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