二叉搜索树实现详解以及二叉树搜索树部分函数实现(C++)

每一个节点的类型

template
struct BStreeNode {
	BStreeNode() :right(nullptr),left(nullptr),data(T()){}
	BStreeNode* right;
	BStreeNode* left;
	T data;
};

构造函数：在这里只需要构造一个空的节点就可以，当作根来使用

typedef BStreeNode Node;
	BStree():root(nullptr){}

二叉树的插入操作：首先如果树是空的那么直接插入都根的位置即可，如果树不空，则先查找插入节点的位置，这里根据二叉搜索树的特点进行查找，找到插入位置时插入数据即可。

void Insert(const T& x) {
		if (root == nullptr)
		{
			root = new Node;
			root->data = x;	
		}
		//找插入位置的双亲节点
		Node* cur = root;
		Node* parent=nullptr;
		while (cur) {
			parent = cur;
			
			if (cur->data > x) cur = cur->left;
		    else if (cur->data < x) cur = cur->right;
			else 
				return;
		}
		//插入节点
		cur = new Node;
		cur->data = x;
		if (parent->data < x) parent->right = cur;
		else if (parent->data > x) parent->left = cur;
		else 
			return;
	}

查找操作：根据二叉搜索树的性质进行查找。

bool Find_tree(const T& data) {
		if (root) {
			Node* cur = root;//记录节点

			while (cur)
			{
				if (data == cur->data)  return true; 
				else if (data > cur->data) cur = cur->right;
				else if (data < cur->data) cur = cur->left;
			}
			return false;
		}
	}

删除操作：这可以说是二叉搜索树的核心操作了，首先查找删除位置，中跟上述的查找是一样的，但是删除时不一样的位置有不一样的删除方法。

void Erase_tree(const T& data) {

		//查找节点
		Node* cur = root;
		Node* parent = nullptr;
		while (cur) {
			if (data == cur->data)  break;
			else if (data > cur->data) { parent = cur; cur = cur->right; }
			else if (data < cur->data) { parent = cur; cur = cur->left; }
		}
		if (cur == nullptr) return;//另一个作用可以判断是否为空树
		//删除节点
		if (nullptr == cur->left&&cur->right!=nullptr)
		{
			if (parent == nullptr) 
				root = cur->right;
			if (cur->right != nullptr&&parent->left==cur) parent->left = cur->right;
			if (cur->right != nullptr&&parent->right==cur) parent->right = cur->right;
		}

		if (nullptr == cur->right&&cur->left!=nullptr)
		{
			if (parent == nullptr) root = cur->left;
			root = cur->right;
			if (cur->left != nullptr && parent->left == cur) parent->left = cur->left;
			if (cur->left != nullptr && parent->right == cur) parent->right = cur->left;

		}
		if (cur->left != nullptr && cur->right != nullptr) {
			Node* DelNode = cur->right;
			parent = cur;
			while(DelNode->left) {//找右子树中最左边的节点
				parent = DelNode;
				DelNode = DelNode->left;
			}
			cur->data = DelNode->data;

			//删除替代节点
			//记录删除的右节点
			if (parent->left == DelNode) parent->left = DelNode->right;
			else parent->right = DelNode->right;

			cur = DelNode;
			
		}
		delete cur;
		cur = nullptr;
	}

二叉树的回收：不能像回收链表一样直接回收根节点，二叉树回收要一个节点一个节点去删除，并且删除过程不能丢失节点，因此本文使用后序遍历回收节点。

	void Destory(Node*& proot) {
		if (proot) {
			Destory(proot->left);
			Destory(proot->right);
			delete proot;
			proot = nullptr;
		}
	}

二叉树的层序遍历：借助队列进行实现。

void Level_Oreder() {//层序遍历
		if (root == nullptr)  return;

		//借助queue容器
		queue q;
		
		q.push(root);
		while (!q.empty()) {
			Node* cur = q.front();
			cout << cur->data<<" ";
			q.pop();
			if (cur->left) q.push(cur->left);
			if (cur->right) q.push(cur->right);
			
		}
	}

以上是较为重要的函数，其中三种递归遍历方式付在源代码中。

#include
#include
using namespace std;
template
struct BStreeNode {
	BStreeNode() :right(nullptr),left(nullptr),data(T()){}
	BStreeNode* right;
	BStreeNode* left;
	T data;
};
template
class BStree {
public:
	typedef BStreeNode Node;
	BStree():root(nullptr){}

	void Insert(const T& x=T()) {
		if (root == nullptr)
		{
			root = new Node;
			root->data = x;	
		}
		//找插入位置的双亲节点
		Node* cur = root;
		Node* parent=nullptr;
		while (cur) {
			parent = cur;
			
			if (cur->data > x) cur = cur->left;
		    else if (cur->data < x) cur = cur->right;
			else 
				return;
		}
		//插入节点
		cur = new Node;
		cur->data = x;
		if (parent->data < x) parent->right = cur;
		else if (parent->data > x) parent->left = cur;
		else 
			return;
	}
	~BStree()
	{
		Destory(root);
	}

	void Show_tree() {
		Show(root);
	}
	bool Find_tree(const T& data) {
		if (root) {
			Node* cur = root;//记录节点

			while (cur)
			{
				if (data == cur->data)  return true; 
				else if (data > cur->data) cur = cur->right;
				else if (data < cur->data) cur = cur->left;
			}
			return false;
		}
	}

	void Erase_tree(const T& data) {

		//查找节点
		Node* cur = root;
		Node* parent = nullptr;
		while (cur) {
			if (data == cur->data)  break;
			else if (data > cur->data) { parent = cur; cur = cur->right; }
			else if (data < cur->data) { parent = cur; cur = cur->left; }
		}
		if (cur == nullptr) return;//另一个作用可以判断是否为空树
		//删除节点
		if (nullptr == cur->left&&cur->right!=nullptr)
		{
			if (parent == nullptr) 
				root = cur->right;
			if (cur->right != nullptr&&parent->left==cur) parent->left = cur->right;
			if (cur->right != nullptr&&parent->right==cur) parent->right = cur->right;
		}

		if (nullptr == cur->right&&cur->left!=nullptr)
		{
			if (parent == nullptr) root = cur->left;
			root = cur->right;
			if (cur->left != nullptr && parent->left == cur) parent->left = cur->left;
			if (cur->left != nullptr && parent->right == cur) parent->right = cur->left;

		}
		if (cur->left != nullptr && cur->right != nullptr) {
			Node* DelNode = cur->right;
			parent = cur;
			while(DelNode->left) {//找右子树中最左边的节点
				parent = DelNode;
				DelNode = DelNode->left;
			}
			cur->data = DelNode->data;

			//删除替代节点
			//记录删除的右节点
			if (parent->left == DelNode) parent->left = DelNode->right;
			else parent->right = DelNode->right;

			cur = DelNode;
			
		}
		delete cur;
		cur = nullptr;
	}
	
	void Level_Oreder() {//层序遍历
		if (root == nullptr)  return;

		//借助queue容器
		queue q;
		
		q.push(root);
		while (!q.empty()) {
			Node* cur = q.front();
			cout << cur->data<<" ";
			q.pop();
			if (cur->left) q.push(cur->left);
			if (cur->right) q.push(cur->right);
			
		}
	}
private:
	Node* root;//根节点
private:
	void Show(Node* root) {
		if (root) {
			Show(root->left);
			cout << root->data << " ";
			Show(root->right);
		}
	}

	void Destory(Node*& proot) {
		if (proot) {
			Destory(proot->left);
			Destory(proot->right);
			delete proot;
			proot = nullptr;
		}
	}
	
};