C# 二叉搜索树<T> 删除

Question

我正在尝试从二叉搜索树中删除项目。我可以很好地插入数字和进一步的工作函数来查找树的高度和大小，但我无法让代码删除函数正常工作。

我已经弄清楚如果需要我需要合并子树并将最小的数字（最少的项目）设置为新节点，但我目前无法让它工作

提前感谢您的帮助。

我目前得到的代码：

主要：

static void Main(string[] args)
    {
        BSTree<int> testTree = new BSTree<int>();

        testTree.InsertItem(6);
        testTree.InsertItem(12);
        testTree.InsertItem(1);

        testTree.RemoveItem(12);
    }

二进制树：

class BinTree<T> where T : IComparable
{
    protected Node<T> root;

    public BinTree()
    {
        root = null;
    }
    public BinTree(Node<T> node)
    {
        root = node;
    }

节点：

class Node<T> where T : IComparable
{
    private T data;
    public Node<T> Left, Right;

    public Node(T item)
    {
        data = item;
        Left = null;
        Right = null;
    }
    public T Data
    {
        set { data = value; }
        get { return data; }
    }
}

BSTree：

class BSTree<T> : BinTree<T> where T:IComparable
{
    public BSTree()
    {
        root = null;
    }
    public void InsertItem(T item)
    {
        insertItem(item, ref root);
    }
    private void insertItem(T item, ref Node<T> tree)
    {
        if (tree == null)
            tree = new Node<T>(item);
        else if (item.CompareTo(tree.Data) < 0)
            insertItem(item, ref tree.Left);
        else if (item.CompareTo(tree.Data) > 0)
            insertItem(item, ref tree.Right);
    }
    public void RemoveItem(T item)
    {
        removeItem(item, ref root);
    }
    private void removeItem(T item, ref Node<T> tree)
    {
        if (tree == null)
            tree = new Node<T>(item);
        if (item.CompareTo(tree.Data) < 0)
            removeItem(item, ref tree.Left);
        else if (item.CompareTo(tree.Data) > 0)
            removeItem(item, ref tree.Right);
        if (tree.Left == null)
            tree = tree.Right;
        else if (tree.Right == null)
            tree = tree.Left;

        T newRoot = leastItem(tree.Right);
        tree.Data = newRoot;
        removeItem(newRoot, ref tree.Right);
    }
    public T leastItem(Node<T> tree) //returns left most item in tree
    {
        if (tree.Left == null) //if tree.Left is empty
            return tree.Data;
        else
        {
            return leastItem(tree.Left);
        }
    }

Answer 1

这是一个基于您的符号的工作示例。

class Program
{
    static void Main(string[] args)
    {
        BSTree<int> testTree = new BSTree<int>();

        //testTree.InsertItem(6);
        //testTree.InsertItem(12);
        //testTree.InsertItem(1);
        //testTree.Print();
        //Console.WriteLine();

        //testTree.RemoveItem(12);
        //testTree.Print();
        //Console.WriteLine();

        List<int> ls = new List<int> { 10, 5, 19, 1, 6, 17, 21, 9 };
        foreach (int i in ls)
            testTree.InsertItem(i);

        testTree.Print();
        Console.WriteLine();

        testTree.RemoveItem(6);
        testTree.Print();
        Console.WriteLine();

        Console.Read();
    }
}

class BinTree<T> where T : IComparable
{
    protected Item<T> root;

    public BinTree()
    {
        root = null;
    }
    public BinTree(Item<T> item)
    {
        root = item;
    }
}

class Item<T> where T : IComparable
{
    public Item<T> Left, Right, Parent;

    public Item(T item)
    {
        Data = item;
        Left = null;
        Right = null;
    }
    public T Data { set; get; }
}

class BSTree<T> : BinTree<T> where T : IComparable
{
    public BSTree()
    {
        root = null;
    }

    public void InsertItem(T item)
    {
        Item<T> tmp = root;
        Item<T> par = tmp;

        while (tmp != null)
        {
            par = tmp;
            if (tmp.Data.CompareTo(item) == 0)
            {
                Console.WriteLine($"Element {item} already exist\n");
                return;
            }
            else if (tmp.Data.CompareTo(item) > 0)
                tmp = tmp.Left;
            else
                tmp = tmp.Right;
        }

        tmp = new Item<T>(item);

        if (par == null)
        {
            tmp.Parent = tmp;
            root = tmp;
        }
        else
        {
            tmp.Parent = par;
            if (item.CompareTo(par.Data) < 0)
                par.Left = tmp;
            else
                par.Right = tmp;
        }
    }

    public void RemoveItem(T item)
    {
        Item<T> theItem = Find(item);
        RemoveItem(theItem);
    }

    private Item<T> Find(T value)
    {
        Item<T> tmp = root;
        while (tmp != null)
        {
            if (value.CompareTo(tmp.Data) == 0)
                return tmp;
            else if (value.CompareTo(tmp.Data) < 0)
                tmp = tmp.Left;
            else
                tmp = tmp.Right;
        }
        return null;
    }

    private void RemoveItem(Item<T> item)
    {
        if (item == null)
            return;

        if (item.Left == null && item.Right == null)
        {
            #region Remove leaf
            if (item == root)
                root = null;
            else
            {
                Item<T> par = item.Parent;
                if (par.Left == item)
                    par.Left = null;
                else
                    par.Right = null;
            }
            #endregion
        }
        else if (item.Left == null || item.Right == null)
        {
            #region Remove item with one child
            bool isroot = item == root;

            var par = item.Parent;
            var newchild = item.Left ?? item.Right;
            newchild.Parent = par;
            if (par.Left == item)
                par.Left = newchild;
            else
                par.Right = newchild;

            if (isroot)
                root = newchild;
            #endregion
        }
        else
        {
            #region Remove item with two children
            Item<T> repl = Max(item.Left);
            item.Data = repl.Data;
            RemoveItem(repl);
            #endregion
        }
    }

    private Item<T> Max(Item<T> node)
    {
        Item<T> tmp = node;
        Item<T> ret = node;
        while (tmp != null)
        {
            ret = tmp;
            tmp = tmp.Right;
        }
        return ret;
    }

    public void Print(Item<T> node = null) => _print(node ?? root);

    private void _print(Item<T> node)
    {
        if (node != null)
        {
            _print(node.Left);
            Console.Write(node.Data + " ");
            _print(node.Right);
        }
    }
}