了解集合本質(zhì)必須要知曉的概念04-二叉查找樹

2019-11-14 16:31:12

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供稿：網(wǎng)友

與鏈表、堆棧和隊列不一樣，二叉查找樹不是線性數(shù)據(jù)結(jié)構(gòu)，是二維數(shù)據(jù)結(jié)構(gòu)。每個節(jié)點都包含一個LeftNode和RightNode，二叉查找樹把比節(jié)點數(shù)據(jù)項小的數(shù)據(jù)放在LeftNode,把比節(jié)點數(shù)據(jù)項大的數(shù)據(jù)放在RightNode。

關(guān)于節(jié)點的類。

    public class TreeNode<T>
    {
        public T Element { get; set; }
        public TreeNode<T>  LeftNode { get; set; }
        public TreeNode<T>  RightNode { get; set; }
        public TreeNode(T element)
        {
            this.Element = element;
            LeftNode = RightNode = null;
        }
        public override string ToString()
        {
            string nodeString = "[" + this.Element + " ";
            if (this.LeftNode == null && this.RightNode == null)
            {
                nodeString += " (葉節(jié)點) ";
            }
            if (this.LeftNode != null)
            {
                nodeString += "左節(jié)點：" + this.LeftNode.ToString();
            }
            if (this.RightNode != null)
            {
                nodeString += "右節(jié)點：" + this.RightNode.ToString();
            }
            nodeString += "]";
            return nodeString;
        }
    }

以上，把比節(jié)點數(shù)據(jù)項Element小的數(shù)據(jù)所在節(jié)點賦值給LeftNode，把比節(jié)點數(shù)據(jù)項Element大的數(shù)據(jù)所在節(jié)點賦值給RightNode。

創(chuàng)建一個泛型二叉樹查找類，維護著一個根節(jié)點，并提供各種對節(jié)點的操作方法。

    public class BinarySearchTree<T>
    {
        public TreeNode<T> Root { get; set; }
        public BinarySearchTree()
        {
            this.Root = null;
        }
        //把某個數(shù)據(jù)項插入到二叉樹
        public void Insert(T x)
        {
            this.Root = Insert(x, this.Root);
        }
        //把某個數(shù)據(jù)項從二叉樹中刪除
        public void Remove(T x)
        {
            this.Root = Remove(x, this.Root);
        }
        //刪除二叉樹中的最小數(shù)據(jù)項
        public void RemoveMin()
        {
            this.Root = RemoveMin(this.Root);
        }
        //獲取二叉樹中的最小數(shù)據(jù)項
        public T FindMin()
        {
            return ElemntAt(FindMin(this.Root));
        }
        //獲取二叉樹中的最大數(shù)據(jù)項
        public T FindMax()
        {
            return ElemntAt(FindMax(this.Root));
        }
        //獲取二叉樹中的某個數(shù)據(jù)項
        public T Find(T x)
        {
            return ElemntAt(Find(x, this.Root));
        }
        //清空
        public void MakeEmpty()
        {
            this.Root = null;
        }
        //判斷二叉樹是否為空，是否存在
        public bool IsEmpty()
        {
            return this.Root == null;
        }
        //獲取某個節(jié)點的數(shù)據(jù)項
        PRivate T ElemntAt(TreeNode<T> t)
        {
            return t == null ? default(T) : t.Element;
        }
        /// <summary>
        /// 查找節(jié)點
        /// </summary>
        /// <param name="x">要查找數(shù)據(jù)項</param>
        /// <param name="t">已存在的節(jié)點</param>
        /// <returns>返回節(jié)點</returns>
        private TreeNode<T> Find(T x, TreeNode<T> t)
        {
            while (t != null)//當沒有找到匹配數(shù)據(jù)項，不斷調(diào)整查找范圍，即t的值
            {
                if ((x as IComparable).CompareTo(t.Element) < 0)
                {
                    t = t.LeftNode;
                }
                else if ((x as IComparable).CompareTo(t.Element) > 0)
                {
                    t = t.RightNode;
                }
                else //如果找到數(shù)據(jù)項，就返回當前t的值
                {
                    return t;
                }
            }
            return null;
        }
        //獲取最小的節(jié)點，
        private TreeNode<T> FindMin(TreeNode<T> t)
        {
            if (t != null)
            {
                while (t.LeftNode != null)//不斷循環(huán)二叉樹的左半邊樹
                {
                    t = t.LeftNode; //不斷設(shè)置t的值
                }
            }
            return t;
        }
        //獲取最大的節(jié)點
        private TreeNode<T> FindMax(TreeNode<T> t)
        {
            if (t != null)
            {
                while (t.RightNode != null)
                {
                    t = t.RightNode;
                }
            }
            return t;
        }
        /// <summary>
        /// 插入節(jié)點
        /// </summary>
        /// <param name="x">要插入的數(shù)據(jù)項</param>
        /// <param name="t">已經(jīng)存在的節(jié)點</param>
        /// <returns>返回已存在的節(jié)點</returns>
        protected TreeNode<T> Insert(T x, TreeNode<T> t)
        {
            if (t == null)
            {
                t = new TreeNode<T>(x);
            }
            else if ((x as IComparable).CompareTo(t.Element) < 0)
            {
                //等號右邊的t.LeftNode是null，因此會創(chuàng)建一個TreeNode實例給t.LeftNode
                t.LeftNode = Insert(x, t.LeftNode);
            }
            else if ((x as IComparable).CompareTo(t.Element) > 0)
            {
                t.RightNode = Insert(x, t.RightNode);
            }
            else
            {
                throw new Exception("插入了相同元素~~");
            }
            return t;
        }
        //刪除最小的節(jié)點
        //返回當前根節(jié)點
        protected TreeNode<T> RemoveMin(TreeNode<T> t)
        {
            if (t == null)
            {
                throw new Exception("節(jié)點不存在~~");
            }
            else if (t.LeftNode != null)
            {
                //通過遞歸不斷設(shè)置t.LeftNode，直到t.LeftNode=null
                t.LeftNode = RemoveMin(t.LeftNode);
                return t;
            }
            else //當t.LeftNode=null的時候，就把t.RightNode當作最小節(jié)點返回
            {
                return t.RightNode;
            }
        }
        //刪除某數(shù)據(jù)項，返回當前根節(jié)點
        protected TreeNode<T> Remove(T x, TreeNode<T> t)
        {
            if (t == null)
            {
                throw new Exception("節(jié)點不存在~~");
            }
            else if((x as IComparable).CompareTo(t.Element) < 0)
            {
                t.LeftNode = Remove(x, t.LeftNode);
            }
            else if ((x as IComparable).CompareTo(t.Element) > 0)
            {
                t.RightNode = Remove(x, t.RightNode);
            }
            else if (t.LeftNode != null && t.RightNode != null)
            {
                t.Element = FindMin(t.RightNode).Element;
                t.RightNode = RemoveMin(t.RightNode);
            }
            else
            {
                t = (t.LeftNode != null) ? t.LeftNode : t.RightNode;
            }
            return t;
        }
        public override string ToString()
        {
            return this.Root.ToString();
        }
    }

客戶端創(chuàng)建二叉查找樹的實例，并調(diào)用實例方法插入隨機數(shù)據(jù)。

            BinarySearchTree<int> intTree = new BinarySearchTree<int>();
            Random r = new Random(DateTime.Now.Millisecond);
            string trace = "";
            //插入5個隨機數(shù)
            for (int i = 0; i < 5; i++)
            {
                int randomInt = r.Next(1, 500);
                intTree.Insert(randomInt);
                trace += randomInt + " ";
            }
            Console.WriteLine("最大的節(jié)點：" + intTree.FindMax());
            Console.WriteLine("最小的節(jié)點：" + intTree.FindMin());
            Console.WriteLine("根節(jié)點：" + intTree.Root.Element);
            Console.WriteLine("插入節(jié)點的依次順序是：" + trace);
            Console.WriteLine("打印樹為：" + intTree);
            Console.ReadKey();