## 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: “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]

**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.
```

**Note:**

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

## Solutions

### 1. Recursion

```
# Time: O(logn)
# Space: O(logn)
# 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 or root == p or root == q:
return root
left = self.lowestCommonAncestor(root.left, p, q)
right = self.lowestCommonAncestor(root.right, p, q)
return root if left and right else left or right
# 31/31 cases passed (68 ms)
# Your runtime beats 88.17 % of python3 submissions
# Your memory usage beats 91.67 % of python3 submissions (23.1 MB)
```

### 2. Iterative

```
# Time: O(logn)
# Space: O(logn)
class Solution:
def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
stack = [root]
parent = {root: None}
while p not in parent or q not in parent:
node = stack.pop()
if node.left:
parent[node.left] = node
stack.append(node.left)
if node.right:
parent[node.right] = node
stack.append(node.right)
ancestors = set()
while p:
ancestors.add(p)
p = parent[p]
while q not in ancestors:
q = parent[q]
return q
# 31/31 cases passed (68 ms)
# Your runtime beats 88.17 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (16.5 MB)
```