Formatted question description: https://leetcode.ca/all/1650.html

# 1650. Lowest Common Ancestor of a Binary Tree III

## Level

Medium

## 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**: “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:**

**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:**

**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, 10^5]`

. `-10^9 <= Node.val <= 10^9`

- All
`Node.val`

are**unique**. `p != q`

`p`

and`q`

exist in the tree.

## Solution

Use a set to store nodes. Start from `p`

and obtain all the nodes from `p`

to the root node using the nodes’ parents. Then start from `q`

and move towards the root. If a node is already in the set, then the node is a common ancestor of `p`

and `q`

. The first common ancestor that is in the set is the lowest common ancestor of `p`

and `q`

.

```
/*
// Definition for a Node.
class Node {
public int val;
public Node left;
public Node right;
public Node parent;
};
*/
class Solution {
public Node lowestCommonAncestor(Node p, Node q) {
Set<Node> set = new HashSet<Node>();
Node temp = p;
while (temp != null) {
set.add(temp);
temp = temp.parent;
}
temp = q;
while (temp != null) {
if (set.contains(temp))
break;
else
temp = temp.parent;
}
return temp;
}
}
```