How to implement the red-black tree algorithm in C#

How to implement the red-black tree algorithm in C# requires specific code examples

Introduction:
The red-black tree is a self-balancing binary search tree . It maintains the specific property such that for any valid red-black tree, the longest path is never more than twice the shortest path. This characteristic makes red-black trees have better performance in insertion, deletion and search operations. This article will introduce how to implement the red-black tree algorithm in C# and provide specific code examples.

Properties of red-black trees:
Red-black trees have the following 5 properties:

1. Each node is either red or black.
2. The root node is black.
3. Each leaf node (NIL node, empty node) is black.
4. If a node is red, both of its child nodes are black.
5. For each node, the simple path from that node to all its descendant leaf nodes contains the same number of black nodes.

Implementation of red-black tree:
The following is a sample code to implement red-black tree in C#:

enum Color
{
    Red,
    Black
}

class Node
{
    public int key;
    public Node parent;
    public Node left;
    public Node right;
    public Color color;

    public Node(int key)
    {
        this.key = key;
        color = Color.Black;
    }
}

class RedBlackTree
{
    private Node root;

    private void Insert(Node newNode)
    {
        Node current = root;
        Node parent = null;

        while (current != null)
        {
            parent = current;

            if (newNode.key < current.key)
                current = current.left;
            else
                current = current.right;
        }

        newNode.parent = parent;

        if (parent == null)
            root = newNode;
        else if (newNode.key < parent.key)
            parent.left = newNode;
        else
            parent.right = newNode;

        newNode.color = Color.Red;

        FixAfterInsertion(newNode);
    }

    private void FixAfterInsertion(Node newNode)
    {
        while (newNode != root && newNode.parent.color == Color.Red)
        {
            if (newNode.parent == newNode.parent.parent.left)
            {
                Node uncle = newNode.parent.parent.right;

                if (uncle != null && uncle.color == Color.Red)
                {
                    newNode.parent.color = Color.Black;
                    uncle.color = Color.Black;
                    newNode.parent.parent.color = Color.Red;
                    newNode = newNode.parent.parent;
                }
                else
                {
                    if (newNode == newNode.parent.right)
                    {
                        newNode = newNode.parent;
                        RotateLeft(newNode);
                    }

                    newNode.parent.color = Color.Black;
                    newNode.parent.parent.color = Color.Red;
                    RotateRight(newNode.parent.parent);
                }
            }
            else
            {
                Node uncle = newNode.parent.parent.left;

                if (uncle != null && uncle.color == Color.Red)
                {
                    newNode.parent.color = Color.Black;
                    uncle.color = Color.Black;
                    newNode.parent.parent.color = Color.Red;
                    newNode = newNode.parent.parent;
                }
                else
                {
                    if (newNode == newNode.parent.left)
                    {
                        newNode = newNode.parent;
                        RotateRight(newNode);
                    }

                    newNode.parent.color = Color.Black;
                    newNode.parent.parent.color = Color.Red;
                    RotateLeft(newNode.parent.parent);
                }
            }
        }

        root.color = Color.Black;
    }

    private void RotateLeft(Node node)
    {
        Node right = node.right;
        node.right = right.left;

        if (right.left != null)
            right.left.parent = node;

        right.parent = node.parent;

        if (node.parent == null)
            root = right;
        else if (node == node.parent.left)
            node.parent.left = right;
        else
            node.parent.right = right;

        right.left = node;
        node.parent = right;
    }

    private void RotateRight(Node node)
    {
        Node left = node.left;
        node.left = left.right;

        if (left.right != null)
            left.right.parent = node;

        left.parent = node.parent;

        if (node.parent == null)
            root = left;
        else if (node == node.parent.right)
            node.parent.right = left;
        else
            node.parent.left = left;

        left.right = node;
        node.parent = left;
    }

    // 其他方法：查找、删除等
    // ...

}

Summary:
This article introduces how to implement red-black tree in C# Implement the red-black tree algorithm and provide detailed code examples. Red-black tree is a self-balancing binary search tree with better performance in insertion, deletion and search operations. By using red-black trees, we can solve some common problems more efficiently. In practical applications, we can appropriately adjust and expand the functions of the red-black tree as needed. I hope this article will be helpful to you and spark your interest and in-depth research on red-black trees.

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