算法精粹(algorithm-essentials)

感谢soulmachine@github提供内容
## LCA of Binary Tree


### 描述

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

According to [the definition of LCA on Wikipedia](https://en.wikipedia.org/wiki/Lowest_common_ancestor): “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow **a node to be a descendant of itself**).”

```
_______3______
/ \
___5__ ___1__
/ \ / \
6 _2 0 8
/ \
7 4
```

For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.


### 分析

用自底向上(bottom-up)的思路,先看看是否能在`root`的左子树中找到`p`或`q`,再看看能否在右子树中找到,

* 如果两边都能找到,说明当前节点就是最近公共祖先
* 如果左边没找到,则说明`p`和`q`都在右子树
* 如果右边没找到,则说明`p`和`q`都在左子树


### 代码

{% if book.java %}
{% codesnippet "./code/lca-of-binary-tree."+book.suffix, language=book.suffix %}{% endcodesnippet %}
{% endif %}

### 相关题目

* [LCA of BST](../bst/lca-of-bst.md)