AVL树C++实现（插入，删除，查找，清空，遍历操作）

AVL.h文件代码

#pragma once
#include<iostream>
#include<stack>

#include <assert.h>
using namespace std;
using namespace std;
template<class T>
struct AVLNode{
	T data;
	AVLNode<T>*left, *right;
	int bf;
	AVLNode() :left(NULL), right(NULL), bf(0) {}
	AVLNode(T d, AVLNode<T>*l=NULL,AVLNode<T>*r=NULL):data(d),left(l),right(r),bf(0){}
};
template<class T>
class AVLTree {
public:
	AVLTree():root(NULL){}
	~AVLTree() {};
	AVLTree(T Ref):Refvalue(Ref),root(NULL){}
	bool insert(AVLNode<T>*&ptr, T&e1);
	bool Remove(AVLNode<T>*&ptr, T x);
	void RotateL(AVLNode<T>*&ptr);
	void RotateR(AVLNode<T>*&ptr);
	void PrintBinTree(AVLNode<T>*&t, int level);
	void RotateLR(AVLNode<T>*&ptr);
	void RotateRL(AVLNode<T>*&ptr);
	AVLNode<T>* search(const T x, AVLNode<T>*ptr);
	friend istream& operator>>(istream&, AVLTree<T>& Tree);
	friend ostream& operator<<(ostream&, AVLTree<T>&Tree);
	void Delete(AVLNode<T>*ptr);
	void output(AVLNode<T>*ptr, ostream&out);
	AVLNode<T>*root;
	T Refvalue;
private:

};
template<class T>
void AVLTree<T>::RotateL(AVLNode<T>*&ptr) {
	AVLNode<T>*subL = ptr;
	ptr = subL->right;
	subL->right = ptr->left;
	ptr->left = subL;
	ptr->bf = subL->bf = 0;
}
template<class T>
void AVLTree<T>::RotateR(AVLNode<T>*&ptr) {
	AVLNode<T>*subR = ptr;
	ptr = subR->left;
	subR->left = ptr->right;
	ptr->right = subR;
	ptr->bf = subR->bf = 0;
}
template<class T>
void AVLTree<T>::RotateLR(AVLNode<T>*&ptr) {
	AVLNode<T>*subR = ptr, *subL = subR->left;
	ptr = subL->right;
	subL->right = ptr->left;
	ptr->left = subL;
	if (ptr->bf <= 0)subL->bf = 0;
	else subL->bf = -1;
	subR->left = ptr->right;
	ptr->right = subR;
	if (ptr->bf == -1)subR->bf = 1;
	else subR->bf = 0;
	ptr->bf = 0;
}
template<class T>
void AVLTree<T>::RotateRL(AVLNode<T>*&ptr) {
	AVLNode<T>*subL = ptr, *subR = subL->right;
	ptr = subR->left;
	subR->left = ptr->right;
	ptr->right = subR;
	if (ptr->bf >= 0)subR->bf = 0;
	else subR->bf = 1;
	subL->right = ptr->left;
	ptr->left = subL;
	if (ptr->bf == 1)subL->bf = -1;
	else subL->bf = 0;
	ptr->bf = 0;
}
template<class T>
bool AVLTree<T>::insert(AVLNode<T>*&ptr, T&e1) {
	AVLNode<T>*pr = NULL, *p = ptr, *q; int d;
	stack<AVLNode<T>*>st;
	while (p!=NULL)
	{
		if (e1 == p->data) {
			cout << "存在，无法插入\n"; return false;
		}
		pr = p; st.push(pr);
		if (e1 < p->data)p = p->left;
		else p = p->right;
	}
	p = new AVLNode<T>(e1);
	if (p == NULL) { cout << "内存不足" << endl; exit(1); }
	if (pr == NULL) { ptr = p; return true; }//空树，根结点插入
	if (e1 < pr->data)pr->left = p;
	else pr->right = p;
	while (st.empty()==false)
	{
		pr = st.top();
		st.pop();
		if (p == pr->left)pr->bf--;
		else pr->bf++;
		if (pr->bf == 0)break;//case 1,平衡退出
		if (abs(pr->bf) == 1) {//case 2
			p = pr;//回溯
		}
		else {//case 3 |bf|==2
			d = (pr->bf < 0) ? -1 : 1;
			if (p->bf == d) {
				if (d == -1)RotateR(pr);
				else RotateL(pr);
			}
			else {
				if (d == -1)RotateLR(pr);
				else RotateRL(pr);
			}
			break;
		}
	}
	if (st.empty() == true)ptr = pr;
	else {
		q = st.top();
		if (q->data > pr->data)q->left = pr;
		else q->right = pr;
	}
	return true;
}
//template<class T>
istream& operator >>(istream& in, AVLTree<int>& Tree) {
	int item;
	in >> item;
	while (item!=Tree.Refvalue)
	{

		Tree.insert(Tree.root,item);
		in >> item;

	}
	return in;
}

//template<class T>
ostream& operator<<(  ostream&out, AVLTree<int>&Tree) {
	out << "中序遍历输出各个结点数值:" << endl;
	Tree.output(Tree.root,out);
	out << endl;
	return out;

}
template<class T>
void AVLTree<T>::output(AVLNode<T>*ptr, ostream&out) {
	if (ptr != NULL) {
		output(ptr->left, out);
		cout << ptr->data << " ";
		output(ptr->right, out);
	}
}
template<class T>
AVLNode<T>* AVLTree<T>::search(const T x, AVLNode<T>*ptr) {
	if (ptr == NULL)return NULL;
	else if (x < ptr->data)return search(x, ptr->left);
	else if (x > ptr->data)return search(x, ptr->right);
	else return ptr;
}

template<class T>
void AVLTree<T>::Delete(AVLNode<T>*ptr) {
	if (ptr != NULL){
		Delete(ptr->left);
		Delete(ptr->right);
		delete ptr;
	}

}

template <class T>
void AVLTree<T>::PrintBinTree(AVLNode<T>*&t, int level)
{
	if (t == NULL)return;
	PrintBinTree(t->right, level + 1);
	for (int i = 0; i < 4 * (level - 1); i++)cout << " ";
	cout << t->data << endl;
	PrintBinTree(t->left, level + 1);
}

template<class T>
bool  AVLTree<T>::Remove(AVLNode<T>*&t, T val)
{
	assert(t != nullptr);

	AVLNode<T> *tmp = t;
	AVLNode<T> *pre_tmp = nullptr;
	AVLNode<T> *ppre_tmp = nullptr;
	AVLNode<T> *it_tmp = nullptr;
	stack<AVLNode<T>*> st;
	int sign, lable;    //符号标记
	int flag = 0;       //子树标记，下文具体解释

	while (tmp != nullptr) {
		if (tmp->data == val)       //找到跳出循环
			break;

		pre_tmp = tmp;
		st.push(pre_tmp);

		if (tmp->data > val)
			tmp = tmp->left;
		else
			tmp = tmp->right;
	}

	if (tmp == nullptr)               //未找到，返回
		return false;
	else if (tmp->left!= nullptr && tmp->right != nullptr) {
		pre_tmp = tmp;               //将有两个孩子的节点转化为只有一个孩子的节点，方法是寻找它中序遍历的直接前驱或后继
		st.push(pre_tmp);

		it_tmp = tmp->left;
		while (it_tmp->right!= nullptr) {
			pre_tmp = it_tmp;
			st.push(pre_tmp);
			it_tmp = it_tmp->right;
		}
		tmp->data = it_tmp->data;      //覆盖要删除的节点
		tmp = it_tmp;                      //tmp指向要删除的节点，函数结束前会delete tmp
	}

	if (tmp->left!= nullptr) {        //这样的判断方式会导致删除一个节点下两个没有孩子节点的节点时，由于左孩子均为空，直接跳入else
		it_tmp = tmp->left;
	}
	else {
		it_tmp = tmp->right;
	}

	if (pre_tmp == nullptr)
		t = it_tmp;
	else {
		if (pre_tmp->left== tmp) {   //上面直接跳入else，但我们在此处加上flag，用来识别它到底是pre_tmp的左孩子还是右孩子。
			flag = 0;
			pre_tmp->left= it_tmp;
		}
		else {
			flag = 1;
			pre_tmp->right = it_tmp;
		}

		while (!st.empty()) {
			pre_tmp = st.top();
			st.pop();

			if (pre_tmp->left == it_tmp && flag == 0)//此处flag=0，防止pre_tmp的左孩子为空，右孩子同样为空，直接进入else
				pre_tmp->bf++;
			else
				pre_tmp->bf--;

			if (!st.empty())
			{
				ppre_tmp = st.top();
				if (ppre_tmp->left == pre_tmp)
				{
					sign = -1;      //sign用来识别是祖父节点的左孩子还是右孩子，下文链接会用上
					flag = 0;
				}
				else {
					sign = 1;
					flag = 1;
				}
			}
			else
				sign = 0;    //栈空，它的祖先节点不存在，pre_tmp即为根节点，但是这里也要写上，否则sign的值会遗留下来

			if (pre_tmp->bf == -1 || pre_tmp->bf == 1)
				break;           //已经平衡，直接跳出
			if (pre_tmp->bf != 0) {      //m_bf为+2/-2
				if (pre_tmp->bf < 0) {
					lable = -1;          //lable表示父节点符号，下面会用来区分同号异号
					it_tmp = pre_tmp->left;
				}
				else {
					lable = 1;
					it_tmp = pre_tmp->right;
				}

				if (it_tmp->bf == 0) {       //pre_tmp的较高子树的头节点m_bf为0
					if (lable == -1) {
						RotateR(pre_tmp);
						pre_tmp->bf = 1;
						pre_tmp->right->bf = -1;
					}
					else {
						RotateL(pre_tmp);
						pre_tmp->bf = -1;
						pre_tmp->left->bf = 1;
					}
					break;           //直接跳出，并没有链接，需要下文写上链接
				}

				if (it_tmp->bf == lable) {       //同号
					lable == 1 ? RotateL(pre_tmp) : RotateLR(pre_tmp);
				}
				else {                            //异号
					lable == -1 ? RotateLR(pre_tmp): RotateRL(pre_tmp);
				}
				//sign == -1 ? ppre_tmp->left_child = pre_tmp                //不能写成这样，因为sign值可能为0，会直接进入后者
				//						: ppre_tmp->right_child = pre_tmp;   //!!!!! sign maybe 0 ! not only1 or -1 !!! warning!
				if (sign == -1)
					ppre_tmp->left = pre_tmp;
				else if (sign == 1)            //else if正确方式
					ppre_tmp->right = pre_tmp;
			}
			it_tmp = pre_tmp;       //回溯
		}
		if (st.empty())              //栈为空，根节点
			t = pre_tmp;
		else {             //这一段else参考书上没有，书是错的，如果不写此处，290break直接跳出while循环，会导致链接不上，数据丢失
			ppre_tmp = st.top();
			if (ppre_tmp->data > pre_tmp->data)
				ppre_tmp->left = pre_tmp;
			else
				ppre_tmp->right = pre_tmp;
		}
	}
	delete tmp;
	tmp = nullptr;
	return true;

}

源cpp代码

#include"AVL.h"
#include<iostream>
using namespace std;
int main()
{
	AVLTree<int> tree;
	cout << "建立AVL树，终止表示设为0" << endl;
	tree.Refvalue = 0;
	cout << "1:建树\n2:插入\n3:搜索\n4:删除\n5:输出\n6:清空\n7:退出\n";
	bool over = false;
	while (!over)
	{
		int c;
		int num;

		cin >> c;
		switch (c)
		{
	case 1: {
		cin >> tree;
		cout << "建树完毕\n";
		break;
	}
	case 2: {
		cin >> num; tree.insert(tree.root, num); cout << "插入完毕\n"; break; }
	case 3: {cin >> num; if (tree.search(num, tree.root) != NULL)cout << num << "已经被找到\n"; else cout << num << "不存在\n"; break; }
	case 4: {cin >> num; tree.Remove(tree.root, num); }
	case 5: {cout << tree; cout << " 凹凸打印AVL树\n"; tree.PrintBinTree(tree.root, 1); break; }
    case 6: {
		//tree.Delete(tree.root);
		tree.root=NULL;
		break; }
	case 7:{  over = true; break; }
		default:cout << "输入有误\n";
			break;
		}
	}

	char ch;
	cin >> ch;
}