BSTree.h

#pragma once

namespace key {

	template<class K>//这里习惯用K而不是T，key
	struct BSTreeNode {
		BSTreeNode<K>* _left;
		BSTreeNode<K>* _right;
		K _key;

		BSTreeNode(const K& key)
			:_left(nullptr)
			, _right(nullptr)
			, _key(key)
		{}
	};

	template<class K>
	class BSTree {//这里简写了，一般应该写全称：BinarySearchTree
		typedef BSTreeNode<K> Node;//在类域内部重命名以防冲突

	public:
		BSTree() = default; // 制定强制生成默认构造

		BSTree(const BSTree<K>& t){
			_root = Copy(t._root);
		}

		BSTree<K>& operator=(BSTree<K> t){
			swap(_root, t._root);
			return *this;
		}

		~BSTree(){
			Destroy(_root);
			//_root = nullptr;
		}

		//插入
		bool Insert(const K& key) {//可能插入失败，BSTree默认不允许冗余，若试图插入已存在的元素便会失败
		//树的形状只取决于插入的先后顺序，最先插入的元素便是根
			if (_root == nullptr) {
				_root = new Node(key);
				return true;
			}
			//找到可插入的位置
			Node* parent = nullptr;
			Node* cur = _root;
			while (cur) {
				if (cur->_key < key) {
					parent = cur;
					cur = cur->_right;
				}
				else if (cur->_key > key) {
					parent = cur;
					cur = cur->_left;
				}
				else {//相等的情况插入失败
					return false;
				}
			}
			cur = new Node(key);
			//链接
			if (parent->_key < key) {
				parent->_right = cur;
			}
			else {
				parent->_left = cur;
			}
			return true;
		}

		//查找
		bool Find(const K& key) {
			Node* cur = _root;
			while (cur) {
				if (cur->_key < key) {
					cur = cur->_right;
				}
				else if (cur->_key > key) {
					cur = cur->_left;
				}
				else {
					return true;
				}
			}
			return false;
		}

		//删除(难点)
		bool Erase(const K& key) {
			Node* parent = nullptr;
			Node* cur = _root;
			while (cur) {
				//找到要删的值
				if (cur->_key < key) {
					parent = cur;
					cur = cur->_right;
				}
				else if (cur->_key > key) {
					parent = cur;
					cur = cur->_left;
				}
				else {//找到目标，开始删除
					if (cur->_left == nullptr) {//1.左为空
						if (cur == _root) {//处理删根的情况
							_root = cur->_right;
						}
						else {
							if (parent->_left == cur) {
								parent->_left = cur->_right;//托孤右子节点
							}
							else {
								parent->_right = cur->_right;
							}
						}
						delete cur;
					}
					else if (cur->_right == nullptr) {//2.右为空
						if (cur == _root) {//处理删根的情况
							_root = cur->_left;
						}
						else {
							if (parent->_left == cur) {
								parent->_left = cur->_left;//托孤左子节点
							}
							else {
								parent->_right = cur->_right;
							}
						}
						delete cur;
					}
					else {//3.左右都不为空，不能托孤两个，改找保姆：左树的最大节点(左树最右节点)或右树的最小节点(右树最左节点)
						//这里找右树的最小节点
						Node* pminRight = cur;//不能是nullptr，若根就是最左节点会进不了循环
						Node* minRight = cur->_right;
						while (minRight->_left) {
							pminRight = minRight;
							minRight = minRight->_left;
						}
						cur->_key = minRight->_key;
						if (pminRight->_left == minRight) {
							pminRight->_left = minRight->_right;
						}
						else {
							pminRight->_right = minRight->_right;
						}
						delete minRight;
					}
					return true;
				}
			}
			return false;//未找到目标数值，故未进行删除操作
		}

		//递归插入
		bool InsertR(const K& key) {
			return _InsertR(_root, key);
		}

		//递归查找
		bool FindR(const K& key){
			return _FindR(_root, key);
		}

		//递归删除
		bool EraseR(const K& key){
			return _EraseR(_root, key);
		}

		//中序递归遍历
		void InOrder() {//为便于调用，套一层无参的壳让子函数带参递归
			_InOrder(_root);
			cout << endl;
		}

	protected:
		Node* Copy(Node* root){
			if (root == nullptr)
				return nullptr;

			Node* newRoot = new Node(root->_key);
			newRoot->_left = Copy(root->_left);
			newRoot->_right = Copy(root->_right);
			return newRoot;
		}

		void Destroy(Node*& root){
			if (root == nullptr) {
				return;
			}

			Destroy(root->_left);
			Destroy(root->_right);

			delete root;
			root = nullptr;
		}

		bool _FindR(Node* root, const K& key){
			if (root == nullptr)
				return false;

			if (root->_key == key)
				return true;

			if (root->_key < key)
				return _FindR(root->_right, key);
			else
				return _FindR(root->_left, key);
		}

		bool _InsertR(Node*& root, const K& key){
			if (root == nullptr){
				root = new Node(key);
				return true;
			}

			if (root->_key < key){
				return _InsertR(root->_right, key);
			}
			else if (root->_key > key){
				return _InsertR(root->_left, key);
			}
			else{
				return false;
			}
		}

		bool _EraseR(Node*& root, const K& key){
			if (root == nullptr)
				return false;

			if (root->_key < key){
				return _EraseR(root->_right, key);
			}
			else if (root->_key > key){
				return _EraseR(root->_left, key);
			}
			else{
				Node* del = root;

				// 开始准备删除
				if (root->_right == nullptr){
					root = root->_left;
				}
				else if (root->_left == nullptr){
					root = root->_right;
				}
				else{
					Node* maxleft = root->_left;
					while (maxleft->_right)
					{
						maxleft = maxleft->_right;
					}

					swap(root->_key, maxleft->_key);

					return _EraseR(root->_left, key);
				}
				delete del;
				return true;
			}
		}

		void _InOrder(Node* root) {
			//↑不能缺省传Node* root = _root ，因为:
			//1.缺省参数必须是常量或全局变量或静态变量2.访问成员变量需要的this指针只能在函数内部使用。
			if (root == nullptr) {
				return;
			}
			_InOrder(root->_left);
			cout << root->_key << " ";
			_InOrder(root->_right);
		}

	private:
		Node* _root = nullptr;
	};

}

namespace key_value{

	template<class K, class V>
	struct BSTreeNode{
		BSTreeNode<K, V>* _left;
		BSTreeNode<K, V>* _right;
		K _key;
		V _value;

		BSTreeNode(const K& key, const V& value)
			:_left(nullptr)
			, _right(nullptr)
			, _key(key)
			, _value(value)
		{}
	};

	template<class K, class V>
	class BSTree{
		typedef BSTreeNode<K, V> Node;
	public:
		bool Insert(const K& key, const V& value){
			if (_root == nullptr){
				_root = new Node(key, value);
				return true;
			}

			Node* parent = nullptr;
			Node* cur = _root;
			while (cur){
				if (cur->_key < key){
					parent = cur;
					cur = cur->_right;
				}
				else if (cur->_key > key){
					parent = cur;
					cur = cur->_left;
				}
				else{
					return false;
				}
			}

			cur = new Node(key, value);
			if (parent->_key < key){
				parent->_right = cur;
			}
			else{
				parent->_left = cur;
			}

			return true;
		}

		Node* Find(const K& key){
			Node* cur = _root;
			while (cur){
				if (cur->_key < key){
					cur = cur->_right;
				}
				else if (cur->_key > key){
					cur = cur->_left;
				}
				else{
					return cur;
				}
			}

			return nullptr;
		}

		bool Erase(const K& key){
			Node* parent = nullptr;
			Node* cur = _root;

			while (cur){
				if (cur->_key < key){
					parent = cur;
					cur = cur->_right;
				}
				else if (cur->_key > key){
					parent = cur;
					cur = cur->_left;
				}
				else{
					if (cur->_left == nullptr){
						if (cur == _root){
							_root = cur->_right;
						}
						else{
							if (parent->_left == cur){
								parent->_left = cur->_right;
							}
							else{
								parent->_right = cur->_right;
							}
						}
						delete cur;

					}
					else if (cur->_right == nullptr){
						if (cur == _root){
							_root = cur->_left;
						}
						else{
							if (parent->_left == cur){
								parent->_left = cur->_left;
							}
							else{
								parent->_right = cur->_left;
							}
						}
						delete cur;
					}
					else{
						Node* pminRight = cur;
						Node* minRight = cur->_right;
						while (minRight->_left){
							pminRight = minRight;
							minRight = minRight->_left;
						}

						cur->_key = minRight->_key;

						if (pminRight->_left == minRight){
							pminRight->_left = minRight->_right;
						}
						else{
							pminRight->_right = minRight->_right;
						}

						delete minRight;
					}
					return true;
				}
			}
			return false;
		}

		void InOrder(){
			_InOrder(_root);
			cout << endl;
		}

	protected:
		void _InOrder(Node* root){
			if (root == nullptr)
				return;

			_InOrder(root->_left);
			cout << root->_key << ":" << root->_value << endl;
			_InOrder(root->_right);
		}
	private:
		Node* _root = nullptr;
	};
}

test.cpp

#include <iostream>
#include <string>
using namespace std;

#include "BSTree.h"

void TestBSTree1(){
	int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };
	key::BSTree<int> t1;

	for (auto e : a){
		t1.Insert(e);
	}
	
	t1.InOrder();

	//t1.Erase(4);
	//t1.InOrder();

	//t1.Erase(14);
	//t1.InOrder();

	//t1.Erase(3);
	//t1.InOrder();

	t1.Erase(8);
	t1.InOrder();


	for (auto e : a){
		t1.Erase(e);
		t1.InOrder();
	}

	t1.InOrder();
}

void TestBSTree2(){
	int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };
	key::BSTree<int> t1;

	for (auto e : a){
		t1.InsertR(e);
	}
	t1.InOrder();

	t1.EraseR(10);
	t1.EraseR(14);
	t1.EraseR(13);
	t1.InOrder();

	for (auto e : a){
		t1.EraseR(e);
		t1.InOrder();
	}

	t1.InOrder();
}

void TestBSTree3(){
	int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };
	key::BSTree<int> t1;
	for (auto e : a){
		t1.InsertR(e);
	}

	t1.InOrder();

	key::BSTree<int> t2(t1);
	t2.InOrder();

	cout << endl;
}

void TestBSTree4(){
	key_value::BSTree<string, string> dict;
	dict.Insert("sort", "排序");
	dict.Insert("left", "左");
	dict.Insert("right", "右");
	dict.Insert("string", "字符串");
	dict.Insert("insert", "插入");
	dict.Insert("erase", "删除");
	dict.Insert("菠萝", "面包");

	string str;
	while (cin >> str){
		auto ret = dict.Find(str);
		if (ret){
			cout << ":" << ret->_value << endl;
		}
		else{
			cout << "无此单词" << endl;
		}
	}
}

void TestBSTree5(){
	string arr[] = { "门", "大桥", "鸭", "鸭", "大桥", "大桥", "大桥", "门", "门", "门", "二四六", "七八" };

	key_value::BSTree<string, int> countTree;
	for (auto str : arr){
		//key_value::BSTreeNode<string, int>* ret = countTree.Find(str);
		auto ret = countTree.Find(str);
		if (ret == nullptr){
			countTree.Insert(str, 1);
		}
		else{
			ret->_value++;
		}
	}

	countTree.InOrder();
}

int main(){
	TestBSTree1();
	TestBSTree2();
	TestBSTree3();
	TestBSTree5();

	TestBSTree4();

	return 0;
}

运行结果：