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Add insert implementation with illustrations
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‎Algorithms/DataStructures/AVLTree.fs‎

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namespace Algorithms.DataStructures
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module AVLTree =
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type AVLNode = {
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Value: int
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Height: int
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LeftChild: Option<AVLNode>
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RightChild: Option<AVLNode>
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}
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module AVLNode =
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let create (value: int) : AVLNode =
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{
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Value = value
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Height = 0
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LeftChild = None
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RightChild = None
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}
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let height (maybeNode: Option<AVLNode>) : int =
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maybeNode
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|> Option.map (fun node -> node.Height)
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|> Option.defaultValue -1
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let balanceFactor (node: AVLNode) : int =
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height node.RightChild - height node.LeftChild
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type AVLNode
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with
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member this.UpdateLeftChild (leftChild: Option<AVLNode>) : AVLNode =
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{
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this with
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LeftChild = leftChild
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Height = 1 + max (AVLNode.height leftChild) (AVLNode.height this.RightChild)
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}
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member this.UpdateRightChild (rightChild: Option<AVLNode>) : AVLNode =
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{
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this with
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RightChild = rightChild
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Height = 1 + max (AVLNode.height this.LeftChild) (AVLNode.height rightChild)
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}
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module AVLTree =
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let rotateRight (node: AVLNode) : AVLNode =
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// Left child becomes the new root
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let leftChild = node.LeftChild |> Option.get
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let oldNode = node.UpdateLeftChild (leftChild.RightChild)
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leftChild.UpdateRightChild (Some oldNode)
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let rotateLeft (node: AVLNode) : AVLNode =
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// Right child becomes the new root
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let rightChild = node.RightChild |> Option.get
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let oldNode = node.UpdateRightChild (rightChild.LeftChild)
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rightChild.UpdateLeftChild (Some oldNode)
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type AVLTree = {
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Root: Option<AVLNode>
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}
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let insert (value: int) (tree: AVLTree) : AVLTree =
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let rec insertImpl (maybeNode: Option<AVLNode>) : AVLNode =
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match maybeNode with
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| None ->
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AVLNode.create value
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| Some node ->
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let node =
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if value < node.Value then
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node.UpdateLeftChild (Some (insertImpl node.LeftChild))
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elif value = node.Value then
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node
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else
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node.UpdateRightChild (Some (insertImpl node.RightChild))
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if AVLNode.balanceFactor node > 1 then
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// Root node is right heavy, current balance factor is 2
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// check the balance factor of the right child
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if node.RightChild |> Option.get |> AVLNode.balanceFactor < 0 then
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// Right child is left heavy
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// rotate right around right child and rotate left around root
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// Illustration: possible heights are shown in brackets,
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// and the balance factor of the node is shown in parentheses
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// Initial state:
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//
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// b (+2) [h+3]
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// / \
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// [h] a f (-1) [h+2]
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// /\
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// [h+1] (0|-1|+1) d g [h]
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// /\
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// [h|h-1] c e [h|h-1]
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// rotate right around f (right child)
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//
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// b (+2) [h+3]
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// / \
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// [h] a d (+1|+2) [h+2]
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// /\
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// [h|h-1] c f (0|-1) [h+1]
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// /\
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// [h|h-1] e g [h]
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// rotate left around b (root)
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// d (0) [h+2]
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// __________/\__________
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// / \
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// [h+1] (0|-1) b f (0|-1) [h+1]
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// / \ /\
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// [h] a c [h|h-1] [h|h-1] e g [h]
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let node =node.UpdateRightChild (Some (AVLTree.rotateRight (node.RightChild |> Option.get)))
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AVLTree.rotateLeft node
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else
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// Right child is balanced or left heavy,
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// rotate left around root
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// Illustration if right child is balanced
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// Initial state:
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// b (+2) [h+3]
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// / \
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// [h] a d (0) [h+2]
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// /\
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// [h+1] c e [h+1]
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// rotate left around b (root)
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// d (-1) [h+3]
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// / \
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// [h+2] (+1) b e [h+1]
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// / \
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// [h] a c [h+1]
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// Illustration if right child is right heavy
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// Initial state:
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// b (+2) [h+3]
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// / \
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// [h] a d (+1) [h+2]
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// /\
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// [h] c e [h+1]
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// rotate left around b (root)
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// d (0) [h+2]
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// / \
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// [h+1] (0) b e [h+1]
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// / \
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// [h] a c [h]
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AVLTree.rotateLeft node
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elif AVLNode.balanceFactor node < -1 then
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// Root node is left heavy, current balance factor is -2
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// check the balance factor of the left child
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if node.LeftChild |> Option.get |> AVLNode.balanceFactor > 0 then
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// Left child is right heavy
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// rotate left around left child and rotate right around root
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// Initial state:
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// f (-2) [h+3]
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// / \
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// [h+2] (+1) b g [h]
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// /\
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// [h] a d (0|-1|+1) [h+1]
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// /\
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// [h|h-1] c e [h|h-1]
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// rotate left around b (left child)
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// f (-2) [h+3]
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// / \
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// [h+2] (-2) d g [h]
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// / \
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// [h+1] b e [h|h-1]
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// /\
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// [h] a c [h|h-1]
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// rotate right around f (root)
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// d (0) [h+2]
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// __________/\__________
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// / \
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// [h+1] (0|-1) b f (0|-1) [h+1]
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// / \ /\
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// [h] a c [h|h-1] [h|h-1] e g [h]
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let node = node.UpdateLeftChild (Some (AVLTree.rotateLeft (node.LeftChild |> Option.get)))
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AVLTree.rotateRight node
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else
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// Left child is balanced or left heavy
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// rotate right around root
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// Illustration if left child is balanced
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// Initial state:
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// d (-2) [h+3]
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// / \
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// [h+2] (0) b e [h]
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// / \
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// [h+1] a c [h+1]
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// rotate right around d (root)
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// b (+1) [h+3]
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// / \
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// [h+1] a d (-1) [h+2]
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// / \
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// [h+1]c e [h]
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// Illustration if left child is left heavy
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// Initial state:
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// d (-2) [h+3]
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// / \
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// [h+2] (-1) b e [h]
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// / \
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// [h+1] a c [h]
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// rotate right around d (root)
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// b (0) [h+2]
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// / \
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// [h+1] a d (0) [h+1]
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// / \
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// [h] c e [h]
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AVLTree.rotateRight node
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else
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// Balance of root is within acceptable range
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node
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insertImpl tree.Root
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|> fun root -> { Root = Some root }
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