236.py

# Time:  O(n)
# Space: O(1)
#
# 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:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def lowestCommonAncestor(self, root, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        # Edge/Condition
        if not root:
            return None
        if root == p or root == q:
            return root

        # Divide
        left = self.lowestCommonAncestor(root.left, p, q)
        right = self.lowestCommonAncestor(root.right, p, q)

        # Conquer
        if left and right:
            return root
        if not left:
            return right
        if not right:
            return left