235.py

'''
	Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

	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 binary search tree:  root = [6,2,8,0,4,7,9,null,null,3,5]

	        _______6______
	       /              \
	    ___2__          ___8__
	   /      \        /      \
	   0      _4       7       9
	         /  \
	         3   5

	Example 1:

	Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
	Output: 6
	Explanation: The LCA of nodes 2 and 8 is 6.

	Example 2:

	Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
	Output: 2
	Explanation: The LCA of nodes 2 and 4 is 2, 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):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        if not root:
        	return None
        
        if root.val > p.val and root.val > q.val:
        	return self.lowestCommonAncestor(root.left, p, q)
        elif root.val < p.val and root.val < q.val:
        	return self.lowestCommonAncestor(root.right, p, q)
        else:
        	return root