node_three.py

class Node(object):
	def __init__(self, value, parentNode):
		self.value = value
		self.parent = parentNode

# match node that has particular value
def match_node(ancs, matcher):
	for node in ancs:
		if matcher(node):
			return node

# find all ancesors for node	
def node_ancesors(node):
	ancesors = [node, ]

	while node.parent:
		node = node.parent
		ancesors.append(node)

	return ancesors

def lca(node1, node2):
	ancs1 = node_ancesors(node1)
	ancs2 = node_ancesors(node2)
    
    	# list out ancesors values for node1, node2
     	# do intersection; get max value, which value of closest ancesor
	closest = max(set([node.value for node in ancs1]) & set([node.value for node in ancs1])) 
	
	# match node that has closest value
	node  = match_node(ancs1, lambda n: n.value == closest)

	print node.value

def improved_lca(node1, node2):
    """
        Add some conditions that could accelerate preforming in some particular cases
    """

	if node1.value == node2.value: # same node
		return node1

	if not node1.parent: # node1 is root
		return node1

	if not node2.parent: # node2 is root
		return node2

	if node1.parent.value == node2.parent.value: # have same ancesor
		return node1.parent

	return lca(node1, node2) # call the same logic if no