module KdTree

open System

type I2DCoords =
    abstract X : float32
    abstract Y : float32

// Compare 'e1' and 'e2' by X.
let cmpX (e1: I2DCoords) (e2: I2DCoords) : int =
    match e1.X.CompareTo(e2.X) with
    | 0 -> match e1.Y.CompareTo(e2.Y) with
           | 0 -> e1.GetHashCode().CompareTo(e2.GetHashCode())
           | v -> v
    | v -> v

// Compare 'e1' and 'e2' by Y.
let cmpY (e1: I2DCoords) (e2: I2DCoords) : int =
    match e1.Y.CompareTo(e2.Y) with
    | 0 -> match e1.X.CompareTo(e2.X) with
           | 0 -> e1.GetHashCode().CompareTo(e2.GetHashCode())
           | v -> v
    | v -> v

type Region = { minX: float32; maxX: float32; minY: float32; maxY: float32 } with
    member this.Contains px py : bool =
        px >= this.minX && px <= this.maxX &&
        py >= this.minY && py <= this.maxY

    member this.IsSub otherRegion : bool =
        this.minX >= otherRegion.minX && this.maxX <= otherRegion.maxX &&
        this.minY >= otherRegion.minY && this.maxY <= otherRegion.maxY

    member this.Intersects otherRegion : bool =
        this.minX < otherRegion.maxX && this.maxX >= otherRegion.minX &&
        this.minY < otherRegion.maxY && this.maxY >= otherRegion.minY

type Tree<'a when 'a :> I2DCoords> =
    | Node of float32 * Tree<'a> * Tree<'a>
    | Leaf of 'a

    static member BuildTree (l: 'a list) : Tree<'a> =
        let xSorted = List.toArray l
        let ySorted = List.toArray l
        Array.sortInPlaceWith cmpX xSorted
        Array.sortInPlaceWith cmpY ySorted

        let rec buildTreeFromSortedArray (pXSorted: 'a[]) (pYSorted: 'a[]) (depth: int) : Tree<'a> =
            if pXSorted.Length = 1
            then
                Leaf pXSorted.[0]
            else
                if depth % 2 = 1 // 'depth' is odd -> vertical splitting else horizontal splitting.
                then
                    let leftX, rightX = Array.splitAt ((pXSorted.Length + 1) / 2) pXSorted
                    let splitElement = Array.last leftX
                    let leftY, rightY = Array.partition (fun (e: 'a) -> cmpX e splitElement <= 0) pYSorted // FIXME: Maybe this operation can be optimized.
                    Node (splitElement.X, buildTreeFromSortedArray leftX leftY (depth + 1), buildTreeFromSortedArray rightX rightY (depth + 1))
                else
                    let downY, upY = Array.splitAt ((pYSorted.Length + 1) / 2) pYSorted
                    let splitElement = Array.last downY
                    let downX, upX = Array.partition (fun (e: 'a) -> cmpY e splitElement <= 0) pXSorted // FIXME: Maybe this operation can be optimized.
                    Node (splitElement.Y, buildTreeFromSortedArray downX downY (depth + 1), buildTreeFromSortedArray upX upY (depth + 1))

        buildTreeFromSortedArray xSorted ySorted 1

    member this.Search (searchRegion: Region) : 'a list =
        let rec valuesFrom (tree: Tree<'a>) : 'a list =
            match tree with
            | Leaf v -> [v]
            | Node (_, part1, part2) -> (valuesFrom part1) @ (valuesFrom part2)

        let rec searchWithRegion (tree: Tree<'a>) (currentRegion: Region) (depth: int) : 'a list =
            match tree with
            | Leaf v -> if searchRegion.Contains v.X v.Y then [v] else []
            | Node (splitValue, part1, part2) ->
                let valuesInRegion (region: Region) (treeRegion: Tree<'a>) =
                    if region.IsSub searchRegion
                    then
                        valuesFrom treeRegion
                    elif region.Intersects searchRegion
                    then
                        searchWithRegion treeRegion region (depth + 1)
                    else
                        []

                if depth % 2 = 1 // Vertical splitting.
                then
                    let leftRegion = { currentRegion with maxX = splitValue }
                    let rightRegion = { currentRegion with minX = splitValue }
                    (valuesInRegion leftRegion part1) @ (valuesInRegion rightRegion part2)
                else // Horizontal splitting.
                    let downRegion = { currentRegion with maxY = splitValue }
                    let upRegion = { currentRegion with minY = splitValue }
                    (valuesInRegion downRegion part1) @ (valuesInRegion upRegion part2)

        searchWithRegion this { minX = Single.MinValue; maxX = Single.MaxValue; minY = Single.MinValue; maxY = Single.MaxValue } 1


///// Tests. TODO: to put in a unit test.

type Point (x: float32, y: float32) =
    interface I2DCoords with
        member this.X = x
        member this.Y = y

    override this.ToString () =
        sprintf "(%.1f, %.1f)" x y

// TODO: test with identical X or Y coords
let test () =
    let pts = [
        Point(1.0f, 1.0f)
        Point(2.0f, 2.0f)
        Point(1.5f, 3.6f)
        Point(3.0f, 3.2f)
        Point(4.0f, 4.0f)
        Point(3.5f, 1.5f)
        Point(2.5f, 0.5f) ]

    let tree = Tree.BuildTree pts
    Utils.dprintfn "Tree: %A" tree

    let s1 = tree.Search { minX = 0.0f; maxX = 5.0f; minY = 0.0f; maxY = 5.0f } // All points.
    Utils.dprintfn "s1: %A" s1

    let s2 = tree.Search { minX = 2.8f; maxX = 4.5f; minY = 3.0f; maxY = 4.5f }
    Utils.dprintfn "s2: %A" s2

    let s3 = tree.Search { minX = 2.0f; maxX = 2.0f; minY = 2.0f; maxY = 2.0f }
    Utils.dprintfn "s3: %A" s3

let test2 () =
    let pts = [
        Point(1.0f, 1.0f)
        Point(1.0f, 2.0f)
        Point(1.0f, 3.0f) ]

    let tree = Tree.BuildTree pts
    Utils.dprintfn "Tree: %A" tree

    let s1 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 1.0f; maxY = 1.0f }
    Utils.dprintfn "s1: %A" s1

    let s2 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 2.0f; maxY = 2.0f }
    Utils.dprintfn "s2: %A" s2

    // This case result is wrong: FIXME
    let s3 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 3.0f; maxY = 3.0f }
    Utils.dprintfn "s3: %A" s3

    let s4 = tree.Search { minX = 0.0f; maxX = 2.0f; minY = 0.0f; maxY = 4.0f }
    Utils.dprintfn "s4: %A" s4