二叉搜索树

二叉搜索树

二叉搜索树又称二叉排序树，它或者是一棵空树，或者是具有以下性质的二叉树:
若它的左子树不为空，则左子树上所有节点的值都小于根节点的值。
若它的右子树不为空，则右子树上所有节点的值都大于根节点的值。
它的左右子树也分别为二叉搜索树。
二叉搜索树的中序遍历是有序的。

二叉搜索树的查找

左子树比根结点小，右子树比根结点大，根据大小判断。如何查找

二叉搜索树的插入

找到插入的位置，记录父节点，左大右小。

二叉搜索树的删除

template <class T>
struct BSTNode
{
	BSTNode(const T& data = T())
		:_pLeft(null),
		 _pRight
	{}
	BSTNode<T>* _pLeft;
	BSTNode<T>* _pRight;
	T _data;
};
template<class T>
class BSTree
{
	typedef BSTNode<T> Node;
	BSTree()
		:pRoot(nullptr)
	{}
	Node* find(int val)
	{
		Node* cur = pRoot;
		if (pRoot == nullptr)
			return nullptr;
		while (cur)
		{
			if (cur->_data == val)
				return cur;
			else if (cur->_data > val)
				cur = cur->_pRight;
			else
			    cur = cur->_pLeft
		}
	}
	bool insert(const T& val)
	{
		Node* node = new Node(val);
		Node* cur = _pRoot;
		Node* pPnode = nullptr;
		if (cur == nullptr)
		{
			_pRoot = node;
			return true;
		}
		while (cur)
		{
			pPnode = cur;
			if (cur->_data < val)
				cur = cur->_pLeft;
			else if (cur->_data < val)
				cur = cur->_pRight;
			else
				return false;
		}
		if (pPnode->_data < val)
			pPnode->_pRight = val;
		else
			pPnode->_pLeft;
		return true;
	}
	bool erase(const T& val)
	{
		Node* parent = nullptr;
		Node* cur = _pRoot;
		while (cur)
		{
			if (cur->_data > val)
			{
				parent = cur;
				cur = cur->_pRight;
			}
			else if (cur->_data < val)
			{
				parent = cur;
				cur = cur->_pLeft;
			}
			else
			{
				Node* del = cur;
				if (cur->_pLeft == nullptr)
				{
					//如果当前节点，是根结点
					if (parent == nullptr)
						_pRoot = cur->_pRight;
					else
					{
						if (cur == parent->_pLeft)
							parent->_pLeft = cur->_pRight;
						else
							parent->_pRight = cur->_pRight;
					}
				}
				else if (cur->_pRight == nullptr)
				{
					if (parent == nullptr)
						_pRoot = cur->_pLeft;
					else
					{
						if (cur == parent->_pLeft)
						{
							parent->_pLeft = cur->_pLeft;
						}
						else
							parent->_pRight = cur->_pLeft;
					}
				}
				else
				{
					Node* rpparent = cur;
					Node* replace = cur->right;
					while (replace->_pLeft)
					{
						pparent = replace;
						replace = replace->_pLeft;
					}
					del = replace;
					cur->_data = replace->_data;
					rpparent->_pLeft = replace->_pRight; 
				}
				delete del;
				return true;
			}
		}
		return false;
	}
private:
	Node* _pRoot;
};

来源：CSDN

作者：阿彬要成为大牛

链接：https://blog.csdn.net/qq_38833257/article/details/104575820