与链表、堆栈和队列不一样,二叉查找树不是线性数据结构,是二维数据结构。每个节点都包含一个LeftNode和RightNode,二叉查找树把比节点数据项小的数据放在LeftNode,把比节点数据项大的数据放在RightNode。
关于节点的类。
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 += " (叶节点) ";
}if (this.LeftNode != null){nodeString += "左节点:" + this.LeftNode.ToString();}if (this.RightNode != null){nodeString += "右节点:" + this.RightNode.ToString();}nodeString += "]";
return nodeString;
}}
以上,把比节点数据项Element小的数据所在节点赋值给LeftNode,把比节点数据项Element大的数据所在节点赋值给RightNode。
创建一个泛型二叉树查找类,维护着一个根节点,并提供各种对节点的操作方法。
public class BinarySearchTree<T>{public TreeNode<T> Root { get; set; }public BinarySearchTree()
{this.Root = null;}//把某个数据项插入到二叉树
public void Insert(T x){this.Root = Insert(x, this.Root);}//把某个数据项从二叉树中删除
public void Remove(T x){this.Root = Remove(x, this.Root);}//删除二叉树中的最小数据项
public void RemoveMin(){this.Root = RemoveMin(this.Root);}//获取二叉树中的最小数据项
public T FindMin()
{return ElemntAt(FindMin(this.Root));}//获取二叉树中的最大数据项
public T FindMax()
{return ElemntAt(FindMax(this.Root));}//获取二叉树中的某个数据项
public T Find(T x)
{return ElemntAt(Find(x, this.Root));}//清空
public void MakeEmpty(){this.Root = null;}//判断二叉树是否为空,是否存在
public bool IsEmpty(){return this.Root == null;}//获取某个节点的数据项
private T ElemntAt(TreeNode<T> t)
{return t == null ? default(T) : t.Element;}/// <summary>
/// 查找节点
/// </summary>
/// <param name="x">要查找数据项</param>
/// <param name="t">已存在的节点</param>
/// <returns>返回节点</returns>
private TreeNode<T> Find(T x, TreeNode<T> t)
{while (t != null)//当没有找到匹配数据项,不断调整查找范围,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 //如果找到数据项,就返回当前t的值{return t;
}}return null;}//获取最小的节点,
private TreeNode<T> FindMin(TreeNode<T> t)
{if (t != null){while (t.LeftNode != null)//不断循环二叉树的左半边树{t = t.LeftNode; //不断设置t的值
}}return t;
}//获取最大的节点
private TreeNode<T> FindMax(TreeNode<T> t)
{if (t != null){while (t.RightNode != null){t = t.RightNode;}}return t;
}/// <summary>
/// 插入节点
/// </summary>
/// <param name="x">要插入的数据项</param>
/// <param name="t">已经存在的节点</param>
/// <returns>返回已存在的节点</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){//等号右边的t.LeftNode是null,因此会创建一个TreeNode实例给t.LeftNode
t.LeftNode = Insert(x, t.LeftNode);}else if ((x as IComparable).CompareTo(t.E