// originally published by Julien

// original implementation taken from http://lepensemoi.free.fr/index.php/2010/02/11/alternative-binary-random-access-list

//J.F. added remove, trys, length, append, rev



namespace FSharpx.DataStructures



open System.Collections

open System.Collections.Generic



type AltBinRndAccList<'a> = 

    | Nil

    | Zero of AltBinRndAccList<'a * 'a>

    | One of 'a * AltBinRndAccList<'a * 'a>

    

    with

    interface IRandomAccessList<'a> with



        member this.Cons (x : 'a) = AltBinRndAccList.cons x this :> _



        member this.Count() = AltBinRndAccList.length (0, 1, this)



        member this.Head() =

            let x, _ = AltBinRndAccList.uncons this

            x



        member this.TryGetHead() =

            match AltBinRndAccList.tryUncons this with

            | None -> None

            | Some( x, _) -> Some(x)



        member this.IsEmpty() = AltBinRndAccList.isEmpty this



        member this.Length() = AltBinRndAccList.length (0, 1, this)



        member this.Lookup i = AltBinRndAccList.lookup i this



        member this.TryLookup i = AltBinRndAccList.tryLookup i this



        member this.Rev() = AltBinRndAccList.rev this :> _



        member this.Tail() =

            let _, xs = AltBinRndAccList.uncons this

            xs :> _



        member this.TryGetTail() =

            match AltBinRndAccList.tryUncons this with

            | None -> None

            | Some( _, Nil) -> None

            | Some( _, xs) -> Some(xs :> _)



        member this.Uncons() =

            let x, xs = AltBinRndAccList.uncons this

            x, xs :> _



        member this.TryUncons() =

            match AltBinRndAccList.tryUncons this with

            | None -> None

            | Some(x, xs) -> Some(x, xs :> _)



        member this.Update i y = AltBinRndAccList.fupdate ((fun x -> y), i, this) :> _

        

        member this.TryUpdate i y =

            match AltBinRndAccList.ftryUpdate ((fun x -> y), i, this) with

            | None -> None

            | Some(x) -> Some(x :> _)



        member this.GetEnumerator() = 

            let e = seq {

                match AltBinRndAccList.tryUncons this with

                | None -> () 

                | Some(x, xs) ->

                    yield x 

                    yield! xs}

            e.GetEnumerator()



        member this.GetEnumerator() = (this :> _ seq).GetEnumerator() :> IEnumerator

            

and AltBinRndAccList<'a> 



    with



    static member internal cons (x : 'a) : AltBinRndAccList<'a> -> AltBinRndAccList<'a> = function

        | Nil ->  One (x, Nil) 

        | Zero ps -> One (x, ps) 

        | One(y, ps) ->  Zero(AltBinRndAccList.cons (x,y) ps) 

             

    static member internal isEmpty : AltBinRndAccList<'a> -> bool = function Nil -> true | _ -> false 



    static member internal length : int * int * AltBinRndAccList<'a> -> int = function

        | len, acc, Nil -> len

        | len, acc, One(x, Nil) -> len + acc

        | len, acc, One(x, ps) -> AltBinRndAccList.length ((len + acc), (2 * acc), ps)

        | len, acc, Zero ps -> AltBinRndAccList.length (len, (2 * acc), ps)



    static member internal lookup (i:int) : AltBinRndAccList<'a> -> 'a = function

        | Nil -> raise Exceptions.OutOfBounds

        | One(x, ps) ->

            if i = 0 then x else AltBinRndAccList.lookup (i-1) (Zero ps)

        | Zero ps ->

            let (x, y) = AltBinRndAccList.lookup (i/2) ps

            if i % 2 = 0 then x else y



    static member internal tryLookup (i:int) : AltBinRndAccList<'a> -> 'a option = function

        | Nil -> None

        | One(x, ps) ->

            if i = 0 then Some(x) else AltBinRndAccList.tryLookup (i-1) (Zero ps)

        | Zero ps ->

            match (AltBinRndAccList.tryLookup (i/2) ps) with

            | None -> None

            | Some (x, y) -> if i % 2 = 0 then Some(x) else Some(y)



    static member internal ofSeq (s:seq<'a>) : AltBinRndAccList<'a> = 

        if Seq.isEmpty s then Nil

        else

            let a = Array.ofSeq s

            let rec loop (acc: AltBinRndAccList<'a>) dec (a': array<'a>) =

                if dec < 0 then acc

                else loop (AltBinRndAccList.cons a'.[dec] acc) (dec - 1) a'

            loop Nil (a.Length - 1) a



    static member internal uncons : AltBinRndAccList<'a> -> 'a * AltBinRndAccList<'a> = function

        | Nil -> raise Exceptions.Empty

        | One(x, Nil) -> (x, Nil)

        | One(x, ps) -> (x, Zero ps)

        | Zero ps ->

              let (x,y), ps' = AltBinRndAccList.uncons ps

              x, (One (y, ps'))



    static member internal tryUncons : AltBinRndAccList<'a> -> ('a * AltBinRndAccList<'a>) option = function

        | Nil -> None

        | One(x, Nil) -> Some(x, Nil)

        | One(x, ps) -> Some(x, Zero ps)

        | Zero ps ->

              let (x,y), ps' = AltBinRndAccList.uncons ps

              Some(x, (One (y, ps')))



    static member internal fremove : int * array<'a> * int * AltBinRndAccList<'a> -> int * AltBinRndAccList<'a> = function

        | i, _, _, Nil -> raise Exceptions.OutOfBounds

        | 0, _, aIdx, One(x, ps) -> aIdx, Zero(ps)

        | i, a, aIdx, One (x, ps) -> 

            Array.set a aIdx x

            AltBinRndAccList.fremove (i-1, a, (aIdx+1), Zero ps)

        | 0, _, aIdx, Zero ps -> 

            let (x,y), ps' = AltBinRndAccList.uncons ps

            aIdx, One(y, ps')

        | 1, _, aIdx, Zero ps -> 

            let (x,y), ps' = AltBinRndAccList.uncons ps

            aIdx, One(x, ps')      

        | i, a, aIdx, Zero ps -> 

            let (x,y), ps' = AltBinRndAccList.uncons ps

            Array.set a aIdx x

            Array.set a (aIdx + 1) y

            AltBinRndAccList.fremove ((i-2), a, (aIdx + 2), Zero ps')



    static member internal ftryRemove : int * array<'a> * int * AltBinRndAccList<'a> -> int * AltBinRndAccList<'a> option = function

        | i, _, _, Nil -> 0, None

        | 0, _, aIdx, One(x, ps) -> aIdx, Some(Zero(ps))

        | i, a, aIdx, One (x, ps) -> 

            Array.set a aIdx x

            AltBinRndAccList.ftryRemove (i-1, a, (aIdx+1), Zero ps)

        | 0, _, aIdx, Zero ps -> 

            let (x,y), ps' = AltBinRndAccList.uncons ps

            aIdx, Some(One(y, ps'))

        | 1, _, aIdx, Zero ps -> 

            let (x,y), ps' = AltBinRndAccList.uncons ps

            aIdx, Some(One(x, ps'))

        | i, a, aIdx, Zero ps -> 

            let (x,y), ps' = AltBinRndAccList.uncons ps

            Array.set a aIdx x

            Array.set a (aIdx + 1) y

            AltBinRndAccList.ftryRemove ((i-2), a, (aIdx + 2), Zero ps')



    static member internal rev : AltBinRndAccList<'a> -> AltBinRndAccList<'a> = function

        | Nil -> Nil

        | xs -> 

            let rec loop xs' acc =

                match (AltBinRndAccList.tryUncons xs') with

                | None -> acc

                | Some(x, xs'') -> loop xs'' (AltBinRndAccList.cons x acc)

            loop xs Nil



    static member internal fupdate : ('a -> 'a) * int * AltBinRndAccList<'a> -> AltBinRndAccList<'a> = function

        | f, i, Nil -> raise Exceptions.OutOfBounds

        | f, 0, One(x, ps) -> One(f x, ps)

        | f, i, One (x, ps) -> AltBinRndAccList.cons x (AltBinRndAccList.fupdate (f, i-1, Zero ps))

        | f, i, Zero ps ->

            let f' (x, y) = if i % 2= 0 then f x, y else x, f y

            Zero(AltBinRndAccList.fupdate(f', i/2, ps))



    static member internal ftryUpdate : ('a -> 'a) * int * AltBinRndAccList<'a> -> AltBinRndAccList<'a> option = function

        | f, i, Nil -> None

        | f, 0, One(x, ps) -> Some(One(f x, ps))

        | f, i, One (x, ps) -> 

            match (AltBinRndAccList.ftryUpdate (f, i-1, Zero ps)) with

            | None -> None

            | Some(ps') -> Some(AltBinRndAccList.cons x ps')

        | f, i, Zero ps ->

            let f' (x, y) = if i % 2= 0 then f x, y else x, f y

            match (AltBinRndAccList.ftryUpdate(f', i/2, ps)) with

            | None -> None

            | Some(ps') -> Some(Zero(ps'))



    static member internal append : AltBinRndAccList<'a> * AltBinRndAccList<'a> -> AltBinRndAccList<'a> = function

        | Nil, Nil -> Nil

        | xs, Nil -> xs

        | Nil, ys -> ys

        | xs, ys -> 

            let xs' = AltBinRndAccList.rev xs

            let rec loop xs'' acc =

                match (AltBinRndAccList.tryUncons xs'') with

                | None -> acc

                | Some(x, xs'') -> loop xs'' (AltBinRndAccList.cons x acc)

            loop xs' ys



    member this.Cons (x : 'a) = AltBinRndAccList.cons x this



    member this.Head() =

        let x, _ = AltBinRndAccList.uncons this

        x



    member this.TryGetHead() =

        match AltBinRndAccList.tryUncons this with

        | None -> None

        | Some( x, _) -> Some(x)



    member this.IsEmpty() = AltBinRndAccList.isEmpty this



    member this.Length() = AltBinRndAccList.length (0, 1, this)



    member this.Lookup i = AltBinRndAccList.lookup i this



    member this.TryLookup i = AltBinRndAccList.tryLookup i this



    member this.Remove i = 

        if i = 0 then 

            match (AltBinRndAccList.uncons this) with

            | _, Zero(Nil) -> Nil

            | _, x -> x

        else

            let front = Array.create i (fst (AltBinRndAccList.uncons this))

            match (AltBinRndAccList.fremove (i, front, 0, this)) with

            | _, Zero(Nil) -> Nil

            | frontLen, x -> 

                let rec loop i' (front':'a array) (back:AltBinRndAccList<'a>) =

                    match i' with

                    

                    | i'' when i'' > -1 -> loop (i''- 1) front' ( AltBinRndAccList.cons front'.[i''] back)

                    | i'' -> back

                        

                loop (frontLen - 1) front x



    member this.TryRemove i = 

        if i = 0 then 

            match (AltBinRndAccList.uncons this) with

            | _, Zero(Nil) -> Some(Nil)

            | _, x -> Some(x)

        else

            let front = Array.create i (fst (AltBinRndAccList.uncons this))

            match (AltBinRndAccList.ftryRemove (i, front, 0, this)) with

            | _, None -> None

            | _, Some(Zero(Nil)) -> Some(Nil)

            | frontLen, Some(x) -> 

                let rec loop i' (front':'a array) (back:AltBinRndAccList<'a>) =

                    match i' with

                    

                    | i'' when i'' > -1 -> loop (i''- 1) front' ( AltBinRndAccList.cons front'.[i''] back)

                    | i'' -> Some(back)

                        

                loop (frontLen - 1) front x



    member this.Rev() = AltBinRndAccList.rev this 



    member this.Tail() =

        let _, xs = AltBinRndAccList.uncons this

        xs 



    member this.TryGetTail() =

        match AltBinRndAccList.tryUncons this with

        | None -> None

        | Some( _, Nil) -> None

        | Some( _, xs) -> Some(xs)



    member this.Uncons() =

        let x, xs = AltBinRndAccList.uncons this

        x, xs



    member this.TryUncons() =

        match AltBinRndAccList.tryUncons this with

        | None -> None

        | Some(x, xs) -> Some(x, xs)



    member this.Update i y = AltBinRndAccList.fupdate ((fun x -> y), i, this)

        

    member this.TryUpdate i y =

        match AltBinRndAccList.ftryUpdate ((fun x -> y), i, this) with

        | None -> None

        | Some(x) -> Some(x)

      

      

[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]

 module AltBinaryRandomAccessList = 

    //pattern discriminator



    let (|Cons|Nil|) (l: AltBinRndAccList<'a>) = match l.TryUncons() with Some(a,b) -> Cons(a,b) | None -> Nil



    ///returns random access list from elements of 2 random access lists concatenated 

    let append xs ys = AltBinRndAccList.append (xs, ys)

   

     ///returns a new random access list with the element added to the beginning

    let inline cons x (xs: AltBinRndAccList<'a>) = xs.Cons x   

  

    ///returns the first element

    let head xs =

        let x, _ = AltBinRndAccList.uncons xs

        x



     ///returns a empty random access list

    let empty = Nil



    ///returns option first element 

    let tryGetHead xs =

        match (AltBinRndAccList.tryUncons xs) with

        | None -> None

        | Some( x, _) -> Some(x)



    ///returns true if the random access list has no elements

    let inline isEmpty (xs: AltBinRndAccList<'a>) = xs.IsEmpty()



    ///returns the count of elememts

    let inline length (xs: AltBinRndAccList<'a>) = xs.Length() 



    ///returns element by index

    let rec lookup i xs = AltBinRndAccList.lookup i xs



    ///returns option element by index

    let rec tryLookup i xs = AltBinRndAccList.tryLookup i xs



    ///returns random access list from the sequence

    let ofSeq s = AltBinRndAccList.ofSeq s



    ///returns random access list with element removed by index

    let inline remove i (xs: AltBinRndAccList<'a>) = xs.Remove i 



    ///returns option random access list with element removed by index

    let inline tryRemove i (xs: AltBinRndAccList<'a>) = xs.TryRemove i



    //returns random access list reversed

    let inline rev (xs: AltBinRndAccList<'a>) = xs.Rev()



    ///returns a new random access list of the elements trailing the first element

    let tail xs =

        let _, xs' = AltBinRndAccList.uncons xs

        xs'



    ///returns a option random access list of the elements trailing the first element

    let tryGetTail xs =

        match (AltBinRndAccList.tryUncons xs) with

        | None -> None

        | Some( _, xs') -> Some(xs')



    ///returns the first element and tail

    let inline uncons (xs: AltBinRndAccList<'a>) = xs.Uncons()



    ///returns the option first element and tail

    let inline tryUncons (xs: AltBinRndAccList<'a>) = xs.TryUncons()



    ///returns random access list with element updated by index

    let inline update i y (xs: AltBinRndAccList<'a>) = xs.Update i y



    ///returns option random access list with element updated by index

    let inline tryUpdate i y (xs: AltBinRndAccList<'a>) = xs.TryUpdate i y