namespace Sanchime.DataStructures.Trees

module RedBlack =

    type Color = Red | Black

    type RedBlackTree<'T> =
        | Node of Color * Left: 'T RedBlackTree * Value: 'T * Right: 'T RedBlackTree
        | Leaf

    let balance = function
        | Black, Node (Red, Node (Red, a, x, b), y, c), z, d
        | Black, Node (Red, a, x, Node (Red, b, y, c)), z, d
        | Black, a, x, Node (Red, Node (Red, b, y, c), z, d)
        | Black, a, x, Node (Red, b, y, Node (Red, c, z, d)) ->
            Node (Red, Node (Black, a, x, b), y, Node (Black, c, z, d))
        | a, b, c, d -> Node (a, b, c, d)

    let insert x s =
        let rec loop = function
            | Leaf -> Node (Red, Leaf, x, Leaf)
            | Node (color, a, y, b) as s ->
                if x < y then balance (color, loop a, y, b)
                elif y < x then balance (color, a, y, loop b)
                else s

        loop s