# Number notation

def encode(n):

if n == 0:

return ''

dct = {'': 0}

while True:

new_items = {}

for k, v in dct.items():

factor = 2 ** len(k)

if len(k) % 2 == 0:

factor *= -1

new_k = k + '1'

new_v = factor + v

if new_v == n:

return new_k

new_items[new_k] = new_v

new_items[k + '0'] = v

dct.update(new_items)

import unittest

class RepresentationTests(unittest.TestCase):

def test_numbers(self):

self.assertEqual('', encode(0))

self.assertEqual('1', encode(-1))

self.assertEqual('01', encode(2))

self.assertEqual('11', encode(1))

self.assertEqual('001', encode(-4))

self.assertEqual('101', encode(-5))

self.assertEqual('011', encode(-2))

self.assertEqual('111', encode(-3))