# 236. Lowest Common Ancestor of a Binary Tree

#### Medium

***

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 `p` and `q` as the lowest node in `T` that has both `p` and `q` as descendants (where we allow **a node to be a descendant of itself**).”

 

**Example 1:**

![](https://assets.leetcode.com/uploads/2018/12/14/binarytree.png)

```
Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2018/12/14/binarytree.png)

```
Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.
```

**Example 3:**

```
Input: root = [1,2], p = 1, q = 2
Output: 1
```

 

**Constraints:**

* The number of nodes in the tree is in the range `[2, 105]`.
* `-109 <= Node.val <= 109`
* All `Node.val` are **unique**.
* `p != q`
* `p` and `q` will exist in the tree.

```python
class Solution:
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        if root is None:
            return None
        if root == q or root == p:
            return root
        left = self.lowestCommonAncestor(root.left, p,q)
        right = self.lowestCommonAncestor(root.right, p ,q)
        if left and right:
            return root
        return left or right
```