Smallest Common Region — Python

# Time:  O(m * n)
# Space: O(n)

class Solution(object):
    def findSmallestRegion(self, regions, region1, region2):
        """
        :type regions: List[List[str]]
        :type region1: str
        :type region2: str
        :rtype: str
        """
        parents = {region[i] : region[0]
                   for region in regions
                   for i in xrange(1, len(region))}
        lookup = {region1}
        while region1 in parents:
            region1 = parents[region1]
            lookup.add(region1)
        while region2 not in lookup:
            region2 = parents[region2]
        return region2