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

Solution Notebook

Problem: Determine the number of bits to flip to convert int a to int b.

Constraints

  • Can we assume A and B are always ints?
    • Yes
  • Is the output an int?
    • Yes
  • Can we assume A and B are always the same number of bits?
    • Yes
  • Can we assume the inputs are valid (not None)?
    • No
  • Can we assume this fits memory?
    • Yes

Test Cases

  • A or B is None -> Exception
  • General case
      A = 11101
      B = 01111
      Result: 2

Algorithm

We can use the xor operator to determine the bit differences between a and b

  • Set count to 0
  • Set c to a xor b
  • Loop while c != 0:
    • Increment count if the LSB in c is a 1
      • We can check this by using a mask of 1
    • Right shift c by 1
  • Return the count

Complexity:

  • Time: O(b), where b is the number of bits
  • Space: O(b), where b is the number of bits

Code

In [1]:
class Bits(object):

    def bits_to_flip(self, a, b):
        if a is None or b is None:
            raise TypeError('a or b cannot be None')
        count = 0
        c = a ^ b
        while c:
            count += c & 1
            c >>= 1
        return count

Unit Test

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


class TestBits(unittest.TestCase):

    def test_bits_to_flip(self):
        bits = Bits()
        a = int('11101', base=2)
        b = int('01111', base=2)
        expected = 2
        self.assertEqual(bits.bits_to_flip(a, b), expected)
        print('Success: test_bits_to_flip')


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


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