RedBlackTree.cs

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Reflection;

namespace Advanced.Algorithms.DataStructures;

/// <summary>
///     A red black tree implementation.
/// </summary>
public class RedBlackTree<T> : IEnumerable<T> where T : IComparable
{
    //if enabled, lookup will fasten deletion/insertion/exists operations. 
    internal readonly Dictionary<T, BstNodeBase<T>> NodeLookUp;

    /// <param name="enableNodeLookUp">
    ///     Enabling lookup will fasten deletion/insertion/exists operations
    ///     at the cost of additional space.
    /// </param>
    /// <param name="equalityComparer">
    ///     Provide equality comparer for node lookup if enabled (required when T is not a value
    ///     type).
    /// </param>
    public RedBlackTree(bool enableNodeLookUp = false, IEqualityComparer<T> equalityComparer = null)
    {
        if (enableNodeLookUp)
        {
            if (!typeof(T).GetTypeInfo().IsValueType && equalityComparer == null)
                throw new ArgumentException(
                    "equalityComparer parameter is required when node lookup us enabled and T is not a value type.");

            NodeLookUp = new Dictionary<T, BstNodeBase<T>>(equalityComparer ?? EqualityComparer<T>.Default);
        }
    }

    /// <summary>
    ///     Initialize the BST with given sorted keys optionally.
    ///     Time complexity: O(n).
    /// </summary>
    /// <param name="sortedCollection">The sorted initial collection.</param>
    /// <param name="enableNodeLookUp">
    ///     Enabling lookup will fasten deletion/insertion/exists operations
    ///     at the cost of additional space.
    /// </param>
    /// <param name="equalityComparer">
    ///     Provide equality comparer for node lookup if enabled (required when T is not a value
    ///     type).
    /// </param>
    public RedBlackTree(IEnumerable<T> sortedCollection, bool enableNodeLookUp = false,
        IEqualityComparer<T> equalityComparer = null)
    {
        BstHelpers.ValidateSortedCollection(sortedCollection);
        var nodes = sortedCollection.Select(x => new RedBlackTreeNode<T>(null, x)).ToArray();
        Root = (RedBlackTreeNode<T>)BstHelpers.ToBst(nodes);
        AssignColors(Root);
        BstHelpers.AssignCount(Root);

        if (enableNodeLookUp)
        {
            if (!typeof(T).GetTypeInfo().IsValueType && equalityComparer == null)
                throw new ArgumentException(
                    "equalityComparer parameter is required when node lookup us enabled and T is not a value type.");

            NodeLookUp = nodes.ToDictionary(x => x.Value, x => x as BstNodeBase<T>,
                equalityComparer ?? EqualityComparer<T>.Default);
        }
    }

    internal RedBlackTreeNode<T> Root { get; set; }

    public int Count => Root == null ? 0 : Root.Count;

    IEnumerator IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }

    public IEnumerator<T> GetEnumerator()
    {
        return new BstEnumerator<T>(Root);
    }

    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    public bool HasItem(T value)
    {
        if (Root == null) return false;

        if (NodeLookUp != null) return NodeLookUp.ContainsKey(value);

        return Find(value).Item1 != null;
    }

    /// <summary>
    ///     Time complexity: O(1)
    /// </summary>
    internal void Clear()
    {
        Root = null;
    }

    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    public T Max()
    {
        var max = Root.FindMax();
        return max == null ? default : max.Value;
    }

    private static RedBlackTreeNode<T> FindMax(RedBlackTreeNode<T> node)
    {
        return node.FindMax() as RedBlackTreeNode<T>;
    }

    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    public T Min()
    {
        var min = Root.FindMin();
        return min == null ? default : min.Value;
    }

    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    public int IndexOf(T item)
    {
        return Root.Position(item);
    }

    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    public T ElementAt(int index)
    {
        if (index < 0 || index >= Count) throw new ArgumentNullException("index");

        return Root.KthSmallest(index).Value;
    }

    internal RedBlackTreeNode<T> FindNode(T value)
    {
        return Root == null ? null : Find(value).Item1;
    }

    internal bool Exists(T value)
    {
        return FindNode(value) != null;
    }

    //find the node with the given identifier among descendants of parent and parent
    //uses pre-order traversal
    internal (RedBlackTreeNode<T>, int) Find(T value)
    {
        if (NodeLookUp != null)
        {
            if (NodeLookUp.ContainsKey(value))
            {
                var node = NodeLookUp[value] as RedBlackTreeNode<T>;
                return (node, Root.Position(value));
            }

            return (null, -1);
        }

        var result = Root.Find(value);
        return (result.Item1 as RedBlackTreeNode<T>, result.Item2);
    }

    /// <summary>
    ///     Time complexity: O(log(n)).
    ///     Returns the position (index) of the value in sorted order of this BST.
    /// </summary>
    public int Insert(T value)
    {
        var node = InsertAndReturnNode(value);
        return node.Item2;
    }

    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    internal (RedBlackTreeNode<T>, int) InsertAndReturnNode(T value)
    {
        //empty tree
        if (Root == null)
        {
            Root = new RedBlackTreeNode<T>(null, value) { NodeColor = RedBlackTreeNodeColor.Black };
            if (NodeLookUp != null) NodeLookUp[value] = Root;

            return (Root, 0);
        }

        var newNode = Insert(Root, value);

        if (NodeLookUp != null) NodeLookUp[value] = newNode.Item1;

        return newNode;
    }

    //O(log(n)) always
    private (RedBlackTreeNode<T>, int) Insert(RedBlackTreeNode<T> currentNode, T newNodeValue)
    {
        var insertionPosition = 0;

        while (true)
        {
            var compareResult = currentNode.Value.CompareTo(newNodeValue);

            //current node is less than new item
            if (compareResult < 0)
            {
                insertionPosition += (currentNode.Left != null ? currentNode.Left.Count : 0) + 1;

                //no right child
                if (currentNode.Right == null)
                {
                    //insert
                    var node = currentNode.Right = new RedBlackTreeNode<T>(currentNode, newNodeValue);
                    BalanceInsertion(currentNode.Right);
                    return (node, insertionPosition);
                }

                currentNode = currentNode.Right;
            }
            //current node is greater than new node
            else if (compareResult > 0)
            {
                if (currentNode.Left == null)
                {
                    //insert
                    var node = currentNode.Left = new RedBlackTreeNode<T>(currentNode, newNodeValue);
                    BalanceInsertion(currentNode.Left);
                    return (node, insertionPosition);
                }

                currentNode = currentNode.Left;
            }
            else
            {
                //duplicate
                throw new ArgumentException("Item with same key exists");
            }
        }
    }

    private void BalanceInsertion(RedBlackTreeNode<T> nodeToBalance)
    {
        while (true)
        {
            if (nodeToBalance == Root)
            {
                nodeToBalance.NodeColor = RedBlackTreeNodeColor.Black;
                break;
            }

            //if node to balance is red
            if (nodeToBalance.NodeColor == RedBlackTreeNodeColor.Red
                && nodeToBalance.Parent.NodeColor == RedBlackTreeNodeColor.Red)
            {
                //red sibling
                if (nodeToBalance.Parent.Sibling != null &&
                    nodeToBalance.Parent.Sibling.NodeColor == RedBlackTreeNodeColor.Red)
                {
                    //mark both children of parent as black and move up balancing 
                    nodeToBalance.Parent.Sibling.NodeColor = RedBlackTreeNodeColor.Black;
                    nodeToBalance.Parent.NodeColor = RedBlackTreeNodeColor.Black;

                    //root is always black
                    if (nodeToBalance.Parent.Parent != Root)
                        nodeToBalance.Parent.Parent.NodeColor = RedBlackTreeNodeColor.Red;

                    nodeToBalance.UpdateCounts();
                    nodeToBalance.Parent.UpdateCounts();
                    nodeToBalance = nodeToBalance.Parent.Parent;
                }
                //absent sibling or black sibling
                else if (nodeToBalance.Parent.Sibling == null ||
                         nodeToBalance.Parent.Sibling.NodeColor == RedBlackTreeNodeColor.Black)
                {
                    if (nodeToBalance.IsLeftChild && nodeToBalance.Parent.IsLeftChild)
                    {
                        var newRoot = nodeToBalance.Parent;
                        SwapColors(nodeToBalance.Parent, nodeToBalance.Parent.Parent);
                        RightRotate(nodeToBalance.Parent.Parent);

                        if (newRoot == Root) Root.NodeColor = RedBlackTreeNodeColor.Black;

                        nodeToBalance.UpdateCounts();
                        nodeToBalance = newRoot;
                    }
                    else if (nodeToBalance.IsLeftChild && nodeToBalance.Parent.IsRightChild)
                    {
                        RightRotate(nodeToBalance.Parent);

                        var newRoot = nodeToBalance;

                        SwapColors(nodeToBalance.Parent, nodeToBalance);
                        LeftRotate(nodeToBalance.Parent);

                        if (newRoot == Root) Root.NodeColor = RedBlackTreeNodeColor.Black;

                        nodeToBalance.UpdateCounts();
                        nodeToBalance = newRoot;
                    }
                    else if (nodeToBalance.IsRightChild && nodeToBalance.Parent.IsRightChild)
                    {
                        var newRoot = nodeToBalance.Parent;
                        SwapColors(nodeToBalance.Parent, nodeToBalance.Parent.Parent);
                        LeftRotate(nodeToBalance.Parent.Parent);

                        if (newRoot == Root) Root.NodeColor = RedBlackTreeNodeColor.Black;

                        nodeToBalance.UpdateCounts();
                        nodeToBalance = newRoot;
                    }
                    else if (nodeToBalance.IsRightChild && nodeToBalance.Parent.IsLeftChild)
                    {
                        LeftRotate(nodeToBalance.Parent);

                        var newRoot = nodeToBalance;

                        SwapColors(nodeToBalance.Parent, nodeToBalance);
                        RightRotate(nodeToBalance.Parent);

                        if (newRoot == Root) Root.NodeColor = RedBlackTreeNodeColor.Black;

                        nodeToBalance.UpdateCounts();
                        nodeToBalance = newRoot;
                    }
                }
            }

            if (nodeToBalance.Parent != null)
            {
                nodeToBalance.UpdateCounts();
                nodeToBalance = nodeToBalance.Parent;
                continue;
            }

            break;
        }

        nodeToBalance.UpdateCounts(true);
    }

    private static void SwapColors(RedBlackTreeNode<T> node1, RedBlackTreeNode<T> node2)
    {
        var tmpColor = node2.NodeColor;
        node2.NodeColor = node1.NodeColor;
        node1.NodeColor = tmpColor;
    }

    /// <summary>
    ///     Delete if value exists.
    ///     Time complexity: O(log(n))
    ///     Returns the position (index) of the item if deleted; otherwise returns -1
    /// </summary>
    public int Delete(T value)
    {
        if (Root == null) return -1;

        var node = Find(value);

        if (node.Item1 == null) return -1;

        var position = node.Item2;

        Delete(node.Item1);

        if (NodeLookUp != null) NodeLookUp.Remove(value);

        return position;
    }


    /// <summary>
    ///     Time complexity: O(log(n))
    /// </summary>
    public T RemoveAt(int index)
    {
        if (index < 0 || index >= Count) throw new ArgumentException("index");

        var node = Root.KthSmallest(index) as RedBlackTreeNode<T>;

        var deletedValue = node.Value;

        Delete(node);

        if (NodeLookUp != null) NodeLookUp.Remove(deletedValue);

        return node.Value;
    }

    //O(log(n)) always
    private void Delete(RedBlackTreeNode<T> node)
    {
        //node is a leaf node
        if (node.IsLeaf)
        {
            //if color is red, we are good; no need to balance
            if (node.NodeColor == RedBlackTreeNodeColor.Red)
            {
                DeleteLeaf(node);
                node.Parent?.UpdateCounts(true);
                return;
            }

            DeleteLeaf(node);
            BalanceNode(node.Parent);
        }
        else
        {
            //case one - right tree is null (move sub tree up)
            if (node.Left != null && node.Right == null)
            {
                DeleteLeftNode(node);
                BalanceNode(node.Left);
            }
            //case two - left tree is null  (move sub tree up)
            else if (node.Right != null && node.Left == null)
            {
                DeleteRightNode(node);
                BalanceNode(node.Right);
            }
            //case three - two child trees 
            //replace the node value with maximum element of left subtree (left max node)
            //and then delete the left max node
            else
            {
                var maxLeftNode = FindMax(node.Left);

                if (NodeLookUp != null)
                {
                    NodeLookUp[node.Value] = maxLeftNode;
                    NodeLookUp[maxLeftNode.Value] = node;
                }

                node.Value = maxLeftNode.Value;

                //delete left max node
                Delete(maxLeftNode);
            }
        }
    }

    private void BalanceNode(RedBlackTreeNode<T> nodeToBalance)
    {
        //handle six cases
        while (nodeToBalance != null)
        {
            nodeToBalance.UpdateCounts();
            nodeToBalance = HandleDoubleBlack(nodeToBalance);
        }
    }

    private void DeleteLeaf(RedBlackTreeNode<T> node)
    {
        //if node is root
        if (node.Parent == null)
            Root = null;
        //assign nodes parent.left/right to null
        else if (node.IsLeftChild)
            node.Parent.Left = null;
        else
            node.Parent.Right = null;
    }

    private void DeleteRightNode(RedBlackTreeNode<T> node)
    {
        //root
        if (node.Parent == null)
        {
            Root.Right.Parent = null;
            Root = Root.Right;
            Root.NodeColor = RedBlackTreeNodeColor.Black;
            return;
        }

        //node is left child of parent
        if (node.IsLeftChild)
            node.Parent.Left = node.Right;
        //node is right child of parent
        else
            node.Parent.Right = node.Right;

        node.Right.Parent = node.Parent;

        if (node.Right.NodeColor != RedBlackTreeNodeColor.Red) return;

        //black deletion! But we can take its red child and recolor it to black
        //and we are done!
        node.Right.NodeColor = RedBlackTreeNodeColor.Black;
    }

    private void DeleteLeftNode(RedBlackTreeNode<T> node)
    {
        //root
        if (node.Parent == null)
        {
            Root.Left.Parent = null;
            Root = Root.Left;
            Root.NodeColor = RedBlackTreeNodeColor.Black;
            return;
        }

        //node is left child of parent
        if (node.IsLeftChild)
            node.Parent.Left = node.Left;
        //node is right child of parent
        else
            node.Parent.Right = node.Left;

        node.Left.Parent = node.Parent;

        if (node.Left.NodeColor != RedBlackTreeNodeColor.Red) return;

        //black deletion! But we can take its red child and recolor it to black
        //and we are done!
        node.Left.NodeColor = RedBlackTreeNodeColor.Black;
    }

    private void RightRotate(RedBlackTreeNode<T> node)
    {
        var prevRoot = node;
        var leftRightChild = prevRoot.Left.Right;

        var newRoot = node.Left;

        //make left child as root
        prevRoot.Left.Parent = prevRoot.Parent;

        if (prevRoot.Parent != null)
        {
            if (prevRoot.Parent.Left == prevRoot)
                prevRoot.Parent.Left = prevRoot.Left;
            else
                prevRoot.Parent.Right = prevRoot.Left;
        }

        //move prev root as right child of current root
        newRoot.Right = prevRoot;
        prevRoot.Parent = newRoot;

        //move right child of left child of prev root to left child of right child of new root
        newRoot.Right.Left = leftRightChild;
        if (newRoot.Right.Left != null) newRoot.Right.Left.Parent = newRoot.Right;

        if (prevRoot == Root) Root = newRoot;

        newRoot.Left.UpdateCounts();
        newRoot.Right.UpdateCounts();
        newRoot.UpdateCounts();
    }

    private void LeftRotate(RedBlackTreeNode<T> node)
    {
        var prevRoot = node;
        var rightLeftChild = prevRoot.Right.Left;

        var newRoot = node.Right;

        //make right child as root
        prevRoot.Right.Parent = prevRoot.Parent;

        if (prevRoot.Parent != null)
        {
            if (prevRoot.Parent.Left == prevRoot)
                prevRoot.Parent.Left = prevRoot.Right;
            else
                prevRoot.Parent.Right = prevRoot.Right;
        }

        //move prev root as left child of current root
        newRoot.Left = prevRoot;
        prevRoot.Parent = newRoot;

        //move left child of right child of prev root to right child of left child of new root
        newRoot.Left.Right = rightLeftChild;
        if (newRoot.Left.Right != null) newRoot.Left.Right.Parent = newRoot.Left;

        if (prevRoot == Root) Root = newRoot;

        newRoot.Left.UpdateCounts();
        newRoot.Right.UpdateCounts();
        newRoot.UpdateCounts();
    }

    private RedBlackTreeNode<T> HandleDoubleBlack(RedBlackTreeNode<T> node)
    {
        //case 1
        if (node == Root)
        {
            node.NodeColor = RedBlackTreeNodeColor.Black;
            return null;
        }

        //case 2
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling != null
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Red
            && (node.Sibling.Left == null && node.Sibling.Right == null
                || node.Sibling.Left != null && node.Sibling.Right != null
                                             && node.Sibling.Left.NodeColor == RedBlackTreeNodeColor.Black
                                             && node.Sibling.Right.NodeColor == RedBlackTreeNodeColor.Black))
        {
            node.Parent.NodeColor = RedBlackTreeNodeColor.Red;
            node.Sibling.NodeColor = RedBlackTreeNodeColor.Black;

            if (node.Sibling.IsRightChild)
                LeftRotate(node.Parent);
            else
                RightRotate(node.Parent);

            return node;
        }

        //case 3
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling != null
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Black
            && (node.Sibling.Left == null && node.Sibling.Right == null
                || node.Sibling.Left != null && node.Sibling.Right != null
                                             && node.Sibling.Left.NodeColor == RedBlackTreeNodeColor.Black
                                             && node.Sibling.Right.NodeColor == RedBlackTreeNodeColor.Black))
        {
            //pushed up the double black problem up to parent
            //so now it needs to be fixed
            node.Sibling.NodeColor = RedBlackTreeNodeColor.Red;

            return node.Parent;
        }


        //case 4
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Red
            && node.Sibling != null
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Black
            && (node.Sibling.Left == null && node.Sibling.Right == null
                || node.Sibling.Left != null && node.Sibling.Right != null
                                             && node.Sibling.Left.NodeColor == RedBlackTreeNodeColor.Black
                                             && node.Sibling.Right.NodeColor == RedBlackTreeNodeColor.Black))
        {
            //just swap the color of parent and sibling
            //which will compensate the loss of black count 
            node.Parent.NodeColor = RedBlackTreeNodeColor.Black;
            node.Sibling.NodeColor = RedBlackTreeNodeColor.Red;
            node.UpdateCounts(true);
            return null;
        }


        //case 5
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling != null
            && node.Sibling.IsRightChild
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling.Left != null
            && node.Sibling.Left.NodeColor == RedBlackTreeNodeColor.Red
            && node.Sibling.Right != null
            && node.Sibling.Right.NodeColor == RedBlackTreeNodeColor.Black)
        {
            node.Sibling.NodeColor = RedBlackTreeNodeColor.Red;
            node.Sibling.Left.NodeColor = RedBlackTreeNodeColor.Black;
            RightRotate(node.Sibling);

            return node;
        }

        //case 5 mirror
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling != null
            && node.Sibling.IsLeftChild
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling.Left != null
            && node.Sibling.Left.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling.Right != null
            && node.Sibling.Right.NodeColor == RedBlackTreeNodeColor.Red)
        {
            node.Sibling.NodeColor = RedBlackTreeNodeColor.Red;
            node.Sibling.Right.NodeColor = RedBlackTreeNodeColor.Black;
            LeftRotate(node.Sibling);

            return node;
        }

        //case 6
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling != null
            && node.Sibling.IsRightChild
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling.Right != null
            && node.Sibling.Right.NodeColor == RedBlackTreeNodeColor.Red)
        {
            //left rotate to increase the black count on left side by one
            //and mark the red right child of sibling to black 
            //to compensate the loss of Black on right side of parent
            node.Sibling.Right.NodeColor = RedBlackTreeNodeColor.Black;
            LeftRotate(node.Parent);
            node.UpdateCounts(true);
            return null;
        }

        //case 6 mirror
        if (node.Parent != null
            && node.Parent.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling != null
            && node.Sibling.IsLeftChild
            && node.Sibling.NodeColor == RedBlackTreeNodeColor.Black
            && node.Sibling.Left != null
            && node.Sibling.Left.NodeColor == RedBlackTreeNodeColor.Red)
        {
            //right rotate to increase the black count on right side by one
            //and mark the red left child of sibling to black
            //to compensate the loss of Black on right side of parent
            node.Sibling.Left.NodeColor = RedBlackTreeNodeColor.Black;
            RightRotate(node.Parent);
            node.UpdateCounts(true);
            return null;
        }

        node.UpdateCounts(true);
        return null;
    }

    //assign valid colors assuming the given tree node and its children are in balanced state.
    private void AssignColors(RedBlackTreeNode<T> current)
    {
        if (current == null) return;

        AssignColors(current.Left);
        AssignColors(current.Right);

        if (current.IsLeaf)
            current.NodeColor = RedBlackTreeNodeColor.Red;
        else
            current.NodeColor = RedBlackTreeNodeColor.Black;
    }

    /// <summary>
    ///     Get the next lower value to given value in this BST.
    /// </summary>
    public T NextLower(T value)
    {
        var node = FindNode(value);
        if (node == null) return default;

        var next = node.NextLower();
        return next != null ? next.Value : default;
    }

    /// <summary>
    ///     Get the next higher to given value in this BST.
    /// </summary>
    public T NextHigher(T value)
    {
        var node = FindNode(value);
        if (node == null) return default;

        var next = node.NextHigher();
        return next != null ? next.Value : default;
    }

    /// <summary>
    ///     Descending enumerable.
    /// </summary>
    public IEnumerable<T> AsEnumerableDesc()
    {
        return GetEnumeratorDesc().AsEnumerable();
    }

    public IEnumerator<T> GetEnumeratorDesc()
    {
        return new BstEnumerator<T>(Root, false);
    }
}

internal enum RedBlackTreeNodeColor
{
    Black,
    Red
}

/// <summary>
///     Red black tree node
/// </summary>
internal class RedBlackTreeNode<T> : BstNodeBase<T> where T : IComparable
{
    internal RedBlackTreeNode(RedBlackTreeNode<T> parent, T value)
    {
        Parent = parent;
        Value = value;
        NodeColor = RedBlackTreeNodeColor.Red;
    }

    internal new RedBlackTreeNode<T> Parent
    {
        get => (RedBlackTreeNode<T>)base.Parent;
        set => base.Parent = value;
    }

    internal new RedBlackTreeNode<T> Left
    {
        get => (RedBlackTreeNode<T>)base.Left;
        set => base.Left = value;
    }

    internal new RedBlackTreeNode<T> Right
    {
        get => (RedBlackTreeNode<T>)base.Right;
        set => base.Right = value;
    }

    internal RedBlackTreeNodeColor NodeColor { get; set; }

    internal RedBlackTreeNode<T> Sibling => Parent.Left == this ? Parent.Right : Parent.Left;
}