"""
236. Lowest Common Ancestor of a Binary Tree
Difficulty: Medium
https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/

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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).”



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.
"""

# 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