C#数据结构-二叉树-顺序存储结构

Posted 2021-04-09 DotNet且行且珍惜

什么是二叉树：每个树的节点只有两个子树的树形结构。

为什么使用顺序存储结构：使用数组存放满二叉树的各结点非常方便，可以根据一个结点的索引号很容易地推算出它的双亲、孩子、兄弟等结点的编号，从而对这些结点进行访问，这是一种存储二叉满二叉树或完全二叉树的最简单、最省空间的做法。

 /// <summary>/// 顺序存储二叉树/// </summary>public class SequentialStorageBinaryTree<T>{ /// <summary> /// 用于存储节点的数组 /// </summary> private T[] data; /// <summary> /// 节点数 /// </summary> private int count;
 public SequentialStorageBinaryTree(T[] arr = null) { if (arr == null) data = new T[0]; else data = arr; count = data.Length; }
 /// <summary> /// 增加 /// </summary> /// <param name="item"></param> public bool Add(T item) { List<T> list = data.ToList<T>(); list.Add(item); data = list.ToArray(); count = data.Length; return true; }}

通过数组存储结构为：

1、层次遍历

/// <summary>/// 层次遍历/// </summary>public void LevelTraversal(){ for (int i = 0; i < count; i++) { Console.Write(data[i] + " "); }}

2、先序遍历

/// <summary>/// 先序遍历/// </summary>/// <param name="index"></param>public void PreorderTraversal(int index =0){ //递归的终止条件 if (index >= count || index <0) return; int number = index + 1; Console.Write(data[index] + " "); int leftIndex = number * 2;//做节点 int rightIndex = number * 2 + 1; PreorderTraversal(leftIndex - 1); PreorderTraversal(rightIndex - 1);}

3、中序遍历

/// <summary>/// 中序遍历/// </summary>/// <param name="index"></param>public void MiddlePrefaceTraversal(int index = 0){ //递归的终止条件 if (index >= count || index < 0) return; int number = index + 1;  int leftIndex = number * 2;//做节点 int rightIndex = number * 2 + 1; MiddlePrefaceTraversal(leftIndex - 1); Console.Write(data[index] + " "); MiddlePrefaceTraversal(rightIndex - 1);}

4、后续遍历

/// <summary>/// 后序遍历/// </summary>/// <param name="index"></param>public void AfterwordTraversal(int index = 0){ //递归的终止条件 if (index >= count || index < 0) return; int number = index + 1; int leftIndex = number * 2;//做节点 int rightIndex = number * 2 + 1; AfterwordTraversal(leftIndex - 1); AfterwordTraversal(rightIndex - 1); Console.Write(data[index] + " ");}

现在我们测试下：

SequentialStorageBinaryTree<string> bTree = new SequentialStorageBinaryTree<string>();bTree.Add("A");bTree.Add("B");bTree.Add("C");bTree.Add("D");bTree.Add("E");bTree.Add("F");bTree.Add("G");
//先序遍历Console.Write("先序遍历：");bTree.PreorderTraversal();Console.WriteLine();
//中序遍历Console.Write("中序遍历：");bTree.MiddlePrefaceTraversal();Console.WriteLine();
//中序遍历Console.Write("后序遍历：");bTree.AfterwordTraversal();Console.WriteLine();
//层次遍历Console.Write("层次遍历：");bTree.LevelTraversal();Console.ReadKey();

输出：