)
            >> (fun (a: Area) -> [for i = 1 to areaGen do a.RandP()]))
        |> List.reduce (@)
        |> List.map ((areaBound a)
            >> ((fun p -> f p, p)))
        |> List.sort |> List.rev
    a, areaShrink * r, points

let f (x, y) = (x - 150.) * (x - 150.) - (y - 200.) * (y - 200.)
let area = Area(0., 0., 1000., 1000.)

let rec repeat f n x =
    if n = 0 then x else f(repeat f (n - 1) x)

[<EntryPoint>]
let main argv =
    let _, _, li =
        initState f area |>
        repeat (iterate f) iterTotal
    printfn "%A" li.[0]
    0