做了這麼多年前端，為什麼你還是不會寫業務程式碼？
阿新 • • 發佈：2020-12-04
對比上一篇文章“順序儲存二叉樹”，鏈式儲存二叉樹的優點是節省空間。
二叉樹的性質：
1、在二叉樹的第i層上至多有2i-1個節點(i>=1)。
2、深度為k的二叉樹至多有2k-1個節點(k>=1)。
3、對任何一棵二叉樹T，如果其終結點數為n0,度為2的節點數為n2,則n0=n2+1。
4、具有n個節點的完全二叉樹的深度為log2n+1。
5、對於一棵有n個節點的完全二叉樹的節點按層序編號，若完全二叉樹中的某節點編號為i，則若有左孩子編號為2i，若有右孩子編號為2i+1，母親節點為i/2。
在此記錄下鏈式二叉樹的實現方式 ：
/// <summary> /// <summary>
/// 二叉樹 連結串列儲存結構
/// </summary>
/// <typeparam name="T"></typeparam>
public class LinkStorageBinaryTree<T>
{
/// <summary>
/// 樹根節
/// </summary>
private TreeNode<T> head { get; set; }
public LinkStorageBinaryTree()
{
head = null;
}
public LinkStorageBinaryTree(T val)
{
head = new TreeNode<T>(val);
}
/// <summary>
/// 獲取左節點
/// </summary>
/// <param name="treeNode"></param>
/// <returns></returns>
public TreeNode<T> GetLeftNode(TreeNode<T> treeNode)
{
if (treeNode == null)
return null;
return treeNode.leftChild;
}
/// <summary>
/// 獲取右節點
/// </summary>
/// <param name="treeNode"></param>
/// <returns></returns>
public TreeNode<T> GetRightNode(TreeNode<T> treeNode)
{
if (treeNode == null)
return null;
return treeNode.rightChild;
}
/// <summary>
/// 獲取根節點
/// </summary>
/// <returns></returns>
public TreeNode<T> GetRoot()
{
return head;
}
/// <summary>
/// 插入左節點
/// </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("引數錯誤");
TreeNode<T> treeNode = new TreeNode<T>(val);
TreeNode<T> childNode = node.leftChild;
treeNode.leftChild = childNode;
node.leftChild = treeNode;
return treeNode;
}
/// <summary>
/// 插入右節點
/// </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("引數錯誤");
TreeNode<T> treeNode = new TreeNode<T>(val);
TreeNode<T> childNode = node.rightChild;
treeNode.rightChild = childNode;
node.rightChild = treeNode;
return treeNode;
}
/// <summary>
/// 刪除當前節點的 左節點
/// </summary>
/// <param name="node"></param>
/// <returns></returns>
public TreeNode<T> DeleteLeftNode(TreeNode<T> node)
{
if (node == null || node.leftChild == null)
throw new ArgumentNullException("引數錯誤");
TreeNode<T> leftChild = node.leftChild;
node.leftChild = null;
return leftChild;
}
/// <summary>
/// 刪除當前節點的 右節點
/// </summary>
/// <param name="node"></param>
/// <returns></returns>
public TreeNode<T> DeleteRightNode(TreeNode<T> node)
{
if (node == null || node.leftChild == null)
throw new ArgumentNullException("引數錯誤");
TreeNode<T> rightChild = node.rightChild;
node.rightChild = null;
return rightChild;
}
/// <summary>
/// 先序遍歷
/// </summary>
/// <param name="index"></param>
public void PreorderTraversal(TreeNode<T> node)
{
//遞迴的終止條件
if (head == null)
{
Console.WriteLine("當前樹為空");
return;
}
if (node != null)
{
Console.Write(node.data+ " ");
PreorderTraversal(node.leftChild);
PreorderTraversal(node.rightChild);
}
}
/// <summary>
/// 中序遍歷
/// </summary>
/// <param name="index"></param>
public void MiddlePrefaceTraversal(TreeNode<T> node)
{
//遞迴的終止條件
if (head == null)
{
Console.WriteLine("當前樹為空");
return;
}
if (node != null)
{
MiddlePrefaceTraversal(node.leftChild);
Console.Write(node.data + " ");
MiddlePrefaceTraversal(node.rightChild);
}
}
/// <summary>
/// 後序遍歷
/// </summary>
/// <param name="index"></param>
public void AfterwordTraversal(TreeNode<T> node)
{
//遞迴的終止條件
if (head == null)
{
Console.WriteLine("當前樹為空");
return;
}
if (node != null)
{
AfterwordTraversal(node.leftChild);
AfterwordTraversal(node.rightChild);
Console.Write(node.data + " ");
}
}
public void LevelTraversal()
{
if (head == null)
return;
//使用佇列先入先出
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>
/// 校驗節點是否是葉子節點
/// </summary>
/// <param name="node"></param>
/// <returns></returns>
public bool ValidLeafNode(TreeNode<T> node)
{
if (node == null)
throw new ArgumentNullException("引數錯誤");
if (node.leftChild != null && node.rightChild != null)
{
Console.WriteLine($"節點 {node.data} 不是葉子節點");
return false;
}
Console.WriteLine($"節點 {node.data} 是葉子節點");
return true;
}
}
遍歷方式在順序儲存一文中已經用圖表示過，在此不做重複說明。
現在測試下：
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);
//先序遍歷
Console.Write("先序遍歷：");
linkStorageBinary.PreorderTraversal(linkStorageBinary.GetRoot());
Console.WriteLine();
//中序遍歷
Console.Write("中序遍歷：");
linkStorageBinary.MiddlePrefaceTraversal(linkStorageBinary.GetRoot());
Console.WriteLine();
//中序遍歷
Console.Write("後序遍歷：");
linkStorageBinary.AfterwordTraversal(linkStorageBinary.GetRoot());
Console.WriteLine();
//層次遍歷
Console.Write("層次遍歷：");
linkStorageBinary.LevelTraversal();
linkStorageBinary.ValidLeafNode(tree1);
linkStorageBinary.ValidLeafNode(tree3);
Console.ReadLine();
輸出：
先序遍歷：A B D E C F G
中序遍歷：D B E A F C G
後序遍歷：D E B F G C A
層次遍歷：A B C D E F G 節點 B 不是葉子節點
節點 D 是葉子節點
