# Lowest Common Ancestor of a Binary Tree

## Description

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**).”

Given the following binary tree:  root = \[3,5,1,6,2,0,8,null,null,7,4]

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

**Example 1:**

> **Input:** root = \[3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1&#x20;
>
> **Output:** 3&#x20;
>
> **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&#x20;
>
> **Output:** 5&#x20;
>
> **Explanation:** The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

**Note:**

* All of the nodes' values will be unique.
* p and q are different and both values will exist in the binary tree.

## **Code**

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root == null || root == p || root == q) return root;
        TreeNode left = lowestCommonAncestor(root.left, p, q);
        TreeNode right = lowestCommonAncestor(root.right, p, q);    
        
        if(left == null && right == null) return null; 
        if(left != null && right != null) return root;  
        return left == null ? right : left;
    }
}
```
