红黑树

最新推荐文章于 2025-09-12 17:31:31 发布

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最新推荐文章于 2025-09-12 17:31:31 发布

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文章标签：数据结构与算法 python

原文链接：https://my.oschina.net/kkkkkkkkkkkkk/blog/749603

本文详细介绍了红黑树的基本性质，包括节点颜色、根节点颜色等，并深入探讨了红黑树插入操作的实现原理及步骤。文章通过具体代码示例展示了如何通过左旋、右旋等操作来保持红黑树的平衡。

2019独角兽企业重金招聘Python工程师标准>>>

5个基本性质

1.每个节点要么是红 要么是黑
2.根节点是黑
3.每个叶子节点是黑的
4.如果一个节点是红的，那么子节点都是黑的
5.对于每个节点，该节点到跟的所有路径包含有相同的黑节点

插入

新节点默认是红，如果是黑肯定破坏了性质，红的话还要分情况讨论

插入有3种情况，先按照平衡二叉树的插入，进行，依然保持查找特性，但是可能会破坏红黑树的性质
因此要对树进行调整，以保持性质。

左右旋转

STL XTREE代码

	void _Lrotate(_Nodeptr _Wherenode)
		{	// promote right node to root of subtree
		_Nodeptr _Pnode = this->_Right(_Wherenode);
		this->_Right(_Wherenode) = this->_Left(_Pnode);

		if (!this->_Isnil(this->_Left(_Pnode)))
			this->_Parent(this->_Left(_Pnode)) = _Wherenode;
		this->_Parent(_Pnode) = this->_Parent(_Wherenode);

		if (_Wherenode == _Root())
			_Root() = _Pnode;
		else if (_Wherenode == this->_Left(this->_Parent(_Wherenode)))
			this->_Left(this->_Parent(_Wherenode)) = _Pnode;
		else
			this->_Right(this->_Parent(_Wherenode)) = _Pnode;

		this->_Left(_Pnode) = _Wherenode;
		this->_Parent(_Wherenode) = _Pnode;
		}


	void _Rrotate(_Nodeptr _Wherenode)
		{	// promote left node to root of subtree
		_Nodeptr _Pnode = this->_Left(_Wherenode);
		this->_Left(_Wherenode) = this->_Right(_Pnode);

		if (!this->_Isnil(this->_Right(_Pnode)))
			this->_Parent(this->_Right(_Pnode)) = _Wherenode;
		this->_Parent(_Pnode) = this->_Parent(_Wherenode);

		if (_Wherenode == _Root())
			_Root() = _Pnode;
		else if (_Wherenode == this->_Right(this->_Parent(_Wherenode)))
			this->_Right(this->_Parent(_Wherenode)) = _Pnode;
		else
			this->_Left(this->_Parent(_Wherenode)) = _Pnode;

		this->_Right(_Pnode) = _Wherenode;
		this->_Parent(_Wherenode) = _Pnode;
		}

插入，mark一下，插入只有四种情况，需要修复

xtree(1833)

	template<class _Valty,
	class _Nodety>
		iterator _Insert_at(bool _Addleft, _Nodeptr _Wherenode,
		_Valty&& _Val, _Nodety _Node)
	{	// add node with value next to _Wherenode, to left if _Addleft
			if (max_size() - 1 <= this->_Mysize)
			{	// tree would get too big, fail
				_Destroy_if_not_nil(_Node);
				_Xlength_error("map/set<T> too long");
			}
			_Nodeptr _Newnode = _Buynode_if_nil(_Node,
				_STD forward<_Valty>(_Val));

			++this->_Mysize;
			_Newnode->_Parent = _Wherenode;

			if (_Wherenode == this->_Myhead)
			{	// first node in tree, just set head values
				_Root() = _Newnode;
				_Lmost() = _Newnode;
				_Rmost() = _Newnode;
			}
			else if (_Addleft)
			{	// add to left of _Wherenode
				this->_Left(_Wherenode) = _Newnode;
				if (_Wherenode == _Lmost())
					_Lmost() = _Newnode;
			}
			else
			{	// add to right of _Wherenode
				this->_Right(_Wherenode) = _Newnode;
				if (_Wherenode == _Rmost())
					_Rmost() = _Newnode;
			}

			for (_Nodeptr _Pnode = _Newnode;
				this->_Color(this->_Parent(_Pnode)) == this->_Red;)
			if (this->_Parent(_Pnode)
				== this->_Left(this->_Parent(this->_Parent(_Pnode))))
			{	// fixup red-red in left subtree
				_Wherenode =
					this->_Right(this->_Parent(this->_Parent(_Pnode)));
				if (this->_Color(_Wherenode) == this->_Red)
				{	// parent has two red children, blacken both
					this->_Color(this->_Parent(_Pnode)) = this->_Black;
					this->_Color(_Wherenode) = this->_Black;
					this->_Color(this->_Parent(this->_Parent(_Pnode)))
						= this->_Red;
					_Pnode = this->_Parent(this->_Parent(_Pnode));
				}
				else
				{	// parent has red and black children
					if (_Pnode == this->_Right(this->_Parent(_Pnode)))
					{	// rotate right child to left
						_Pnode = this->_Parent(_Pnode);
						_Lrotate(_Pnode);
					}
					this->_Color(this->_Parent(_Pnode)) =
						this->_Black;	// propagate red up
					this->_Color(this->_Parent(this->_Parent(_Pnode))) =
						this->_Red;
					_Rrotate(this->_Parent(this->_Parent(_Pnode)));
				}
			}
			else
			{	// fixup red-red in right subtree
				_Wherenode =
					this->_Left(this->_Parent(this->_Parent(_Pnode)));
				if (this->_Color(_Wherenode) == this->_Red)
				{	// parent has two red children, blacken both
					this->_Color(this->_Parent(_Pnode)) = this->_Black;
					this->_Color(_Wherenode) = this->_Black;
					this->_Color(this->_Parent(this->_Parent(_Pnode))) =
						this->_Red;
					_Pnode = this->_Parent(this->_Parent(_Pnode));
				}
				else
				{	// parent has red and black children
					if (_Pnode == this->_Left(this->_Parent(_Pnode)))
					{	// rotate left child to right
						_Pnode = this->_Parent(_Pnode);
						_Rrotate(_Pnode);
					}
					this->_Color(this->_Parent(_Pnode)) =
						this->_Black;	// propagate red up
					this->_Color(this->_Parent(this->_Parent(_Pnode))) =
						this->_Red;
					_Lrotate(this->_Parent(this->_Parent(_Pnode)));
				}
			}

			this->_Color(_Root()) = this->_Black;	// root is always black
			return (iterator(_Newnode, this));
		}

转载于:https://my.oschina.net/kkkkkkkkkkkkk/blog/749603