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Persistent Data Structures

, 24 Feb 2005 MIT
An article describing the basic principles of persistent data structures.
persistentdatastructures_src.zip
ImmutableCollections
ImmutableCollections
AVL Tree Classes
ImmutableCollections.csproj.user
RAL Helper Classes
/*
 * Created by: Leslie Sanford 
 * 
 * Last modified: 02/23/2005
 * 
 * Contact: jabberdabber@hotmail.com
 */

using System;
using System.Diagnostics;

namespace ImmutableCollections
{
	/// <summary>
	/// Represents a node in an AVL tree.
	/// </summary>
	internal class AvlNode : IAvlNode
	{
        #region AvlNode Members

        #region Class Fields

        // For use as a null node.
        public static readonly NullAvlNode NullNode = new NullAvlNode();

        #endregion

        #region Instance Fields

        // The data represented by this node.
        private readonly object data;

        // The number of nodes in the subtree.
        private readonly int count;

        // The height of this node.
        private readonly int height;

        // Left and right children.
        private readonly IAvlNode leftChild;
        private readonly IAvlNode rightChild;

        #endregion

        #region Construction

        /// <summary>
        /// Initializes a new instance of the AvlNode class with the specified 
        /// data and left and right children.
        /// </summary>
        /// <param name="data">
        /// The data for the node.
        /// </param>
        /// <param name="leftChild">
        /// The left child.
        /// </param>
        /// <param name="rightChild">
        /// The right child.
        /// </param>
		public AvlNode(object data, IAvlNode leftChild, IAvlNode rightChild)
		{
            // Preconditions.
            Debug.Assert(leftChild != null && rightChild != null);

            this.data = data;
            this.leftChild = leftChild;
            this.rightChild = rightChild;

            count = 1 + leftChild.Count + rightChild.Count;
            height = 1 + Math.Max(leftChild.Height, rightChild.Height);
		}

        #endregion

        #region Methods
        
        #region Rotation Methods

        // Left - left single rotation.
        private IAvlNode DoLLRotation(IAvlNode node)
        {
            /*
             *  An LL rotation looks like the following:  
             * 
             *             A          B    
             *            /          / \
             *           B    --->  C   A
             *          /
             *         C 
             */

            // Create right child of the new root.
            IAvlNode a = new AvlNode(
                node.Data, 
                node.LeftChild.RightChild, 
                node.RightChild);

            IAvlNode b = new AvlNode(
                node.LeftChild.Data, 
                node.LeftChild.LeftChild, 
                a);

            // Postconditions.
            Debug.Assert(b.Data == node.LeftChild.Data);
            Debug.Assert(b.LeftChild == node.LeftChild.LeftChild);
            Debug.Assert(b.RightChild.Data == node.Data);

            return b;
        }

        // Left - right double rotation.
        private IAvlNode DoLRRotation(IAvlNode node)
        {
            /*
             *  An LR rotation looks like the following: 
             * 
             *       Perform an RR rotation at B:
             *   
             *           A              A
             *          /              /
             *         B      --->    C
             *          \            / 
             *           C          B
             * 
             *       Perform an LL rotation at A:
             *     
             *             A          C    
             *            /          / \
             *           C    --->  B   A
             *          /
             *         B 
             */

            IAvlNode a = new AvlNode(
                node.Data, 
                DoRRRotation(node.LeftChild), 
                node.RightChild);

            IAvlNode c = DoLLRotation(a);

            // Postconditions.
            Debug.Assert(c.Data == node.LeftChild.RightChild.Data);
            Debug.Assert(c.LeftChild.Data == node.LeftChild.Data);
            Debug.Assert(c.RightChild.Data == node.Data);

            return c;
        }

        // Right - right single rotation.
        private IAvlNode DoRRRotation(IAvlNode node)
        { 
            /*
             *  An RR rotation looks like the following:  
             * 
             *        A              B    
             *         \            / \
             *          B    --->  A   C
             *           \
             *            C 
             */

            // Create left child of the new root.
            IAvlNode a = new AvlNode(
                node.Data, 
                node.LeftChild, 
                node.RightChild.LeftChild);

            IAvlNode b = new AvlNode(
                node.RightChild.Data, 
                a, 
                node.RightChild.RightChild);

            // Postconditions.
            Debug.Assert(b.Data == node.RightChild.Data);
            Debug.Assert(b.RightChild == node.RightChild.RightChild);
            Debug.Assert(b.LeftChild.Data == node.Data);

            return b;
        }

        // Right - left double rotation.
        private IAvlNode DoRLRotation(IAvlNode node)
        {
            /*
             *  An RL rotation looks like the following: 
             * 
             *       Perform an LL rotation at B:
             *   
             *         A            A
             *          \            \ 
             *           B    --->    C
             *          /              \ 
             *         C                B
             * 
             *       Perform an RR rotation at A:
             *     
             *         A              C    
             *          \            / \
             *           C    --->  A   B
             *            \
             *             B 
             */

            IAvlNode a = new AvlNode(
                node.Data, 
                node.LeftChild,
                DoLLRotation(node.RightChild));

            IAvlNode c = DoRRRotation(a);

            // Postconditions.
            Debug.Assert(c.Data == node.RightChild.LeftChild.Data);
            Debug.Assert(c.LeftChild.Data == node.Data);
            Debug.Assert(c.RightChild.Data == node.RightChild.Data);                

            return c;
        }

        #endregion

        #endregion

        #endregion

        #region IAvlNode Members

        /// <summary>
        /// Removes the current node from the AVL tree.
        /// </summary>
        /// <returns>
        /// The node to in the tree to replace the current node.
        /// </returns>
        public IAvlNode Remove()
        {
            IAvlNode result; 

            /*
             * Deal with the three cases for removing a node from a binary tree.
             */

            // If the node has no right children.
            if(this.RightChild == AvlNode.NullNode)
            {  
                // The replacement node is the node's left child.
                result = this.LeftChild;
            }
                // Else if the node's right child has no left children.
            else if(this.RightChild.LeftChild == AvlNode.NullNode)
            {
                // The replacement node is the node's right child.
                result = new AvlNode(
                    this.RightChild.Data,
                    this.LeftChild,
                    this.RightChild.RightChild);
            }
                // Else the node's right child has left children.
            else
            {
                /*
                 * Go to the node's right child and descend as far left as 
                 * possible. The node found at this point will replace the 
                 * node to be removed.
                 */

                IAvlNode replacement = AvlNode.NullNode;
                IAvlNode rightChild = RemoveReplacement(this.RightChild, ref replacement);

                // Create new node with the replacement node and the new
                // right child.
                result = new AvlNode(
                    replacement.Data,
                    this.LeftChild,
                    rightChild);
            }

            return result;
        }

        // Finds and removes replacement node for deletion (third case).
        private IAvlNode RemoveReplacement(IAvlNode node, ref IAvlNode replacement)
        {
            IAvlNode newNode;

            // If the bottom of the left tree has been found.
            if(node.LeftChild == AvlNode.NullNode)
            {
                // The replacement node is the node found at this point.
                replacement = node;

                // Get the node's right child. This will be needed as we 
                // ascend back up the tree.
                newNode = node.RightChild;
            }
                // Else the bottom of the left tree has not been found.
            else
            {
                // Create new node and continue descending down the left tree.
                newNode = new AvlNode(node.Data,
                    RemoveReplacement(node.LeftChild, ref replacement),
                    node.RightChild);

                // If the node is out of balance.
                if(!newNode.IsBalanced())
                {
                    // Rebalance the node.
                    newNode = newNode.Balance();
                }
            }

            // Postconditions.
            Debug.Assert(newNode.IsBalanced());

            return newNode;
        }

        /// <summary>
        /// Balances the subtree represented by the node.
        /// </summary>
        /// <returns>
        /// The root node of the balanced subtree.
        /// </returns>
        public IAvlNode Balance()
        {
            IAvlNode result;

            if(BalanceFactor < -1)
            {
                if(leftChild.BalanceFactor < 0)
                {
                    result = DoLLRotation(this);
                }
                else
                {
                    result = DoLRRotation(this);
                }
            }
            else if(BalanceFactor > 1)
            {
                if(rightChild.BalanceFactor > 0)
                {
                    result = DoRRRotation(this);
                }
                else
                {
                    result = DoRLRotation(this);
                }
            } 
            else
            {
                result = this;
            }

            Debug.Assert(result.IsBalanced());

            return result;
        }

        /// <summary>
        /// Indicates whether or not the subtree the node represents is in 
        /// balance.
        /// </summary>
        /// <returns>
        /// <b>true</b> if the subtree is in balance; otherwise, <b>false</b>.
        /// </returns>
        public bool IsBalanced()
        {
            return BalanceFactor >= -1 && BalanceFactor <= 1;
        }

        /// <summary>
        /// Gets the balance factor of the subtree the node represents.
        /// </summary>
        public int BalanceFactor
        {
            get
            {
                return rightChild.Height - leftChild.Height;
            }
        }

        /// <summary>
        /// Gets the number of nodes in the subtree.
        /// </summary>
        public int Count
        {
            get
            {
                return count;
            }
        }

        /// <summary>
        /// Gets the node's data.
        /// </summary>
        public object Data
        {
            get
            {
                return data;
            }
        }

        /// <summary>
        /// Gets the height of the subtree the node represents.
        /// </summary>
        public int Height
        {
            get
            {
                return height;
            }
        }

        /// <summary>
        /// Gets the node's left child.
        /// </summary>
        public IAvlNode LeftChild
        {
            get
            {
                return leftChild;
            }
        }

        /// <summary>
        /// Gets the node's right child.
        /// </summary>
        public IAvlNode RightChild
        {
            get
            {
                return rightChild;
            }
        }

        #endregion
    }
}

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About the Author

Leslie Sanford

United States United States
Aside from dabbling in BASIC on his old Atari 1040ST years ago, Leslie's programming experience didn't really begin until he discovered the Internet in the late 90s. There he found a treasure trove of information about two of his favorite interests: MIDI and sound synthesis.

After spending a good deal of time calculating formulas he found on the Internet for creating new sounds by hand, he decided that an easier way would be to program the computer to do the work for him. This led him to learn C. He discovered that beyond using programming as a tool for synthesizing sound, he loved programming in and of itself.

Eventually he taught himself C++ and C#, and along the way he immersed himself in the ideas of object oriented programming. Like many of us, he gotten bitten by the design patterns bug and a copy of GOF is never far from his hands.

Now his primary interest is in creating a complete MIDI toolkit using the C# language. He hopes to create something that will become an indispensable tool for those wanting to write MIDI applications for the .NET framework.

Besides programming, his other interests are photography and playing his Les Paul guitars.

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