236. Lowest Common Ancestor of a Binary Tree.py

# 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 v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

#         _______3______
#        /              \
#     ___5__          ___1__
#    /      \        /      \
#    6      _2       0       8
#          /  \
#          7   4
# For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

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

class Solution(object):
    def lowestCommonAncestor(self, root, p, q):
        """
        O(ST)
        
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode

        """
        if not root:
            return None
        if root == p or root == q:
            return root
        left = self.lowestCommonAncestor(root.left,p,q)
        right = self.lowestCommonAncestor(root.right,p,q)
        if left and right:
            return root
        return left if left else right