Trying to understand binary trees, I'm getting there but there is still some more to do.

noworky.cs

public class BSPTreeNode<T>
{
	public T Data { get; set; }

	public BSPTreeNode<T> Parent { get; set; }
	public BSPTreeNode<T> Left { get; set; }
	public BSPTreeNode<T> Right { get; set; }
}

public class BSPTree<T>
{
	private IComparer<T> comparer;
	private BSPTreeNode<T> root;

	public BSPTree()
	{
		comparer = Comparer<T>.Default;
	}

	public BSPTree(IComparer<T> comparer)
	{
		this.comparer = comparer;
	}

	public void Add(T data)
	{
		BSPTreeNode<T> node = new BSPTreeNode<T>()
		{
			Data = data
		};

		if (root == null)
			root = node;
		else
			Add(root, node);
	}

	private void Add(BSPTreeNode<T> root, BSPTreeNode<T> node)
	{
		node.Parent = root;

		if (comparer.Compare(node.Data, root.Data) <= 0)
		{
			if (root.Left == null)
				root.Left = node;
			else
				Add(root.Left, node);
		}
		else
		{
			if (root.Right == null)
				root.Right = node;
			else
				Add(root.Right, node);
		}
	}

	public void Iterate(Action<BSPTreeNode<T>> action)
	{
		Iterate(root, action);
	}

	private void Iterate(BSPTreeNode<T> parent, Action<BSPTreeNode<T>> action)
	{
		action(parent);

		if (parent.Left != null)
			Iterate(parent.Left, action);

		if (parent.Right != null)
			Iterate(parent.Right, action);
	}
}

class Program
{
	static void Main(string[] args)
	{
		BSPTree<string> bstree = new BSPTree<string>();

		bstree.Add("Hello");
		bstree.Add("World");
		bstree.Add("12345");
		bstree.Add("67890");
		bstree.Add("abcdef");
		bstree.Iterate(node => Console.WriteLine("Data: {0} | Parent: {1}", node.Data, (node.Parent != null) ? node.Parent.Data : "null"));
	}
}