# 1650. Lowest Common Ancestor of a Binary Tree III

https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree-iii

## Description

Given two nodes of a binary tree `p` and `q`, return _their lowest common ancestor (LCA)_.

Each node will have a reference to its parent node. The definition for `Node` is below:

```
class Node {
    public int val;
    public Node left;
    public Node right;
    public Node parent;
}
```

According to the [**definition of LCA on Wikipedia**](https://en.wikipedia.org/wiki/Lowest_common_ancestor): "The lowest common ancestor of two nodes p and q in a tree T is the lowest node 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` exist in the tree.

## ac

```java
```
