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


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, 105].
-109 <= Node.val <= 109
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 recursive_solution(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
         def dfs(node: 'Node') -> bool:
            if not node:
                return False
                    
            left = dfs(node.left)
            right = dfs(node.right)
            
            mid = node == q or node == p
            
            if mid + left + right == 2:
                self.ans = node
            
            return mid or left or right
        
        dfs(root)
        return self.ans
        
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        return self.recursive_solution(root, p, q)
        
        
        
    