This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Challenge Notebook

Problem: Given an array of 32 integers, find an int not in the input. Use a minimal amount of memory.


  • Are we working with non-negative ints?
    • Yes
  • What is the range of the integers?
    • Discuss the approach for 4 billion integers
    • Implement for 32 integers
  • Can we assume the inputs are valid?
    • No

Test Cases

  • None -> Exception
  • [] -> Exception
  • General case
    • There is an int excluded from the input -> int
    • There isn't an int excluded from the input -> None


Refer to the Solution Notebook. If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start.


In [ ]:
from bitstring import BitArray  # run pip install bitstring

class Bits(object):

    def new_int(self, array, max_size):
        # TODO: Implement me

Unit Test

The following unit test is expected to fail until you solve the challenge.

In [ ]:
# %load
import unittest

class TestBits(unittest.TestCase):

    def test_new_int(self):
        bits = Bits()
        max_size = 32
        self.assertRaises(TypeError, bits.new_int, None, max_size)
        self.assertRaises(TypeError, bits.new_int, [], max_size)
        data = [item for item in range(30)]
        self.assertEqual(bits.new_int(data, max_size), 30)
        data = [item for item in range(32)]
        self.assertEqual(bits.new_int(data, max_size), None)
        print('Success: test_find_int_excluded_from_input')

def main():
    test = TestBits()

if __name__ == '__main__':

Solution Notebook

Review the Solution Notebook for a discussion on algorithms and code solutions.