红黑树（C#）

红黑树C#算法。

在线javascript演示地址：http://sandbox.runjs.cn/show/2nngvn8w

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using System.Threading;
using System.IO;
using System.Collections;

namespace ConsoleApplication2
{
    public class Program
    {
        public static void Main()
        {
            int[] a = {10,40,30,60,90,70,20,50,80};

            RBTree<int> rbTree = new RBTree<int>();
            foreach (var item in a)
            {
                rbTree.Insert(item);
            }
            rbTree.Remove(30);

            rbTree.PreOrder(t => Console.Write(t.ToString()+" "));

            Console.Read();
        }
    }

    #region 实体
    public enum NodeColor
    {
        Black,
        Red
    }

    public class RBTreeNode<T> where T : IComparable
    {
        public T Key { get; set; }
        public NodeColor Color { get; set; }
        public RBTreeNode<T> Parent { get; set; }
        public RBTreeNode<T> LeftNode { get; set; }
        public RBTreeNode<T> RightNode { get; set; }

        public RBTreeNode(T key, NodeColor color, RBTreeNode<T> parent, RBTreeNode<T> leftNode, RBTreeNode<T> rightNode)
        {
            this.Key = key;
            this.Color = color;
            this.Parent = parent;
            this.LeftNode = leftNode;
            this.RightNode = rightNode;
        }

        public override string ToString()
        {
            return this.Key + "(" + Color.ToString() + ")";
        }
    }
    #endregion

    public class RBTree<T> where T : IComparable
    {
        public RBTreeNode<T> RootNode { get; set; }//根节点

        #region 插入
        public void Insert(T key)
        {
            if (this.RootNode == null)
            {
                this.RootNode = new RBTreeNode<T>(key, NodeColor.Black, null, null, null);
            }
            else
            {
                var newNode = Inserts(key);
                InsertFixUp(newNode);
            }
        }

        private RBTreeNode<T> Inserts(T key)
        {
            var node = RootNode;

            var newNode = new RBTreeNode<T>(key, NodeColor.Red, null, null, null);
            while (true)
            {
                if (key.CompareTo(node.Key) > 0)
                {
                    if (node.RightNode == null)
                    {
                        newNode.Parent = node;
                        node.RightNode = newNode;
                        break;
                    }
                    node = node.RightNode;
                }
                else if (key.CompareTo(node.Key) < 0)
                {
                    if (node.LeftNode == null)
                    {
                        newNode.Parent = node;
                        node.LeftNode = newNode;
                        break;
                    }
                    node = node.LeftNode;
                }
                else
                {
                    break;
                }
            }
            return newNode;
        }

        private void InsertFixUp(RBTreeNode<T> node)
        {
            var parentNode = node.Parent;
            if (parentNode != null && NodeColor.Red == parentNode.Color)
            {
                var gparentNode = parentNode.Parent;
                if (parentNode == gparentNode.LeftNode)
                {
                    var uncleNode = gparentNode.RightNode;
                    if (uncleNode != null && NodeColor.Red == uncleNode.Color)//case1
                    {
                        parentNode.Color = NodeColor.Black;
                        uncleNode.Color = NodeColor.Black;
                        gparentNode.Color = NodeColor.Red;
                        InsertFixUp(gparentNode);
                    }
                    else
                    {
                        if (parentNode.RightNode == node)//case2
                        {
                            LeftRotation(parentNode);
                            InsertFixUp(parentNode);
                        }
                        else if (parentNode.LeftNode == node)//case3
                        {
                            parentNode.Color = NodeColor.Black;
                            gparentNode.Color = NodeColor.Red;
                            RightRotion(gparentNode);
                        }
                    }
                }
                else
                {
                    var uncleNode = gparentNode.LeftNode;
                    if (uncleNode != null && NodeColor.Red == uncleNode.Color)//case1
                    {
                        parentNode.Color = NodeColor.Black;
                        uncleNode.Color = NodeColor.Black;
                        gparentNode.Color = NodeColor.Red;
                        InsertFixUp(gparentNode);
                    }
                    else
                    {
                        if (parentNode.LeftNode == node)//case2
                        {
                            RightRotion(parentNode);
                            InsertFixUp(parentNode);
                        }
                        else if (parentNode.RightNode == node)//case3
                        {
                            parentNode.Color = NodeColor.Black;
                            gparentNode.Color = NodeColor.Red;
                            LeftRotation(gparentNode);
                        }
                    }
                }
            }
            RootNode.Color = NodeColor.Black; //直接将根节点设置为黑色
        }
        #endregion

        #region 旋转
        private void LeftRotation(RBTreeNode<T> node)
        {
            RBTreeNode<T> temp = node.RightNode;

            node.RightNode = temp.LeftNode;
            if (temp.LeftNode != null)
            {
                temp.LeftNode.Parent = node;
            }

            temp.Parent = node.Parent;

            if (node.Parent == null)
            {
                RootNode = temp;
            }
            else
            {
                if (node.Parent.LeftNode == node)
                {
                    node.Parent.LeftNode = temp;
                }
                else
                {
                    node.Parent.RightNode = temp;
                }
            }
            temp.LeftNode = node;
            node.Parent = temp;
        }

        private void RightRotion(RBTreeNode<T> node)
        {
            RBTreeNode<T> temp = node.LeftNode;

            node.LeftNode = temp.RightNode;
            if (temp.RightNode != null)
            {
                temp.RightNode.Parent = node;
            }

            temp.Parent = node.Parent;

            if (node.Parent == null)
            {
                RootNode = temp;
            }
            else
            {
                if (node == node.Parent.RightNode)
                {
                    node.Parent.RightNode = temp;
                }
                else
                {
                    node.Parent.LeftNode = temp;
                }
            }
            temp.RightNode = node;
            node.Parent = temp;
        }
        #endregion

        #region 删除
        public void Remove(T key)
        {
            RBTreeNode<T> node = Search(key);
            if (node == null)
            {
                return;
            }
            else
            {
                Remove(node);
            }
        }

        private void Remove(RBTreeNode<T> itWasDeletedNode)
        {
            RBTreeNode<T> child;
            RBTreeNode<T> parent;
            NodeColor nodeColor;

            if (itWasDeletedNode.LeftNode != null && itWasDeletedNode.RightNode != null)
            {
                var tempNode = this.FindMin(itWasDeletedNode.RightNode);
                if (itWasDeletedNode.Parent == null)
                {
                    this.RootNode = tempNode;
                }
                else
                {
                    if (itWasDeletedNode.Parent.LeftNode.Key.CompareTo(itWasDeletedNode.Key) == 0)
                    {
                        itWasDeletedNode.Parent.LeftNode = tempNode;
                    }
                    else
                    {
                        itWasDeletedNode.Parent.RightNode = tempNode;
                    }
                }

                child = tempNode.RightNode;
                parent = tempNode.Parent;
                nodeColor = tempNode.Color;

                if (parent.Key.CompareTo(itWasDeletedNode.Key) == 0)
                {
                    parent = tempNode;
                }
                else
                {
                    if (child != null)
                    {
                        child.Parent = parent;
                    }
                    parent.LeftNode = child;

                    tempNode.RightNode = itWasDeletedNode.RightNode;
                    itWasDeletedNode.RightNode.Parent = tempNode;
                }

                tempNode.Parent = itWasDeletedNode.Parent;
                tempNode.Color = itWasDeletedNode.Color;
                tempNode.LeftNode = itWasDeletedNode.LeftNode;
                itWasDeletedNode.LeftNode.Parent = tempNode;

                if (nodeColor == NodeColor.Black)
                {
                    RemoveFixUp(child, parent);
                }

                itWasDeletedNode = null;
                return;
            }

            if (itWasDeletedNode.LeftNode != null)
            {
                child = itWasDeletedNode.LeftNode;
            }
            else
            {
                child = itWasDeletedNode.RightNode;
            }

            parent = itWasDeletedNode.Parent;
            nodeColor = itWasDeletedNode.Color;

            if (child != null)
            {
                child.Parent = parent;
            }

            if (parent != null)
            {
                if (parent.LeftNode != null && parent.LeftNode.Key.CompareTo(itWasDeletedNode.Key) == 0)
                {
                    parent.LeftNode = child;
                }
                else
                {
                    parent.RightNode = child;
                }
            }
            else
            {
                this.RootNode = child;
            }

            if (nodeColor == NodeColor.Black)
            {
                RemoveFixUp(child, parent);
            }
            itWasDeletedNode = null;
        }

        private void RemoveFixUp(RBTreeNode<T> node, RBTreeNode<T> parentNode)
        {
            RBTreeNode<T> otherNode;

            while ((node == null || node.Color == NodeColor.Black) && (node != this.RootNode))
            {
                if (parentNode.LeftNode == node)
                {
                    otherNode = parentNode.RightNode;
                    if (otherNode.Color == NodeColor.Red)
                    {
                        otherNode.Color = NodeColor.Black;
                        parentNode.Color = NodeColor.Red;
                        LeftRotation(parentNode);
                        otherNode = parentNode.RightNode;
                    }

                    if ((otherNode.LeftNode == null || otherNode.LeftNode.Color == NodeColor.Black) &&
                        (otherNode.RightNode == null || otherNode.RightNode.Color == NodeColor.Black))
                    {
                        otherNode.Color = NodeColor.Red;
                        node = parentNode;
                        parentNode = node.Parent;
                    }
                    else
                    {
                        if (otherNode.RightNode == null || otherNode.RightNode.Color == NodeColor.Black)
                        {
                            otherNode.LeftNode.Color = NodeColor.Black;
                            otherNode.Color = NodeColor.Red;
                            RightRotion(otherNode);
                            otherNode = parentNode.RightNode;
                        }

                        otherNode.Color = parentNode.Color;
                        parentNode.Color = NodeColor.Black;
                        otherNode.RightNode.Color = NodeColor.Black;
                        LeftRotation(parentNode);
                        node = this.RootNode;
                        break;
                    }
                }
                else
                {
                    otherNode = parentNode.LeftNode;
                    if (otherNode.Color == NodeColor.Red)
                    {
                        otherNode.Color = NodeColor.Black;
                        parentNode.Color = NodeColor.Red;
                        RightRotion(parentNode);
                        otherNode = parentNode.LeftNode;
                    }

                    if ((otherNode.LeftNode == null || otherNode.LeftNode.Color == NodeColor.Black) &&
                        (otherNode.RightNode == null || otherNode.RightNode.Color == NodeColor.Black))
                    {
                        otherNode.Color = NodeColor.Red;
                        node = parentNode;
                        parentNode = node.Parent;
                    }
                    else
                    {
                        if (otherNode.LeftNode == null || otherNode.LeftNode.Color == NodeColor.Black)
                        {
                            otherNode.RightNode.Color = NodeColor.Black;
                            otherNode.Color = NodeColor.Red;
                            LeftRotation(otherNode);
                            otherNode = parentNode.LeftNode;
                        }

                        otherNode.Color = parentNode.Color;
                        parentNode.Color = NodeColor.Black;
                        otherNode.LeftNode.Color = NodeColor.Black;
                        RightRotion(parentNode);
                        node = this.RootNode;
                        break;
                    }
                }
            }

            if (node != null)
            {
                node.Color = NodeColor.Black;
            }
        }
        #endregion

        #region 查找
        public RBTreeNode<T> Search(T key)
        {
            return Search(RootNode, key);
        }

        private RBTreeNode<T> Search(RBTreeNode<T> node, T key)
        {
            if (node == null)
            {
                return null;
            }

            if (node.Key.CompareTo(key) > 0)
            {
                return Search(node.LeftNode, key);
            }
            else if (node.Key.CompareTo(key) < 0)
            {
                return Search(node.RightNode, key);
            }
            else
            {
                return node;
            }
        }

        public RBTreeNode<T> FindMin()
        {
            return FindMin(RootNode);
        }

        private RBTreeNode<T> FindMin(RBTreeNode<T> node)
        {
            if (node.LeftNode == null)
            {
                return node;
            }
            return FindMin(node.LeftNode);
        }

        public RBTreeNode<T> FindMax()
        {
            return FindMax(RootNode);
        }

        private RBTreeNode<T> FindMax(RBTreeNode<T> node)
        {
            if (node.RightNode == null)
            {
                return node.RightNode;
            }

            return FindMax(node.RightNode);
        }

        public List<RBTreeNode<T>> SearchRange(T minKey, T maxKey)
        {
            return SearchRange(minKey,maxKey,this.RootNode,new List<RBTreeNode<T>>());
        }

        private List<RBTreeNode<T>> SearchRange(T minKey, T maxKey, RBTreeNode<T> node,List<RBTreeNode<T>> nodeList)
        {
            if (node == null)
            {
                return nodeList;
            }

            if (node.Key.CompareTo(minKey) > 0)
            {
                SearchRange(minKey,maxKey,node.LeftNode,nodeList);
            }

            if (node.Key.CompareTo(minKey) >= 0 && node.Key.CompareTo(maxKey) <= 0)
            {
                nodeList.Add(node);
            }

            if (node.Key.CompareTo(maxKey) < 0)
            {
                SearchRange(minKey,maxKey,node.RightNode,nodeList);
            }

            return nodeList;
        }
        #endregion

        #region 遍历
        public void LevelOrder(Action<RBTreeNode<T>> action)
        {
            LevelOrder(RootNode, action);
        }

        private void LevelOrder(RBTreeNode<T> note, Action<RBTreeNode<T>> action)
        {
            Queue<RBTreeNode<T>> queue = new Queue<RBTreeNode<T>>();
            queue.Enqueue(note);

            while (queue.Count > 0)
            {
                var temp = queue.Dequeue();

                action(temp);

                if (temp.LeftNode != null)
                {
                    queue.Enqueue(temp.LeftNode);
                }

                if (temp.RightNode != null)
                {
                    queue.Enqueue(temp.RightNode);
                }
            }
        }

        public void PreOrder(Action<RBTreeNode<T>> action)
        {
            TreeOrder(RootNode, preOrderAction: action);
        }

        public void InOrder(Action<RBTreeNode<T>> action)
        {
            TreeOrder(RootNode, inOrderAction: action);
        }

        public void PostOrderAction(Action<RBTreeNode<T>> action)
        {
            TreeOrder(RootNode, postOrderAction: action);
        }

        private void TreeOrder(RBTreeNode<T> node, Action<RBTreeNode<T>> preOrderAction = null, Action<RBTreeNode<T>> inOrderAction = null, Action<RBTreeNode<T>> postOrderAction = null)
        {
            if (preOrderAction != null)
            {
                preOrderAction(node);
            }

            if (node.LeftNode != null)
            {
                TreeOrder(node.LeftNode, preOrderAction, inOrderAction, postOrderAction);
            }

            if (inOrderAction != null)
            {
                inOrderAction(node);
            }

            if (node.RightNode != null)
            {
                TreeOrder(node.RightNode, preOrderAction, inOrderAction, postOrderAction);
            }

            if (postOrderAction != null)
            {
                postOrderAction(node);
            }
        }
        #endregion

    }
}

算法参考：http://www.cnblogs.com/skywang12345/p/3603935.html