---
title: '236. 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
icon: dot
topics:
  - { name: "Tree", slug: "tree" }
  - { name: "Depth-First Search", slug: "depth-first-search" }
  - { name: "Binary Tree", slug: "binary-tree" }
  - { name: "Binary Lifting", slug: "binary-lifting" }
  - { name: "Lowest Common Ancestor", slug: "lowest-common-ancestor" }
issue: "https://github.com/prdlk/leetcode/issues/98"
sidebar:
  label: 'Lowest Common Ancestor of a Binary Tree'
  badge: 'Medium'
---

### 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 will exist in the tree.

## Approach

```mermaid
flowchart TD
  S(["lowestCommonAncestor(root, p, q)"]) --> B{"not root?"}
  B -- yes --> N(["return None"])
  B -- no --> M{"root == p or root == q?"}
  M -- yes --> R(["return root — a node is its own ancestor"])
  M -- no --> L["l = self.lowestCommonAncestor(root.left, p, q)"]
  L --> Q["r = self.lowestCommonAncestor(root.right, p, q)"]
  Q --> D{"l and r?"}
  D -- yes --> A(["return root — p and q were found on different sides"])
  D -- no --> E(["return l or r — pass up whichever side found something"])
```

## Solution

```py
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None


class Solution:
    def lowestCommonAncestor(
        self, root: "TreeNode", p: "TreeNode", q: "TreeNode"
    ) -> "TreeNode":

        if not root:
            return None

        if root == p or root == q:
            return root

        l = self.lowestCommonAncestor(root.left, p, q)
        r = self.lowestCommonAncestor(root.right, p, q)

        if l and r:
            return root
        else:
            return l or r
```