/// m13 life rules: the next generation is a function of the whole old board, and nothing else.
module Snake.Life.Rules

open Snake
open Snake.Model
open Snake.Life.Model

// Every cell of the board, row-major (y, then x). Filtering this list keeps any result in canonical order for free.
let private board: Point list =
    [ for y in 0 .. LH - 1 do
          for x in 0 .. LW - 1 -> { X = x; Y = y } ]

let private onBoard (p: Point) : bool = p.X >= 0 && p.X < LW && p.Y >= 0 && p.Y < LH

// A cell's position in row-major order: the order the canonical list is sorted by.
let private index (p: Point) : int = p.Y * LW + p.X

let private offsets = [ (-1, -1); (0, -1); (1, -1); (-1, 0); (1, 0); (-1, 1); (0, 1); (1, 1) ]

// The up to eight neighbours of `p` that are on the board (the edges are dead: nothing wraps around).
let private neighbours (p: Point) : Point list =
    offsets |> List.map (fun (dx, dy) -> { X = p.X + dx; Y = p.Y + dy }) |> List.filter onBoard

// B3/S23, every cell judged on the *old* list only. A Set of the old cells makes "is this neighbour alive?" one
// lookup, so a generation is 1200 x 8 lookups however many cells live. The set is built once and only read.
let lifeStep (cells: Point list) : Point list =
    let alive = Set.ofList cells
    let count p = neighbours p |> List.filter alive.Contains |> List.length

    board
    |> List.filter (fun p ->
        let n = count p
        n = 3 || (n = 2 && alive.Contains p))

// Add a dead cell or remove a live one, keeping the list sorted row-major without duplicates. Off the board: unchanged.
let private toggle (cells: Point list) (p: Point) : Point list =
    if not (onBoard p) then
        cells
    elif List.contains p cells then
        List.filter (fun c -> c <> p) cells
    else
        List.filter (fun c -> index c < index p) cells
        @ [ p ]
        @ List.filter (fun c -> index c > index p) cells

// A random board: one `intBelow 4` per cell in row-major order, the cell alive when the draw is 0 (about one cell in
// four). mapFold threads the seed through the 1200 draws; the result is the cells and the seed after the last draw.
let private randomCells (seed: uint32) : Point list * uint32 =
    let draws, next = List.mapFold (fun s _ -> Random.run s (Random.intBelow 4)) seed board
    List.zip board draws |> List.filter (fun (_, d) -> d = 0) |> List.map fst, next

let private nextGeneration (state: LifeState) : LifeState =
    { state with
        Cells = lifeStep state.Cells
        Generation = state.Generation + 1 }

let lifeUpdate (state: LifeState) (action: LifeAction) : LifeState =
    match action with
    | LifeAction.Frame -> if state.Running then nextGeneration state else state
    | LifeAction.Step -> if state.Running then state else nextGeneration state
    | LifeAction.TogglePause -> { state with Running = not state.Running }
    // Clicking edits the world whether it runs or not: the click is one action between two generations.
    | LifeAction.Toggle p -> { state with Cells = toggle state.Cells p }
    | LifeAction.Clear -> { state with Cells = []; Generation = 0 }
    | LifeAction.Randomize ->
        let cells, seed = randomCells state.Seed

        { state with
            Cells = cells
            Seed = seed
            Generation = 0 }