【C++篇】平衡二叉搜索树（下篇）：红黑树详解

1. 二叉搜索树的概念

二叉搜索树又称二叉排序树，它可以是一颗空树。它是具有以下性质的二叉树：如果树不为空时：

1. 非空左子树的所有节点的值小于其根节点的值。
2. 非空左子树的所有节点的值小于其根节点的值。
3. 左右子树都是二叉搜索树
4. 节点的值都是唯一的，不存在相等值的两个节点

为什么又可以叫二叉排序树呢？ 因为二叉搜索树的中序遍历的结果一定是一个升序序列

那么，二叉搜索树应该是链式结构还是顺序结构呢？ 其实很容易想到，这棵树需要具备增删的功能，若是顺序结构，每次都得挪动数据，效率太差。 因此，二叉搜索树是链式结构。

2. 二叉搜索树的操作及模拟实现

这里操作的实现可以有两种方式：递归和非递归（迭代）。这里我们两者一起实现。

2.1 查找

1. 从根开始比较，查找，比根大则往右边走查找，比根小则往左边走查找。
2. 最多查找高度次，走到到空，还没找到，这个值不存在。

非递归：

代码语言：javascript

AI代码解释

bool Find(const K& key) { Node* cur = _root; while (cur) { if (cur->_key > key)//比根小就往左走 { cur = cur->_left; } else if (cur->_key < key)//比根大就往右走 { cur = cur->_right; } else//与根相等就找到了 { return true; } } return false; }

递归：

代码语言：javascript

AI代码解释

bool _FindR(Node* root, const K& key) { if (root == nullptr) { return false; } if (root->_key > key)//比根小了,就在左子树上查找 { _FindR(root->_left, key); } else if (root->_key < key)//比根大了,就在右子树上查找 { _FindR(root->_right, key); } else { return true; } }

2.2 插入

插入的具体过程分两种情况： a. 树为空，则直接新增节点，赋值给root指针 b. 树不空，按二叉搜索树性质查找插入位置，插入新节点

如果有重复的节点，则插入失败，返回false。

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