博客 https://blog.lenyiin.com/avltree/ 的代码仓库

Linux/AVLTree.hpp

@@ -0,0 +1,612 @@
+#pragma once
+
+#include <iostream>
+#include <stack>
+#include <queue>
+
+namespace Lenyiin
+{
+    template <class K, class V>
+    struct AVLTreeNode
+    {
+        AVLTreeNode<K, V> *_left;
+        AVLTreeNode<K, V> *_right;
+        AVLTreeNode<K, V> *_parent;
+
+        int _bf;             // balance factor	平衡因子
+        std::pair<K, V> _kv; // key-value
+
+        // 普通构造
+        AVLTreeNode(const std::pair<K, V> &kv)
+            : _left(nullptr), _right(nullptr), _parent(nullptr), _bf(0), _kv(kv)
+        {
+        }
+    };
+
+    template <class K, class V>
+    class AVLTree
+    {
+    private:
+        typedef AVLTreeNode<K, V> Node;
+
+    public:
+        bool Insert(const std::pair<K, V> &kv)
+        {
+            // 1. 先按搜索树的规则进行插入
+            if (_root == nullptr)
+            {
+                _root = new Node(kv);
+                return true;
+            }
+
+            Node *parent = nullptr;
+            Node *cur = _root;
+            while (cur)
+            {
+                if (cur->_kv.first > kv.first)
+                {
+                    parent = cur;
+                    cur = cur->_left;
+                }
+                else if (cur->_kv.first < kv.first)
+                {
+                    parent = cur;
+                    cur = cur->_right;
+                }
+                else
+                {
+                    return false; // 如果相等, 表示已经有了, 不需要插入
+                }
+            }
+
+            // 找到位置
+            cur = new Node(kv);
+            if (parent->_kv.first > kv.first)
+            {
+                parent->_left = cur;
+                cur->_parent = parent;
+            }
+            else
+            {
+                parent->_right = cur;
+                cur->_parent = parent;
+            }
+
+            // 2. 更新平衡因子
+            while (parent)
+            {
+                if (cur == parent->_right)
+                {
+                    parent->_bf++; // 插在右边, 平衡因子++
+                }
+                else
+                {
+                    parent->_bf--; // 插在左边, 平衡因子--
+                }
+
+                if (parent->_bf == 0)
+                {
+                    // 说明 parent 所在的子树高度不变, 更新结束
+                    break;
+                }
+                else if (parent->_bf == 1 || parent->_bf == -1)
+                {
+                    // 说明 parent 所在子树的高度变了, 继续往上更新
+                    cur = parent;
+                    parent = parent->_parent;
+                }
+                else if (parent->_bf == 2 || parent->_bf == -2)
+                {
+                    // parent 所在的子树出现问题了, 需要旋转处理一下
+                    // 1. 旋转前提是保持它依旧是搜索二叉树
+                    // 2. 旋转成平衡树
+                    if (parent->_bf == 2)
+                    {
+                        if (cur->_bf == 1)
+                        {
+                            // 左旋
+                            RotateL(parent);
+                        }
+                        else if (cur->_bf == -1)
+                        {
+                            // 右左双旋
+                            RotateRL(parent);
+                        }
+                    }
+                    else if (parent->_bf == -2)
+                    {
+                        if (cur->_bf == -1)
+                        {
+                            // 右旋
+                            RotateR(parent);
+                        }
+                        else if (cur->_bf == 1)
+                        {
+                            // 左右双旋
+                            RotateLR(parent);
+                        }
+                    }
+
+                    // 旋转完成后, parent 所在的树的高度恢复到了插入节点前的高度
+                    // 如果是子树, 对上一层没有影响, 更新结束
+                    break;
+                }
+            }
+
+            return true;
+        }
+
+        // 左单旋
+        void RotateL(Node *parent)
+        {
+            Node *ppNode = parent->_parent;
+            Node *subR = parent->_right;
+            Node *subRL = subR->_left;
+
+            parent->_right = subRL;
+            if (subRL)
+            {
+                subRL->_parent = parent;
+            }
+            subR->_left = parent;
+            parent->_parent = subR;
+
+            // 1. 原来 parent 是这棵树的根, 现在 subR 是根
+            if (parent == _root)
+            {
+                _root = subR;
+                subR->_parent = nullptr;
+            }
+            // 2. parent 为根的树只是整棵树中的子树, 改变链接关系, 那么 subR 要顶替他的位置
+            else
+            {
+                if (ppNode->_left == parent)
+                {
+                    ppNode->_left = subR;
+                }
+                else
+                {
+                    ppNode->_right = subR;
+                }
+                subR->_parent = ppNode;
+            }
+
+            parent->_bf = subR->_bf = 0;
+        }
+
+        // 右单旋
+        void RotateR(Node *parent)
+        {
+            Node *ppNode = parent->_parent;
+            Node *subL = parent->_left;
+            Node *subLR = subL->_right;
+
+            parent->_left = subLR;
+            if (subLR)
+            {
+                subLR->_parent = parent;
+            }
+            subL->_right = parent;
+            parent->_parent = subL;
+
+            if (parent == _root)
+            {
+                _root = subL;
+                subL->_parent = nullptr;
+            }
+            else
+            {
+                if (ppNode->_left == parent)
+                {
+                    ppNode->_left = subL;
+                }
+                else
+                {
+                    ppNode->_right = subL;
+                }
+                subL->_parent = ppNode;
+            }
+
+            parent->_bf = subL->_bf = 0;
+        }
+
+        // 右左双旋
+        void RotateRL(Node *parent)
+        {
+            Node *subR = parent->_right;
+            Node *subRL = subR->_left;
+            int bf = subRL->_bf;
+
+            RotateR(parent->_right);
+            RotateL(parent);
+
+            if (bf == -1)
+            {
+                parent->_bf = 0;
+                subR->_bf = 1;
+                subRL->_bf = 0;
+            }
+            else if (bf == 1)
+            {
+                parent->_bf = -1;
+                subR->_bf = 0;
+                subRL->_bf = 0;
+            }
+            else if (bf == 0)
+            {
+                parent->_bf = 0;
+                subR->_bf = 0;
+                subRL->_bf = 0;
+            }
+        }
+
+        // 左右双旋
+        void RotateLR(Node *parent)
+        {
+            Node *subL = parent->_left;
+            Node *subLR = subL->_right;
+            int bf = subLR->_bf;
+
+            RotateL(subL);
+            RotateR(parent);
+
+            if (bf == 1)
+            {
+                parent->_bf = 0;
+                subL->_bf = -1;
+                subLR->_bf = 0;
+            }
+            else if (bf == -1)
+            {
+                parent->_bf = 1;
+                subL->_bf = 0;
+                subLR->_bf = 0;
+            }
+            else if (bf == 0)
+            {
+                parent->_bf = 0;
+                subL->_bf = 0;
+                subLR->_bf = 0;
+            }
+        }
+
+        // 中序遍历
+        // void _InOrder(Node* root)
+        //{
+        //	if (root == nullptr)
+        //	{
+        //		return;
+        //	}
+
+        //	_InOrder(root->_left);
+        //	std::cout << root->_kv.first << ":" << root->_kv.second << std::endl;
+        //	_InOrder(root->_right);
+        //}
+
+        // void InOrder()
+        //{
+        //	_InOrder(_root);
+        //	std::cout << std::endl;
+        // }
+
+        // 中序遍历 非递归
+        void InOrder()
+        {
+            std::stack<Node *> stack;
+            Node *cur = _root;
+
+            while (cur != nullptr || !stack.empty())
+            {
+                // 找到最左边的节点
+                while (cur != nullptr)
+                {
+                    stack.push(cur);
+                    cur = cur->_left;
+                }
+
+                // 处理当前节点
+                cur = stack.top();
+                stack.pop();
+                std::cout << cur->_kv.first << ":" << cur->_kv.second << std::endl;
+
+                // 转向右子树
+                cur = cur->_right;
+            }
+            std::cout << std::endl;
+        }
+
+        // 前序遍历的递归实现
+        // 辅助函数
+        // void _PreOrder(Node* root)
+        //{
+        //	if (root == nullptr)
+        //	{
+        //		return;
+        //	}
+
+        //	std::cout << root->_kv.first << ":" << root->_kv.second << std::endl;   // 访问根节点
+        //	_PreOrder(root->_left);   // 访问左子树
+        //	_PreOrder(root->_right);  // 访问右子树
+        //}
+
+        // void PreOrder()
+        //{
+        //	_PreOrder(_root);
+        //	std::cout << std::endl;
+        // }
+
+        // 前序遍历的非递归实现
+        void PreOrder()
+        {
+            if (_root == nullptr)
+            {
+                return;
+            }
+
+            std::stack<Node *> stack;
+            stack.push(_root);
+
+            while (!stack.empty())
+            {
+                Node *cur = stack.top();
+                stack.pop();
+                std::cout << cur->_kv.first << ":" << cur->_kv.second << std::endl; // 访问当前节点
+
+                // 先压入右子树再压入左子树（确保左子树先处理）
+                if (cur->_right != nullptr)
+                {
+                    stack.push(cur->_right);
+                }
+                if (cur->_left != nullptr)
+                {
+                    stack.push(cur->_left);
+                }
+            }
+            std::cout << std::endl;
+        }
+
+        // 后序遍历的递归实现
+        // 辅助函数
+        // void _PostOrder(Node* root) {
+        //	if (root == nullptr)
+        //	{
+        //		return;
+        //	}
+
+        //	_PostOrder(root->_left);    // 访问左子树
+        //	_PostOrder(root->_right);   // 访问右子树
+        //	std::cout << root->_kv.first << ":" << root->_kv.second << std::endl;     // 访问根节点
+        //}
+
+        // void PostOrder()
+        //{
+        //	_PostOrder(_root);
+        //	std::cout << std::endl;
+        // }
+
+        // 后序遍历的非递归实现
+        void PostOrder()
+        {
+            if (_root == nullptr)
+            {
+                return;
+            }
+
+            std::stack<Node *> st;
+            Node *cur = _root;
+            Node *lastNode = nullptr; // 最近访问的节点
+            while (cur || !st.empty())
+            {
+                while (cur)
+                {
+                    st.push(cur);
+                    cur = cur->_left;
+                }
+
+                Node *top = st.top();
+                if ((top->_right == nullptr) || (lastNode == top->_right))
+                {
+                    std::cout << top->_kv.first << ":" << top->_kv.second << std::endl;
+                    lastNode = top;
+                    st.pop();
+                }
+                else
+                {
+                    cur = top->_right;
+                }
+            }
+            std::cout << std::endl;
+        }
+
+        // 层序遍历
+        void LevelOrder()
+        {
+            if (_root == nullptr)
+            {
+                return;
+            }
+
+            std::queue<Node *> queue;
+            queue.push(_root);
+
+            while (!queue.empty())
+            {
+                Node *cur = queue.front();
+                queue.pop();
+                std::cout << cur->_kv.first << ":" << cur->_kv.second << std::endl; // 访问当前节点
+
+                if (cur->_left != nullptr)
+                {
+                    queue.push(cur->_left); // 将左子树压入队列
+                }
+                if (cur->_right != nullptr)
+                {
+                    queue.push(cur->_right); // 将右子树压入队列
+                }
+            }
+            std::cout << std::endl;
+        }
+
+        // 查找后继节点
+        Node *findMin(Node *node)
+        {
+            while (node->_left != nullptr)
+            {
+                node = node->_left;
+            }
+            return node;
+        }
+
+        Node *FindSuccessor(Node *node)
+        {
+            if (node->_right != nullptr)
+            {
+                return findMin(node->_right);
+            }
+
+            Node *cur = _root;
+            Node *successor = nullptr;
+            while (cur != nullptr)
+            {
+                if (node->_kv.first < cur->_kv.first)
+                {
+                    successor = cur;
+                    cur = cur->_left;
+                }
+                else if (node->_kv.first > cur->_kv.first)
+                {
+                    cur = cur->_right;
+                }
+                else
+                {
+                    break;
+                }
+            }
+            return successor;
+        }
+
+        // 查找前驱节点
+        Node *findMax(Node *node)
+        {
+            while (node->_right != nullptr)
+            {
+                node = node->_right;
+            }
+            return node;
+        }
+
+        Node *FindPredecessor(Node *node)
+        {
+            if (node->_left != nullptr)
+            {
+                return findMax(node->_left);
+            }
+
+            Node *cur = _root;
+            Node *predecessor = nullptr;
+            while (cur != nullptr)
+            {
+                if (node->_kv.first < cur->_kv.first)
+                {
+                    cur = cur->_left;
+                }
+                else if (node->_kv.first > cur->_kv.first)
+                {
+                    predecessor = cur;
+                    cur = cur->_right;
+                }
+                else
+                {
+                    break;
+                }
+            }
+            return predecessor;
+        }
+
+        // 获取树的高度
+        int Height(Node *root)
+        {
+            if (root == nullptr)
+            {
+                return 0;
+            }
+
+            int leftHeight = Height(root->_left);
+            int rightHeight = Height(root->_right);
+
+            return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
+        }
+
+        // 判断是否是平衡二叉树
+        bool _IsBalance(Node *root)
+        {
+            if (root == nullptr)
+            {
+                return true;
+            }
+
+            int leftHeight = Height(root->_left);
+            int rightHeight = Height(root->_right);
+            if (abs(leftHeight - rightHeight) > 1)
+            {
+                return false;
+            }
+
+            return _IsBalance(root->_left) && _IsBalance(root->_right);
+        }
+
+        bool IsBalance()
+        {
+            return _IsBalance(_root);
+        }
+
+        // 查找 非递归
+        // Node* Find(const K& key)
+        //{
+        //	Node* cur = _root;
+        //	while (cur)
+        //	{
+        //		if (cur->_kv.first > key)
+        //		{
+        //			cur = cur->_left;
+        //		}
+        //		else if (cur->_kv.first < key)
+        //		{
+        //			cur = cur->_right;
+        //		}
+        //		else
+        //		{
+        //			return cur;
+        //		}
+        //	}
+        //	return nullptr;
+        //}
+
+        // 查找的递归实现
+        // 辅助函数
+        Node *_find(Node *root, const K &key)
+        {
+            if (root == nullptr || root->_kv.first == key)
+            {
+                return root;
+            }
+            if (key < root->_kv.first)
+            {
+                return _find(root->_left, key);
+            }
+            else
+            {
+                return _find(root->_right, key);
+            }
+        }
+
+        // 查找节点
+        Node *Find(const K &key)
+        {
+            return _find(_root, key);
+        }
+
+    private:
+        Node *_root = nullptr;
+    };
+}

Linux/Main.cc

@@ -0,0 +1,58 @@
+#include "AVLTree.hpp"
+
+using namespace Lenyiin;
+
+void test_AVLTree()
+{
+    // int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
+    int a[] = {4, 2, 6, 1, 3, 5, 15, 7, 16, 14};
+    AVLTree<int, int> t;
+    for (const auto &e : a)
+    {
+        t.Insert(std::make_pair(e, e));
+    }
+
+    t.InOrder();
+    t.PreOrder();
+    t.PostOrder();
+    t.LevelOrder();
+    std::cout << t.IsBalance() << std::endl;
+
+    auto ret = t.Find(6);
+    if (ret == nullptr)
+    {
+        std::cout << "没有找到" << std::endl;
+    }
+    else
+    {
+        std::cout << "找到了" << std::endl;
+        std::cout << ret->_kv.first << ":" << ret->_kv.second << std::endl;
+    }
+
+    auto pre = t.FindPredecessor(ret);
+    if (pre != nullptr)
+    {
+        std::cout << ret->_kv.first << " 的前驱节点是: " << pre->_kv.first << std::endl;
+    }
+    else
+    {
+        std::cout << "前驱节点为空" << std::endl;
+    }
+
+    auto suc = t.FindSuccessor(ret);
+    if (suc != nullptr)
+    {
+        std::cout << ret->_kv.first << " 的后继节点是: " << suc->_kv.first << std::endl;
+    }
+    else
+    {
+        std::cout << "后继节点为空" << std::endl;
+    }
+}
+
+int main()
+{
+    test_AVLTree();
+
+    return 0;
+}

Linux/Makefile

@@ -0,0 +1,6 @@
+main:Main.cc
+	g++ -o $@ $^
+
+.PHONY:clean
+clean:
+	rm -f main;

Windows_AVLTree/AVLTree.cpp

@@ -0,0 +1,58 @@
+#include "AVLTree.hpp"
+
+using namespace Lenyiin;
+
+void test_AVLTree()
+{
+	//int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
+	int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
+	AVLTree<int, int> t;
+	for (const auto& e : a)
+	{
+		t.Insert(std::make_pair(e, e));
+	}
+
+	t.InOrder();
+	t.PreOrder();
+	t.PostOrder();
+	t.LevelOrder();
+	std::cout << t.IsBalance() << std::endl;
+
+	auto ret = t.Find(6);
+	if (ret == nullptr)
+	{
+		std::cout << "没有找到" << std::endl;
+	}
+	else
+	{
+		std::cout << "找到了" << std::endl;
+		std::cout << ret->_kv.first << ":" << ret->_kv.second << std::endl;
+	}
+
+	auto pre = t.FindPredecessor(ret);
+	if (pre != nullptr)
+	{
+		std::cout << ret->_kv.first << " 的前驱节点是: " << pre->_kv.first << std::endl;
+	}
+	else
+	{
+		std::cout << "前驱节点为空" << std::endl;
+	}
+
+	auto suc = t.FindSuccessor(ret);
+	if (suc != nullptr)
+	{
+		std::cout << ret->_kv.first << " 的后继节点是: " << suc->_kv.first << std::endl;
+	}
+	else
+	{
+		std::cout << "后继节点为空" << std::endl;
+	}
+}
+
+int main()
+{
+	test_AVLTree();
+
+	return 0;
+}

Windows_AVLTree/AVLTree.hpp

@@ -0,0 +1,605 @@
+#pragma once
+
+#include <iostream>
+#include <stack>
+#include <queue>
+
+namespace Lenyiin
+{
+	template <class K, class V>
+	struct AVLTreeNode
+	{
+		AVLTreeNode<K, V>* _left;
+		AVLTreeNode<K, V>* _right;
+		AVLTreeNode<K, V>* _parent;
+
+		int _bf;		// balance factor	平衡因子
+		std::pair<K, V> _kv;	// key-value
+
+		// 普通构造
+		AVLTreeNode(const std::pair<K, V>& kv)
+			: _left(nullptr), _right(nullptr), _parent(nullptr), _bf(0), _kv(kv)
+		{}
+	};
+
+	template <class K, class V>
+	class AVLTree
+	{
+	private:
+		typedef AVLTreeNode<K, V> Node;
+
+	public:
+		bool Insert(const std::pair<K, V>& kv)
+		{
+			// 1. 先按搜索树的规则进行插入
+			if (_root == nullptr)
+			{
+				_root = new Node(kv);
+				return true;
+			}
+
+			Node* parent = nullptr;
+			Node* cur = _root;
+			while (cur)
+			{
+				if (cur->_kv.first > kv.first)
+				{
+					parent = cur;
+					cur = cur->_left;
+				}
+				else if (cur->_kv.first < kv.first)
+				{
+					parent = cur;
+					cur = cur->_right;
+				}
+				else
+				{
+					return false;	// 如果相等, 表示已经有了, 不需要插入
+				}
+			}
+
+			// 找到位置
+			cur = new Node(kv);
+			if (parent->_kv.first > kv.first)
+			{
+				parent->_left = cur;
+				cur->_parent = parent;
+			}
+			else
+			{
+				parent->_right = cur;
+				cur->_parent = parent;
+			}
+
+			// 2. 更新平衡因子
+			while (parent)
+			{
+				if (cur == parent->_right)
+				{
+					parent->_bf++;	// 插在右边, 平衡因子++
+				}
+				else
+				{
+					parent->_bf--;	// 插在左边, 平衡因子--
+				}
+
+				if (parent->_bf == 0)
+				{
+					// 说明 parent 所在的子树高度不变, 更新结束
+					break;
+				}
+				else if (parent->_bf == 1 || parent->_bf == -1)
+				{
+					// 说明 parent 所在子树的高度变了, 继续往上更新
+					cur = parent;
+					parent = parent->_parent;
+				}
+				else if (parent->_bf == 2 || parent->_bf == -2)
+				{
+					// parent 所在的子树出现问题了, 需要旋转处理一下
+					// 1. 旋转前提是保持它依旧是搜索二叉树
+					// 2. 旋转成平衡树
+					if (parent->_bf == 2)
+					{
+						if (cur->_bf == 1)
+						{
+							// 左旋
+							RotateL(parent);
+						}
+						else if (cur->_bf == -1)
+						{
+							// 右左双旋
+							RotateRL(parent);
+						}
+					}
+					else if (parent->_bf == -2)
+					{
+						if (cur->_bf == -1)
+						{
+							// 右旋
+							RotateR(parent);
+						}
+						else if (cur->_bf == 1)
+						{
+							// 左右双旋
+							RotateLR(parent);
+						}
+					}
+
+					// 旋转完成后, parent 所在的树的高度恢复到了插入节点前的高度
+					// 如果是子树, 对上一层没有影响, 更新结束
+					break;
+				}
+			}
+
+			return true;
+		}
+
+		// 左单旋
+		void RotateL(Node* parent)
+		{
+			Node* ppNode = parent->_parent;
+			Node* subR = parent->_right;
+			Node* subRL = subR->_left;
+
+			parent->_right = subRL;
+			if (subRL)
+			{
+				subRL->_parent = parent;
+			}
+			subR->_left = parent;
+			parent->_parent = subR;
+
+			// 1. 原来 parent 是这棵树的根, 现在 subR 是根
+			if (parent == _root)
+			{
+				_root = subR;
+				subR->_parent = nullptr;
+			}
+			// 2. parent 为根的树只是整棵树中的子树, 改变链接关系, 那么 subR 要顶替他的位置
+			else
+			{
+				if (ppNode->_left == parent)
+				{
+					ppNode->_left = subR;
+				}
+				else
+				{
+					ppNode->_right = subR;
+				}
+				subR->_parent = ppNode;
+			}
+
+			parent->_bf = subR->_bf = 0;
+		}
+
+		// 右单旋
+		void RotateR(Node* parent)
+		{
+			Node* ppNode = parent->_parent;
+			Node* subL = parent->_left;
+			Node* subLR = subL->_right;
+
+			parent->_left = subLR;
+			if (subLR)
+			{
+				subLR->_parent = parent;
+			}
+			subL->_right = parent;
+			parent->_parent = subL;
+
+			if (parent == _root)
+			{
+				_root = subL;
+				subL->_parent = nullptr;
+			}
+			else
+			{
+				if (ppNode->_left == parent)
+				{
+					ppNode->_left = subL;
+				}
+				else
+				{
+					ppNode->_right = subL;
+				}
+				subL->_parent = ppNode;
+			}
+
+			parent->_bf = subL->_bf = 0;
+		}
+
+		// 右左双旋
+		void RotateRL(Node* parent)
+		{
+			Node* subR = parent->_right;
+			Node* subRL = subR->_left;
+			int bf = subRL->_bf;
+
+			RotateR(parent->_right);
+			RotateL(parent);
+
+			if (bf == -1)
+			{
+				parent->_bf = 0;
+				subR->_bf = 1;
+				subRL->_bf = 0;
+			}
+			else if (bf == 1)
+			{
+				parent->_bf = -1;
+				subR->_bf = 0;
+				subRL->_bf = 0;
+			}
+			else if (bf == 0)
+			{
+				parent->_bf = 0;
+				subR->_bf = 0;
+				subRL->_bf = 0;
+			}
+		}
+
+		// 左右双旋
+		void RotateLR(Node* parent)
+		{
+			Node* subL = parent->_left;
+			Node* subLR = subL->_right;
+			int bf = subLR->_bf;
+
+			RotateL(subL);
+			RotateR(parent);
+
+			if (bf == 1)
+			{
+				parent->_bf = 0;
+				subL->_bf = -1;
+				subLR->_bf = 0;
+			}
+			else if (bf == -1)
+			{
+				parent->_bf = 1;
+				subL->_bf = 0;
+				subLR->_bf = 0;
+			}
+			else if (bf == 0)
+			{
+				parent->_bf = 0;
+				subL->_bf = 0;
+				subLR->_bf = 0;
+			}
+		}
+
+
+		// 中序遍历
+		//void _InOrder(Node* root)
+		//{
+		//	if (root == nullptr)
+		//	{
+		//		return;
+		//	}
+
+		//	_InOrder(root->_left);
+		//	std::cout << root->_kv.first << ":" << root->_kv.second << std::endl;
+		//	_InOrder(root->_right);
+		//}
+
+		//void InOrder()
+		//{
+		//	_InOrder(_root);
+		//	std::cout << std::endl;
+		//}
+
+		// 中序遍历 非递归
+		void InOrder()
+		{
+			std::stack<Node*> stack;
+			Node* cur = _root;
+
+			while (cur != nullptr || !stack.empty()) {
+				// 找到最左边的节点
+				while (cur != nullptr) {
+					stack.push(cur);
+					cur = cur->_left;
+				}
+
+				// 处理当前节点
+				cur = stack.top();
+				stack.pop();
+				std::cout << cur->_kv.first << ":" << cur->_kv.second << std::endl;
+
+				// 转向右子树
+				cur = cur->_right;
+			}
+			std::cout << std::endl;
+		}
+
+		// 前序遍历的递归实现
+		// 辅助函数
+		//void _PreOrder(Node* root)
+		//{
+		//	if (root == nullptr)
+		//	{
+		//		return;
+		//	}
+
+		//	std::cout << root->_kv.first << ":" << root->_kv.second << std::endl;   // 访问根节点
+		//	_PreOrder(root->_left);   // 访问左子树
+		//	_PreOrder(root->_right);  // 访问右子树
+		//}
+
+		//void PreOrder()
+		//{
+		//	_PreOrder(_root);
+		//	std::cout << std::endl;
+		//}
+
+		// 前序遍历的非递归实现
+		void PreOrder()
+		{
+			if (_root == nullptr)
+			{
+				return;
+			}
+
+			std::stack<Node*> stack;
+			stack.push(_root);
+
+			while (!stack.empty()) {
+				Node* cur = stack.top();
+				stack.pop();
+				std::cout << cur->_kv.first << ":" << cur->_kv.second << std::endl;  // 访问当前节点
+
+				// 先压入右子树再压入左子树（确保左子树先处理）
+				if (cur->_right != nullptr)
+				{
+					stack.push(cur->_right);
+				}
+				if (cur->_left != nullptr) {
+					stack.push(cur->_left);
+				}
+			}
+			std::cout << std::endl;
+		}
+
+		// 后序遍历的递归实现
+		// 辅助函数
+		//void _PostOrder(Node* root) {
+		//	if (root == nullptr)
+		//	{
+		//		return;
+		//	}
+
+		//	_PostOrder(root->_left);    // 访问左子树
+		//	_PostOrder(root->_right);   // 访问右子树
+		//	std::cout << root->_kv.first << ":" << root->_kv.second << std::endl;     // 访问根节点
+		//}
+
+		//void PostOrder()
+		//{
+		//	_PostOrder(_root);
+		//	std::cout << std::endl;
+		//}
+
+		// 后序遍历的非递归实现
+		void PostOrder()
+		{
+			if (_root == nullptr)
+			{
+				return;
+			}
+
+			std::stack<Node*> st;
+			Node* cur = _root;
+			Node* lastNode = nullptr; // 最近访问的节点
+			while (cur || !st.empty())
+			{
+				while (cur)
+				{
+					st.push(cur);
+					cur = cur->_left;
+				}
+
+				Node* top = st.top();
+				if ((top->_right == nullptr) || (lastNode == top->_right))
+				{
+					std::cout << top->_kv.first << ":" << top->_kv.second << std::endl;
+					lastNode = top;
+					st.pop();
+				}
+				else {
+					cur = top->_right;
+				}
+			}
+			std::cout << std::endl;
+		}
+
+		// 层序遍历
+		void LevelOrder()
+		{
+			if (_root == nullptr)
+			{
+				return;
+			}
+
+			std::queue<Node*> queue;
+			queue.push(_root);
+
+			while (!queue.empty())
+			{
+				Node* cur = queue.front();
+				queue.pop();
+				std::cout << cur->_kv.first << ":" << cur->_kv.second << std::endl;   // 访问当前节点
+
+				if (cur->_left != nullptr) {
+					queue.push(cur->_left);      // 将左子树压入队列
+				}
+				if (cur->_right != nullptr) {
+					queue.push(cur->_right);     // 将右子树压入队列
+				}
+			}
+			std::cout << std::endl;
+		}
+
+		// 查找后继节点
+		Node* findMin(Node* node)
+		{
+			while (node->_left != nullptr)
+			{
+				node = node->_left;
+			}
+			return node;
+		}
+
+		Node* FindSuccessor(Node* node)
+		{
+			if (node->_right != nullptr)
+			{
+				return findMin(node->_right);
+			}
+
+			Node* cur = _root;
+			Node* successor = nullptr;
+			while (cur != nullptr)
+			{
+				if (node->_kv.first < cur->_kv.first)
+				{
+					successor = cur;
+					cur = cur->_left;
+				}
+				else if (node->_kv.first > cur->_kv.first)
+				{
+					cur = cur->_right;
+				}
+				else
+				{
+					break;
+				}
+			}
+			return successor;
+		}
+
+		// 查找前驱节点
+		Node* findMax(Node* node)
+		{
+			while (node->_right != nullptr)
+			{
+				node = node->_right;
+			}
+			return node;
+		}
+
+		Node* FindPredecessor(Node* node)
+		{
+			if (node->_left != nullptr)
+			{
+				return findMax(node->_left);
+			}
+
+			Node* cur = _root;
+			Node* predecessor = nullptr;
+			while (cur != nullptr)
+			{
+				if (node->_kv.first < cur->_kv.first)
+				{
+					cur = cur->_left;
+				}
+				else if (node->_kv.first > cur->_kv.first)
+				{
+					predecessor = cur;
+					cur = cur->_right;
+				}
+				else
+				{
+					break;
+				}
+			}
+			return predecessor;
+		}
+
+		// 获取树的高度
+		int Height(Node* root)
+		{
+			if (root == nullptr)
+			{
+				return 0;
+			}
+
+			int leftHeight = Height(root->_left);
+			int rightHeight = Height(root->_right);
+
+			return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
+		}
+
+		// 判断是否是平衡二叉树
+		bool _IsBalance(Node* root)
+		{
+			if (root == nullptr)
+			{
+				return true;
+			}
+
+			int leftHeight = Height(root->_left);
+			int rightHeight = Height(root->_right);
+			if (abs(leftHeight - rightHeight) > 1)
+			{
+				return false;
+			}
+
+			return _IsBalance(root->_left) && _IsBalance(root->_right);
+		}
+
+		bool IsBalance()
+		{
+			return _IsBalance(_root);
+		}
+
+		// 查找 非递归
+		//Node* Find(const K& key)
+		//{
+		//	Node* cur = _root;
+		//	while (cur)
+		//	{
+		//		if (cur->_kv.first > key)
+		//		{
+		//			cur = cur->_left;
+		//		}
+		//		else if (cur->_kv.first < key)
+		//		{
+		//			cur = cur->_right;
+		//		}
+		//		else
+		//		{
+		//			return cur;
+		//		}
+		//	}
+		//	return nullptr;
+		//}
+
+		// 查找的递归实现
+		// 辅助函数
+		Node* _find(Node* root, const K& key)
+		{
+			if (root == nullptr || root->_kv.first == key)
+			{
+				return root;
+			}
+			if (key < root->_kv.first)
+			{
+				return _find(root->_left, key);
+			}
+			else
+			{
+				return _find(root->_right, key);
+			}
+		}
+
+		// 查找节点
+		Node* Find(const K& key)
+		{
+			return _find(_root, key);
+		}
+
+	private:
+		Node* _root = nullptr;
+	};
+}

Windows_AVLTree/Windows_AVLTree.sln

@@ -0,0 +1,31 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.7.34221.43
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "Windows_AVLTree", "Windows_AVLTree.vcxproj", "{3C530849-DC24-4616-BE04-AC7136C26007}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|x64 = Debug|x64
+		Debug|x86 = Debug|x86
+		Release|x64 = Release|x64
+		Release|x86 = Release|x86
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Debug|x64.ActiveCfg = Debug|x64
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Debug|x64.Build.0 = Debug|x64
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Debug|x86.ActiveCfg = Debug|Win32
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Debug|x86.Build.0 = Debug|Win32
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Release|x64.ActiveCfg = Release|x64
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Release|x64.Build.0 = Release|x64
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Release|x86.ActiveCfg = Release|Win32
+		{3C530849-DC24-4616-BE04-AC7136C26007}.Release|x86.Build.0 = Release|Win32
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {5CA83C61-F3A5-432C-8E40-DD56D62438F7}
+	EndGlobalSection
+EndGlobal

Windows_AVLTree/Windows_AVLTree.vcxproj

@@ -0,0 +1,138 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations">
+    <ProjectConfiguration Include="Debug|Win32">
+      <Configuration>Debug</Configuration>
+      <Platform>Win32</Platform>
+    </ProjectConfiguration>
+    <ProjectConfiguration Include="Release|Win32">
+      <Configuration>Release</Configuration>
+      <Platform>Win32</Platform>
+    </ProjectConfiguration>
+    <ProjectConfiguration Include="Debug|x64">
+      <Configuration>Debug</Configuration>
+      <Platform>x64</Platform>
+    </ProjectConfiguration>
+    <ProjectConfiguration Include="Release|x64">
+      <Configuration>Release</Configuration>
+      <Platform>x64</Platform>
+    </ProjectConfiguration>
+  </ItemGroup>
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+    <VCProjectVersion>17.0</VCProjectVersion>
+    <Keyword>Win32Proj</Keyword>
+    <ProjectGuid>{3c530849-dc24-4616-be04-ac7136c26007}</ProjectGuid>
+    <RootNamespace>WindowsAVLTree</RootNamespace>
+    <WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion>
+  </PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'" Label="Configuration">
+    <ConfigurationType>Application</ConfigurationType>
+    <UseDebugLibraries>true</UseDebugLibraries>
+    <PlatformToolset>v143</PlatformToolset>
+    <CharacterSet>Unicode</CharacterSet>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" Label="Configuration">
+    <ConfigurationType>Application</ConfigurationType>
+    <UseDebugLibraries>false</UseDebugLibraries>
+    <PlatformToolset>v143</PlatformToolset>
+    <WholeProgramOptimization>true</WholeProgramOptimization>
+    <CharacterSet>Unicode</CharacterSet>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|x64'" Label="Configuration">
+    <ConfigurationType>Application</ConfigurationType>
+    <UseDebugLibraries>true</UseDebugLibraries>
+    <PlatformToolset>v143</PlatformToolset>
+    <CharacterSet>Unicode</CharacterSet>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'" Label="Configuration">
+    <ConfigurationType>Application</ConfigurationType>
+    <UseDebugLibraries>false</UseDebugLibraries>
+    <PlatformToolset>v143</PlatformToolset>
+    <WholeProgramOptimization>true</WholeProgramOptimization>
+    <CharacterSet>Unicode</CharacterSet>
+  </PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <ImportGroup Label="ExtensionSettings">
+  </ImportGroup>
+  <ImportGroup Label="Shared">
+  </ImportGroup>
+  <ImportGroup Label="PropertySheets" Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">
+    <Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
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+      <FunctionLevelLinking>true</FunctionLevelLinking>
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+      <PreprocessorDefinitions>WIN32;NDEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
+      <ConformanceMode>true</ConformanceMode>
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+    <Link>
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+      <EnableCOMDATFolding>true</EnableCOMDATFolding>
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+    <ClCompile>
+      <WarningLevel>Level3</WarningLevel>
+      <SDLCheck>true</SDLCheck>
+      <PreprocessorDefinitions>_DEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
+      <ConformanceMode>true</ConformanceMode>
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+    <ClCompile>
+      <WarningLevel>Level3</WarningLevel>
+      <FunctionLevelLinking>true</FunctionLevelLinking>
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+      <SDLCheck>true</SDLCheck>
+      <PreprocessorDefinitions>NDEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
+      <ConformanceMode>true</ConformanceMode>
+    </ClCompile>
+    <Link>
+      <SubSystem>Console</SubSystem>
+      <EnableCOMDATFolding>true</EnableCOMDATFolding>
+      <OptimizeReferences>true</OptimizeReferences>
+      <GenerateDebugInformation>true</GenerateDebugInformation>
+    </Link>
+  </ItemDefinitionGroup>
+  <ItemGroup>
+    <ClCompile Include="AVLTree.cpp" />
+  </ItemGroup>
+  <ItemGroup>
+    <ClInclude Include="AVLTree.hpp" />
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <ImportGroup Label="ExtensionTargets">
+  </ImportGroup>
+</Project>

Windows_AVLTree/Windows_AVLTree.vcxproj.filters

@@ -0,0 +1,27 @@
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+<Project ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup>
+    <Filter Include="源文件">
+      <UniqueIdentifier>{4FC737F1-C7A5-4376-A066-2A32D752A2FF}</UniqueIdentifier>
+      <Extensions>cpp;c;cc;cxx;c++;cppm;ixx;def;odl;idl;hpj;bat;asm;asmx</Extensions>
+    </Filter>
+    <Filter Include="头文件">
+      <UniqueIdentifier>{93995380-89BD-4b04-88EB-625FBE52EBFB}</UniqueIdentifier>
+      <Extensions>h;hh;hpp;hxx;h++;hm;inl;inc;ipp;xsd</Extensions>
+    </Filter>
+    <Filter Include="资源文件">
+      <UniqueIdentifier>{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}</UniqueIdentifier>
+      <Extensions>rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms</Extensions>
+    </Filter>
+  </ItemGroup>
+  <ItemGroup>
+    <ClCompile Include="AVLTree.cpp">
+      <Filter>源文件</Filter>
+    </ClCompile>
+  </ItemGroup>
+  <ItemGroup>
+    <ClInclude Include="AVLTree.hpp">
+      <Filter>头文件</Filter>
+    </ClInclude>
+  </ItemGroup>
+</Project>

Windows_AVLTree/Windows_AVLTree.vcxproj.user

@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project ToolsVersion="Current" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <PropertyGroup />
+</Project>

Windows_AVLTree/x64/Debug/Windows_AVLTree.exe.recipe

@@ -0,0 +1,11 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project>
+  <ProjectOutputs>
+    <ProjectOutput>
+      <FullPath>E:\Git 仓库\公开仓库\7_AVLTree\Windows_AVLTree\x64\Debug\Windows_AVLTree.exe</FullPath>
+    </ProjectOutput>
+  </ProjectOutputs>
+  <ContentFiles />
+  <SatelliteDlls />
+  <NonRecipeFileRefs />
+</Project>

Windows_AVLTree/x64/Debug/Windows_AVLTree.log

@@ -0,0 +1,2 @@
+  AVLTree.cpp
+  Windows_AVLTree.vcxproj -> E:\Git 仓库\公开仓库\7_AVLTree\Windows_AVLTree\x64\Debug\Windows_AVLTree.exe

Windows_AVLTree/x64/Debug/Windows_AVLTree.tlog/Cl.items.tlog

@@ -0,0 +1 @@
+E:\Git 仓库\公开仓库\7_AVLTree\Windows_AVLTree\AVLTree.cpp;E:\Git 仓库\公开仓库\7_AVLTree\Windows_AVLTree\x64\Debug\AVLTree.obj

Windows_AVLTree/x64/Debug/Windows_AVLTree.tlog/Windows_AVLTree.lastbuildstate

@@ -0,0 +1,2 @@
+PlatformToolSet=v143:VCToolArchitecture=Native64Bit:VCToolsVersion=14.37.32822:TargetPlatformVersion=10.0.22000.0:
+Debug|x64|E:\Git 仓库\公开仓库\7_AVLTree\Windows_AVLTree\|

Windows_AVLTree/x64/Debug/Windows_AVLTree.vcxproj.FileListAbsolute.txt

@@ -0,0 +1 @@
+E:\Git 仓库\公开仓库\7_AVLTree\Windows_AVLTree\x64\Debug\Windows_AVLTree.exe