c++ 二叉搜索树（BinarySearchTree）

⼆叉搜索树：左⼦树上所有结点的值都⼩于等于根结点的值；右⼦树上所有结点的值都⼤于等于根结点的值。

⼆叉搜索树默认定义，不允许冗余。

中序遍历就是一个升序。

二叉搜索树的删除：

二叉树搜索key的代码实现：

只有key作为关键码，结构中只需要存储key即可，关键码即为需要搜索到的值，搜索场景只需要判断 key在不在。

template<class K>
struct BSTreeNode
{
	BSTreeNode<K>* _left;
	BSTreeNode<K>* _right; |
	K _key;
	BSTreeNode(const K& key)//构造函数
		:_left(nullptr)
		, _right(nullptr)
		, _key(key)
	{

	}
};

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

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

	void InOrder()//为了便于传参
	{
		_InOrder(_root);
	}

	bool erase(const K& key)
	{
		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			if (cur->_key < key)
			{
				parent = cur;
				cur = cur->_right;
			}
			else if (cur->_key > key)
			{
				parent = cur;
				cur = cur->_left;
			}
			else
			{
				if (cur->_left == nullptr)//左位空，父亲指向cur的右边
				{
					if (cur == _root)
					{
						_root = cur->_right;
					}
					else
					{
						if (cur == parent->_left)
						{
							parent->_left = cur->_right;
						}
						else
						{
							parent->_right = cur->_right;
						}
					}
					delete cur;
				}
				else if (cur->_right == nullptr)//右位空，父亲指向cur的左边
				{
					if (cur == _root)
					{
						_root = cur->_left;
					}
					else
					{
						if (cur == parent->_left)
						{
							parent->_left = cur->_left;
						}
						else
						{
							parent->_right = cur->_left;
						}
					}
					delete cur;
				}
				else//左右都不为空，进行替换
				{
					Node* rightMinParent = cur;
					Node* rightMin = cur->_right;
					while (rightMin->_left)
					{
						rightMinParent = rightMin;
						rightMin = rightMin->_left;
					}
					swap(cur->_key, rightMin->_key);
					if (rightMinParent->_left == rightMin)
						rightMinParent->_left = rightMin->_right;//因为rightMin与cur交换了，删除它就不能指向它了，指向它的右边
					else
						rightMinParent->_right = rightMin->_right;

					delete rightMin;
				}
				return true;
			}
		}
		return false
	}

private:
	void _Inorder(Node* root)
	{
		if (root == nullptr)
		{
			return;
		}
		_InOrder(root->_left);
		cout << root->_key << " ";
		_InOrder(root->_right);
	}
private:
	Node* _root = nullptr;
};

二叉搜索树key/value的代码实现：

每⼀个关键码key，都有与之对应的值value，value可以任意类型对象。（通过一个值找到另一个）；还是根据key来实现的。

template<class K, class V>
	class BSTree
	{
		typedef BSTreeNode<K, V> Node;
	public:
		// logN
		bool Insert(const K& key, const V& value)
		{
			if (_root == nullptr)
			{
				_root = new Node(key, value);
				return true;
			}

			Node* parent = nullptr;
			Node* cur = _root;
			while (cur)
			{
				if (cur->_key < key)
				{
					parent = cur;
					cur = cur->_right;
				}
				else if (cur->_key > key)
				{
					parent = cur;
					cur = cur->_left;
				}
				else
				{
					return false;
				}
			}

			cur = new Node(key, value);
			if (parent->_key < key)
			{
				parent->_right = cur;
			}
			else
			{
				parent->_left = cur;
			}

			return true;
		}

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

			return cur;
		}

		bool Erase(const K& key)
		{
			Node* parent = nullptr;
			Node* cur = _root;
			while (cur)
			{
				if (cur->_key < key)
				{
					parent = cur;
					cur = cur->_right;
				}
				else if (cur->_key > key)
				{
					parent = cur;
					cur = cur->_left;
				}
				else
				{
					// 删除
					// 左为空，父亲指向我的右
					if (cur->_left == nullptr)
					{
						//if(parent == nullptr)
						if (cur == _root)
						{
							_root = cur->_right;
						}
						else
						{
							if (cur == parent->_left)
							{
								parent->_left = cur->_right;
							}
							else
							{
								parent->_right = cur->_right;
							}
						}

						delete cur;
					}
					else if (cur->_right == nullptr)
					{
						//if(parent == nullptr)
						if (cur == _root)
						{
							_root = cur->_left;
						}
						else
						{
							// 右为空，父亲指向我的左
							if (cur == parent->_left)
							{
								parent->_left = cur->_left;
							}
							else
							{
								parent->_right = cur->_left;
							}
						}

						delete cur;
					}
					else
					{
						// 左右都不为空，替换法删除
						// 
						// 查找右子树的最左节点替代删除
						Node* rightMinParent = cur;
						Node* rightMin = cur->_right;
						while (rightMin->_left)
						{
							rightMinParent = rightMin;
							rightMin = rightMin->_left;
						}

						swap(cur->_key, rightMin->_key);

						if (rightMinParent->_left == rightMin)
							rightMinParent->_left = rightMin->_right;
						else
							rightMinParent->_right = rightMin->_right;

						delete rightMin;
					}

					return true;
				}
			}

			return false;
		}

		void InOrder()
		{
			_InOrder(_root);
			cout << endl;
		}
	private:
		void _InOrder(Node* root)
		{
			if (root == nullptr)
			{
				return;
			}

			_InOrder(root->_left);
			cout << root->_key << ":" << root->_value << endl;
			_InOrder(root->_right);
		}
	private:
		Node* _root = nullptr;
	};