"""
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.
"""


# 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, p, q):
        if not root:
            return 
        elif root in [p, q]:
            return root
        else:
            left = self.lowestCommonAncestor(root.left, p, q)
            right = self.lowestCommonAncestor(root.right, p, q)
            if left and right:
                return root
            elif left:
                return left
            elif right:
                return right
