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

Solution Notebook

Problem: Given a real number between 0 and 1, print the binary representation. If the length of the representation is > 32, return 'ERROR'.

Constraints

  • Is the input a float?
    • Yes
  • Is the output a string?
    • Yes
  • Is 0 and 1 inclusive?
    • No
  • Does the result include a trailing zero and decimal point?
    • Yes
  • Is the leading zero and decimal point counted in the 32 char limit?
    • Yes
  • Can we assume the inputs are valid?
    • No
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> 'ERROR'
  • Out of bounds (0, 1) -> 'ERROR'
  • General case
    • 0.625 -> 0.101
    • 0.987654321 -> 'ERROR'

Algorithm

  • Set the result to '0.'
  • Start with a fraction of 0.5, which is 0.1 in base 2
  • Loop while num > 0
    • Check num versus fraction
      • If num > fraction, add a 1 to the result, num -= fraction
      • Else, add a 0 to the result
      • If the len(result) > 32, return 'ERROR'

Complexity:

  • Time: O(1)
  • Space: O(1)

Code

In [1]:
from __future__ import division


class Bits(object):

    MAX_BITS = 32

    def print_binary(self, num):
        if num is None or num >= 1 or num <= 0:
            return 'ERROR'
        result = ['0', '.']
        fraction = 0.5
        while num:
            if num >= fraction:
                result.append('1')
                num -= fraction
            else:
                result.append('0')
            if len(result) > self.MAX_BITS:
                return 'ERROR'
            fraction /= 2
        return ''.join(result)

Unit Test

In [2]:
%%writefile test_print_binary.py
import unittest


class TestBits(unittest.TestCase):

    def test_print_binary(self):
        bit = Bits()
        self.assertEqual(bit.print_binary(None), 'ERROR')
        self.assertEqual(bit.print_binary(0), 'ERROR')
        self.assertEqual(bit.print_binary(1), 'ERROR')
        num = 0.625
        expected = '0.101'
        self.assertEqual(bit.print_binary(num), expected)
        num = 0.987654321
        self.assertEqual(bit.print_binary(num), 'ERROR')
        print('Success: test_print_binary')


def main():
    test = TestBits()
    test.test_print_binary()


if __name__ == '__main__':
    main()
Overwriting test_print_binary.py
In [3]:
%run -i test_print_binary.py
Success: test_print_binary