C#数据结构-二叉树-链式存储结构
对比上一篇文章“顺序存储二叉树”，链式存储二叉树的优点是节省空间。
二叉树的性质：
1、在二叉树的第i层上至多有2i-1个节点(i>=1)。
2、深度为k的二叉树至多有2k-1个节点(k>=1)。
3、对任何一棵二叉树T，如果其终结点数为n0,度为2的节点数为n2,则n0=n2+1。
4、具有n个节点的完全二叉树的深度为log2n+1。
5、对于一棵有n个节点的完全二叉树的节点按层序编号，若完全二叉树中的某节点编号为i，则若有左孩子编号为2i，若有右孩子编号为2i+1，母亲节点为i/2。
在此记录下链式二叉树的实现方式 ：
/// <summary> /// 树节点 /// </summary> /// <typeparam name="T"></typeparam> public class TreeNode<T> { /// <summary> /// 节点数据 /// </summary> public T data { get; set; } /// <summary> /// 左节点 /// </summary> public TreeNode<T> leftChild { get; set; } /// <summary> /// 右节点 /// </summary> public TreeNode<T> rightChild { get; set; } public TreeNode() { data = default(T); leftChild = null; rightChild = null; } public TreeNode(T item) { data = item; leftChild = null; rightChild = null; } }
/// <summary> /// 二叉树 链表存储结构 /// </summary> /// <typeparam name="T"></typeparam> public class LinkStorageBinaryTree<T> { /// <summary> /// 树根节 /// </summary> private TreeNode<T> head { get; set; } public LinkStorageBinaryTree() { head = null; } public LinkStorageBinaryTree(T val) { head = new TreeNode<T>(val); } /// <summary> /// 获取左节点 /// </summary> /// <param name="treeNode"></param> /// <returns></returns> public TreeNode<T> GetLeftNode(TreeNode<T> treeNode) { if (treeNode == null) return null; return treeNode.leftChild; } /// <summary> /// 获取右节点 /// </summary> /// <param name="treeNode"></param> /// <returns></returns> public TreeNode<T> GetRightNode(TreeNode<T> treeNode) { if (treeNode == null) return null; return treeNode.rightChild; } /// <summary> /// 获取根节点 /// </summary> /// <returns></returns> public TreeNode<T> GetRoot() { return head; } /// <summary> /// 插入左节点 /// </summary> /// <param name="val"></param> /// <param name="node"></param> /// <returns></returns> public TreeNode<T> AddLeftNode(T val,TreeNode<T> node) { if (node == null) throw new ArgumentNullException("参数错误"); TreeNode<T> treeNode = new TreeNode<T>(val); TreeNode<T> childNode = node.leftChild; treeNode.leftChild = childNode; node.leftChild = treeNode; return treeNode; } /// <summary> /// 插入右节点 /// </summary> /// <param name="val"></param> /// <param name="node"></param> /// <returns></returns> public TreeNode<T> AddRightNode(T val, TreeNode<T> node) { if (node == null) throw new ArgumentNullException("参数错误"); TreeNode<T> treeNode = new TreeNode<T>(val); TreeNode<T> childNode = node.rightChild; treeNode.rightChild = childNode; node.rightChild = treeNode; return treeNode; } /// <summary> /// 删除当前节点的 左节点 /// </summary> /// <param name="node"></param> /// <returns></returns> public TreeNode<T> DeleteLeftNode(TreeNode<T> node) { if (node == null || node.leftChild == null) throw new ArgumentNullException("参数错误"); TreeNode<T> leftChild = node.leftChild; node.leftChild = null; return leftChild; } /// <summary> /// 删除当前节点的 右节点 /// </summary> /// <param name="node"></param> /// <returns></returns> public TreeNode<T> DeleteRightNode(TreeNode<T> node) { if (node == null || node.leftChild == null) throw new ArgumentNullException("参数错误"); TreeNode<T> rightChild = node.rightChild; node.rightChild = null; return rightChild; } /// <summary> /// 先序遍历 /// </summary> /// <param name="index"></param> public void PreorderTraversal(TreeNode<T> node) { //递归的终止条件 if (head == null) { Console.WriteLine("当前树为空"); return; } if (node != null) { Console.Write(node.data+ " "); PreorderTraversal(node.leftChild); PreorderTraversal(node.rightChild); } } /// <summary> /// 中序遍历 /// </summary> /// <param name="index"></param> public void MiddlePrefaceTraversal(TreeNode<T> node) { //递归的终止条件 if (head == null) { Console.WriteLine("当前树为空"); return; } if (node != null) { MiddlePrefaceTraversal(node.leftChild); Console.Write(node.data + " "); MiddlePrefaceTraversal(node.rightChild); } } /// <summary> /// 后序遍历 /// </summary> /// <param name="index"></param> public void AfterwordTraversal(TreeNode<T> node) { //递归的终止条件 if (head == null) { Console.WriteLine("当前树为空"); return; } if (node != null) { AfterwordTraversal(node.leftChild); AfterwordTraversal(node.rightChild); Console.Write(node.data + " "); } } public void LevelTraversal() { if (head == null) return; //使用队列先入先出 Queue<TreeNode<T>> queue = new Queue<TreeNode<T>>(); queue.Enqueue(head); while (queue.Any()) { TreeNode<T> item = queue.Dequeue(); Console.Write(item.data +" "); if (item.leftChild != null) queue.Enqueue(item.leftChild); if (item.rightChild != null) queue.Enqueue(item.rightChild); } } /// <summary> /// 校验节点是否是叶子节点 /// </summary> /// <param name="node"></param> /// <returns></returns> public bool ValidLeafNode(TreeNode<T> node) { if (node == null) throw new ArgumentNullException("参数错误"); if (node.leftChild != null && node.rightChild != null) { Console.WriteLine($"节点 {node.data} 不是叶子节点"); return false; } Console.WriteLine($"节点 {node.data} 是叶子节点"); return true; } }
遍历方式在顺序存储一文中已经用图表示过，在此不做重复说明。
现在测试下：
LinkStorageBinaryTree<string> linkStorageBinary = new LinkStorageBinaryTree<string>("A"); TreeNode<string> tree1 = linkStorageBinary.AddLeftNode("B", linkStorageBinary.GetRoot()); TreeNode<string> tree2 = linkStorageBinary.AddRightNode("C", linkStorageBinary.GetRoot()); TreeNode<string> tree3 =linkStorageBinary.AddLeftNode("D", tree1); linkStorageBinary.AddRightNode("E",tree1); linkStorageBinary.AddLeftNode("F", tree2); linkStorageBinary.AddRightNode("G", tree2); //先序遍历 Console.Write("先序遍历："); linkStorageBinary.PreorderTraversal(linkStorageBinary.GetRoot()); Console.WriteLine(); //中序遍历 Console.Write("中序遍历："); linkStorageBinary.MiddlePrefaceTraversal(linkStorageBinary.GetRoot()); Console.WriteLine(); //中序遍历 Console.Write("后序遍历："); linkStorageBinary.AfterwordTraversal(linkStorageBinary.GetRoot()); Console.WriteLine(); //层次遍历 Console.Write("层次遍历："); linkStorageBinary.LevelTraversal(); linkStorageBinary.ValidLeafNode(tree1); linkStorageBinary.ValidLeafNode(tree3); Console.ReadKey();
输出：
先序遍历：A B D E C F G
中序遍历：D B E A F C G
后序遍历：D E B F G C A
层次遍历：A B C D E F G 节点 B 不是叶子节点
节点 D 是叶子节点
