二叉搜索树基本概念与实现

目录

基本概念

模拟实现

完整代码

基本概念

根的左节点比根小

根的右节点比根大

左右子树都满足

搜索二叉树的中序遍历是升序

模拟实现

完整代码

#pragma once

template<class K>
struct BSNode
{
	BSNode<K>* _left;
	BSNode<K>* _right;
	K _val;

	BSNode(const K& val)
		:_left(nullptr)
		, _right(nullptr)
		, _val(val)
	{

	}
};

template<class K>
class BSTree
{
	typedef BSNode<K> Node;
public:
	bool insert(const K& key)
	{
		if (_root == nullptr)
		{
			_root = new Node(key);
			return true;
		}
		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			if (cur->_val > key)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (cur->_val < key)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
			{
				return false;
			}
		}
		cur = new Node(key);
		if (parent->_val > key)
		{
			parent->_left = cur;
		}
		else
		{
			parent->_right = cur;
		}
		return true;
	}

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

	bool Erase(const K& key)
	{
		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			if (cur->_val > key)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (cur->_val < key)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
			{
				//左为空
				if (cur->_left == nullptr)
				{
					if (cur == _root)
					{
						_root = cur->_right;
					}
					else
					{
						if (cur == parent->_left)
						{
							parent->_left = cur->_right;
						}
						else
						{
							parent->_right = cur->_right;
						}
					}
					delete cur;
				}
				//右为空
				else if (cur->_right == nullptr)
				{
					if (cur == _root)
					{
						_root = cur->_left;
					}
					else
					{
						if (cur == parent->_left)
						{
							parent->_left = cur->_left;
						}
						else
						{
							parent->_right = cur->_left;
						}
					}
					delete cur;
				}
				//左右都不为空
				else
				{
					Node* parent = cur;
					Node* subnode = cur->_right;

					while (subnode->_left!=nullptr)
					{
						parent = subnode;
						subnode = subnode->_left;
					}
					swap(subnode->_val, cur->_val);
					
					if (subnode == parent->_left)
					{
						parent->_left = subnode->_right;
					}
					else
					{
						parent->_right = subnode->_right;
					}

					delete subnode;
				}
				return true;
			}
		}
		return false;
	}

	bool insertR(const K& key)
	{
		return _insertR(_root,key);
	}

	bool FindR(const K& key)
	{
		return _FindR(_root, key);
	}

	bool EraseR(const K& key)
	{
		return _EraseR(_root, key);
	}

	void Inorder()
	{
		_Inorder(_root);
		cout << endl;
	}

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

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

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

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

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

		if (root->_val > key)
		{
			return _EraseR(root->_left, key);
		}
		else if (root->_val < key)
		{
			return _EraseR(root->_right, key);
		}
		else
		{//删除
			if (root->_left == nullptr)
			{
				Node* del = root;
				root = root->_right;
				delete del;

				return true;
			}
			else if (root->_right == nullptr)
			{
				Node* del = root;
				root = root->_left;
				delete del;

				return true;
			}
			else
			{
				Node* subnode = root->_right;
				while (subnode->_left != nullptr)
				{
					subnode = subnode->_left;
				}
				swap(root->_val, subnode->_val);

				return _EraseR(root->_right, key);
			}
		}
	}

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

		_Inorder(root->_left);
		cout << root->_val << ' ';
		_Inorder(root->_right);
	}

	Node* _root = nullptr;
};