neighbors.py

north_south = {
    '0': '2',
    '2': '0',
    '1': '3',
    '3': '1'
}

east_west = {
    '2': '3',
    '3': '2',
    '1': '0',
    '0': '1'
}

north_wall = ['0', '1']
south_wall = ['2', '3']
east_wall = ['1', '3']
west_wall = ['0', '2']

def parent(quadkey):
    return quadkey[:-1]

def next_in_line(ancestor, descendants):
    return [ancestor[-1], *descendants]

def inheritance(mapping, descendants, ancestor):
    if len(descendants) == 0:
        return ancestor
    else:
        return inheritance(mapping, descendants[1:], ancestor + mapping[descendants[0]])

def next_lineage(mapping, stop, descendants, ancestor):
    if ancestor[-1] in stop:
        return inheritance(mapping, next_in_line(ancestor, descendants), parent(ancestor))
    elif len(ancestor) == 2:
        return None
    else:
        return next_lineage(mapping, stop, next_in_line(ancestor, descendants), parent(ancestor))

def lineage(mapping, stop, quadkey):
    return next_lineage(mapping, stop, [], quadkey)

def southern(quadkey):
    return lineage(north_south, north_wall, quadkey)

def northern(quadkey):
    return lineage(north_south, south_wall, quadkey)

def western(quadkey):
    return lineage(east_west, east_wall, quadkey)

def eastern(quadkey):
    return lineage(east_west, west_wall, quadkey)

def neighbors(quadkey):
    return (northern(quadkey), southern(quadkey), eastern(quadkey), western(quadkey))
    
class TestNeighbors(unittest.TestCase):

    def test_neighbors_top(self):
        north, south, east, west = neighbors('01')
        self.assertEqual('03', south)
        self.assertEqual('00', west)
        self.assertEqual(None, north)
        self.assertEqual(None, east)

    def test_neighbors_shared_grandparent(self):
        north, south, east, west = neighbors('003')
        self.assertEqual('021', south)
        self.assertEqual('002', west)
        self.assertEqual('001', north)
        self.assertEqual('012', east)

    def test_neighbors_shared_great_grandparent(self):
        north, south, east, west = neighbors('0122')
        self.assertEqual('0300', south)
        self.assertEqual('0033', west)
        self.assertEqual('0120', north)
        self.assertEqual('0123', east)