1 二叉搜索树
二叉搜索树（BST，Binary Search Tree）又称二叉查找树或二叉排序树。
一棵二叉搜索树是以二叉树来组织的，可以使用一个链表数据结构来表示，其中每一个结点就是一个对象。
一般地，除了key和位置数据之外，每个结点还包含属性Left、Right和Parent，分别指向结点的左、右子节点和父结点。
如果某个子结点或父结点不存在，则相应属性的值为空（null）。
根结点是树中唯一父指针为null的结点。
叶子结点的孩子结点指针也为null。
2 节点数据定义
/// <summary>
/// 二叉树的节点类
/// </summary>
public class BinaryNode
{
/// <summary>
/// 名称
/// </summary>
public string Name { get; set; } = "";
/// <summary>
/// 数据
/// </summary>
public string Data { get; set; } = "";
/// <summary>
/// 左节点
/// </summary>
public BinaryNode Left { get; set; } = null;
/// <summary>
/// 右节点
/// </summary>
public BinaryNode Right { get; set; } = null;
/// <summary>
/// 构造函数
/// </summary>
public BinaryNode()
{
}
/// <summary>
/// 单数值构造函数
/// </summary>
/// <param name="d"></param>
public BinaryNode(string d)
{
Name = d;
Data = d;
}
public BinaryNode(int d)
{
Name = d + "";
Data = d + "";
}
/// <summary>
/// 构造函数
/// </summary>
/// <param name="n"></param>
/// <param name="d"></param>
public BinaryNode(string n, string d)
{
Name = n;
Data = d;
}
/// <summary>
/// 返回邻接的三元组数据
/// </summary>
/// <returns></returns>
public string[] ToAdjacency()
{
string adj = "";
if (Left != null)
{
adj += Left.Name;
}
if (Right != null)
{
if (adj.Length > 0) adj += ",";
adj += Right.Name;
}
return new string[] { Name, Data, adj };
}
/// <summary>
/// 邻接表
/// </summary>
/// <returns></returns>
public List<string> ToList()
{
return new List<string>(ToAdjacency());
}
public int Key
{
get
{
return Int32.Parse(Data);
}
set
{
Data = value.ToString();
}
}
}
/// <summary>/// 二叉树的节点类/// </summary>public class BinaryNode{/// <summary>/// 名称/// </summary>public string Name { get; set; } = "";/// <summary>/// 数据/// </summary>public string Data { get; set; } = "";/// <summary>/// 左节点/// </summary>public BinaryNode Left { get; set; } = null;/// <summary>/// 右节点/// </summary>public BinaryNode Right { get; set; } = null;/// <summary>/// 构造函数/// </summary>public BinaryNode(){}/// <summary>/// 单数值构造函数/// </summary>/// <param name="d"></param>public BinaryNode(string d){Name = d;Data = d;}public BinaryNode(int d){Name = d + "";Data = d + "";}/// <summary>/// 构造函数/// </summary>/// <param name="n"></param>/// <param name="d"></param>public BinaryNode(string n, string d){Name = n;Data = d;}/// <summary>/// 返回邻接的三元组数据/// </summary>/// <returns></returns>public string[] ToAdjacency(){string adj = "";if (Left != null){adj += Left.Name;}if (Right != null){if (adj.Length > 0) adj += ",";adj += Right.Name;}return new string[] { Name, Data, adj };}/// <summary>/// 邻接表/// </summary>/// <returns></returns>public List<string> ToList(){return new List<string>(ToAdjacency());}public int Key{get{return Int32.Parse(Data);}set{Data = value.ToString();}}}
3 二叉树的节点插入与搜索与验证代码
using System;
using System.Collections;
using System.Collections.Generic;
namespace Legalsoft.Truffer.Algorithm
{
/// <summary>
/// BST(二叉搜索树的迭代方法)
/// </summary>
public static partial class Algorithm_Gallery
{
public static BinaryNode Insert(BinaryNode node, int key)
{
if (node == null)
{
return new BinaryNode(key);
}
if (key < node.Key)
{
node.Left = Insert(node.Left, key);
}
else if (key > node.Key)
{
node.Right = Insert(node.Right, key);
}
return node;
}
public static int BST_Find_Floor(BinaryNode root, int key)
{
BinaryNode curr = root;
BinaryNode ans = null;
while (curr != null)
{
if (curr.Key <= key)
{
ans = curr;
curr = curr.Right;
}
else
{
curr = curr.Left;
}
}
if (ans != null)
{
return ans.Key;
}
return -1;
}
public static int BST_Drive()
{
int N = 25;
BinaryNode root = new BinaryNode("19");
Insert(root, 2);
Insert(root, 1);
Insert(root, 3);
Insert(root, 12);
Insert(root, 9);
Insert(root, 21);
Insert(root, 19);
Insert(root, 25);
return BST_Find_Floor(root, N);
}
}
}
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using System;
using System.Collections;
using System.Collections.Generic;namespace Legalsoft.Truffer.Algorithm
{/// <summary>/// BST(二叉搜索树的迭代方法)/// </summary>public static partial class Algorithm_Gallery{public static BinaryNode Insert(BinaryNode node, int key){if (node == null){return new BinaryNode(key);}if (key < node.Key){node.Left = Insert(node.Left, key);}else if (key > node.Key){node.Right = Insert(node.Right, key);}return node;}public static int BST_Find_Floor(BinaryNode root, int key){BinaryNode curr = root;BinaryNode ans = null;while (curr != null){if (curr.Key <= key){ans = curr;curr = curr.Right;}else{curr = curr.Left;}}if (ans != null){return ans.Key;}return -1;}public static int BST_Drive(){int N = 25;BinaryNode root = new BinaryNode("19");Insert(root, 2);Insert(root, 1);Insert(root, 3);Insert(root, 12);Insert(root, 9);Insert(root, 21);Insert(root, 19);Insert(root, 25);return BST_Find_Floor(root, N);}}
}
