北邮数据结构（二叉平衡树）

题目要求：

根据平衡二叉树的抽象数据类型的定义，使用二叉链表实现一个平衡二叉树。

二叉树的基本功能：

1、平衡二叉树的建立

2、平衡二叉树的查找

3、平衡二叉树的插入

4、平衡二叉树的删除

5、平衡二叉树的销毁

6、其他：自定义操作

编写测试main()函数测试平衡二叉树的正确性。

 头文件：

BalancedTree.h

#include
#include 
#include
#include
using	namespace	std;

templateclass	BiNode
{
public:
	T	val;
	BiNode	*lch;
	BiNode	*rch;
	BiNode(T	v) :val(v), lch(NULL), rch(NULL) {};	//构造函数 
	BiNode() :lch(NULL), rch(NULL) {};	//构造函数
	//BinaryTreeNode(keyType v):value(v),m_pLeft(nullptr),m_pRight(nullptr){}

};

templateclass	BST
{

public:
	BST(T	r[], int	n);	//构造函数   
	//~BST();	//析构函数 
	void destroy();
	void Release(BiNode*root);//析构辅助函数
	bool Search(BiNode*R, T	key);	//查找关键字key
	BiNode *insertBiNode(BiNode *&root, T val);	//插入结点
	void	Delete(BiNode*&R);	//删除结点
	bool	DeleteBST(BiNode*&R, T	key);	//删除关键字key 
	int 	height(BiNode* root); 	//判断树的高度 	 
	bool 	isBalanced(BiNode* root); //判断树是否为二叉平衡树 
	int		diff(BiNode	*root);	//计算平衡因子 
	BiNode	*balance(BiNode	*root);	//平衡操作 
	void    inorder(BiNode*	root, vector&res);
	vector inorderTraversal(BiNode* root);	//中序遍历函数 
	vector>	levelOrder(BiNode* root);	//层序遍历函数 


	//旋转函数集 
	BiNode *LL_Rotation(BiNode *root);
	BiNode *LR_Rotation(BiNode *root);
	BiNode *RL_Rotation(BiNode *root);
	BiNode *RR_Rotation(BiNode *root);


	BiNode*root; 	//根节点 
};

//计算平衡因子
template
int BST::diff(BiNode *root)
{
	if (root == NULL)
		return 0;
	return height(root->lch) - height(root->rch);
}


//四个旋转操作

template 
BiNode *BST::LL_Rotation(BiNode *root)
{
	BiNode *temp = root->lch;
	root->lch = temp->rch;
	temp->rch = root;
	return temp;//返回要旋转子树的主结点 
}


template 
BiNode *BST::RR_Rotation(BiNode *root)
{
	BiNode *temp = root->rch;
	root->rch = temp->lch;
	temp->lch = root;
	return temp;
}

template 
BiNode *BST::LR_Rotation(BiNode *root)
{//先进行RR操作，再进行LL操作 

	//注意这里一定要对root->m_Pleft重新赋值 
	root->lch = RR_Rotation(root->lch);//先对root后的左结点进行RR操作 
	return LL_Rotation(root);//再对root进行LL操作 
}

template 
BiNode *BST::RL_Rotation(BiNode *root)
{//先进行LL操作，再进行RR操作 

	//注意这里一定要对root->m_pRight重新赋值 
	root->rch = LL_Rotation(root->rch);//先对root后的右结点进行LL操作 
	return RR_Rotation(root);//再对root进行RR操作 
}


//平衡操作 
template 
BiNode *BST::balance(BiNode *root)
{
	int dis = diff(root);//计算结点的平衡因子 
	if (dis > 1) {//左 
		if (diff(root->lch) > 0)
			return LL_Rotation(root);
		else
			return LR_Rotation(root);
	}
	else if (dis < -1) {//右 
		if (diff(root->rch) < 0)
			return RR_Rotation(root);
		else
			return RL_Rotation(root);
	}

	return root;//无需转换时记得返回root 
}


//插入结点 
template 
BiNode * BST::insertBiNode(BiNode *&root, T val)	//树的根节点和要插入的值 
{
	if (root == NULL)
	{
		root = new BiNode(val);
		return root;
	}
	if (val == root->val)
	{
		return root;
	}
	else if (val < root->val)
	{
		//root->lch = insertBiNode(root->lch,val);
		insertBiNode(root->lch, val);
		root = balance(root); //注意这里是把平衡后的返回置temp赋值给root 
		return root;
	}
	else {
		//root->rch = insertBiNode(root->rch,val);
		insertBiNode(root->rch, val);
		root = balance(root);
		return root;
	}
}


//构造函数
template
BST::BST(T	r[], int	n)	//构造函数 
{
	root = NULL;
	for (int i = 0; i < n; i++)
		insertBiNode(root, r[i]);
}









template
int BST::height(BiNode* root) 	//判断树的高度 
{
	if (root == NULL)
	{
		return 0;
	}
	else
	{
		return max(height(root->lch), height(root->rch)) + 1;
	}
}
template
bool	BST::isBalanced(BiNode* root) //判断树是否为二叉平衡树 
{
	if (root == NULL)
	{
		return true;
	}
	else
	{
		return abs(height(root->left) - height(root->right)) <= 1 && isBalanced(root->left) && isBalanced(root->right);
	}
}



//中序遍历
template
void	BST::inorder(BiNode*	root, vector&res)
{
	if (!root)
		return;
	inorder(root->lch, res);
	res.push_back(root->val);
	inorder(root->rch, res);
}

template
vector	BST::inorderTraversal(BiNode* root)
{
	vectorres;
	inorder(root, res);
	return	res;
}


//层序遍历
template
vector>	BST::levelOrder(BiNode* root)
{
	vector > ret;
	if (!root)
	{
		return ret;
	}

	queue*>q;
	q.push(root);
	while (!q.empty())
	{
		int currentLevelSize = q.size();
		ret.push_back(vector ());
		for (int i = 1; i <= currentLevelSize; ++i)
		{
			auto node = q.front(); q.pop();
			ret.back().push_back(node->val);
			if (node->lch) q.push(node->lch);
			if (node->rch) q.push(node->rch);
		}
	}

	return ret;
}

//查找函数
template
bool	BST::Search(BiNode*R, T	key)
{
	if (R == NULL)
		return	false;
	if (key == R->val)
		return	true;
	else if (key < R->val)
		return Search(R->lch, key);
	else
		return Search(R->rch, key);
}


//删除函数
template
bool	BST::DeleteBST(BiNode*&R, T key)
{
	if (R == NULL)
		return	false;
	else
	{
		if (key == R->val)
		{
			Delete(R);
			return	true;
		}
		else	if (key < R->val)
			return	DeleteBST(R->lch, key);
		else
			return	DeleteBST(R->rch, key);
	}
}

template
void	BST::Delete(BiNode*&R)
{
	BiNode*q, *s;
	if (R->lch == NULL)
	{
		q = R;
		R = R->rch;
		delete	q;
	}
	else	if (R->rch == NULL)
	{
		q = R;
		R = R->lch;
		delete	q;
	}
	else
	{
		q = R;
		s = R->lch;
		while (s->rch != NULL)
		{
			q = s;
			s = s->rch;
		}
		R->val = s->val;
		if (q != R)
			q->rch = s->lch;
		else
			R->lch = s->lch;
		delete	s;
	}
}


析构函数
//template
//BST::~BST()
//{
//	Release(root);
//}
//
template
void BST::Release(BiNode*root)
{
	if (root)
	{
		Release(root->lch);
		Release(root->rch);
		delete root;
	}
}

template
void BST::destroy()
{
	Release(root);
}

主函数main.cpp

#include
#include
#include"BalancedTree.h" 
using	namespace	std;

void	print(BSTbt);
int	main()
{
	int	arr[] = { 13,24,37,90,53 };
	//3,7,9,11,15,14,16,18,26
	int	n = sizeof(arr) / sizeof(arr[0]);
	BSTbt(arr,n);

	print(bt);


	cout << "请输入你想插入的数字" << endl;
	int	insernum;//插入数字
	cin >> insernum;
	bt.insertBiNode(bt.root, insernum);
	print(bt);

	cout << "请输入你想查找的数字" << endl;
	int sernum;//查找数字
	cin >> sernum;
	if (bt.Search(bt.root, sernum))
		cout << "查到" << endl;
	else
		cout << "未查到" << endl;

	cout << "请输入你想删除的数字" << endl;
	int	delnum;//删除数字
	cin >> delnum;
	if (bt.DeleteBST(bt.root, delnum))
		cout << "删除成功" << endl;
	else
		cout << "删除失败" << endl;
	print(bt);
	bt.destroy();
	//bt.~BST();
	
}


void	print(BSTbt)
{
	cout << "中序遍历的结果为：" << endl;
	vectorres;
	res = bt.inorderTraversal(bt.root);
	for (int i : res)
		cout << i << " ";
	cout << endl;
	cout << "层序遍历的结果为：" << endl;
	int conlev = 0;//层数
	vector>ret;
	ret = bt.levelOrder(bt.root);
	for (vector i : ret)
	{
		cout << ++conlev << "层" << endl;
		for (int j : i)
		{
			cout << j << " ";
		}
		cout << endl;
	}
	cout << "树的平衡因子为：";
	cout << bt.diff(bt.root) << endl;
	cout << endl;
}

样例原理图示：

结果展示：

参考代码C++ 平衡二叉树的创建_love music.的博客-CSDN博客

及北邮C++数据结构课本二叉搜索树部分

leetcode中序遍历与层序遍历