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

- Can we assume the inputs are valid?
- No, check for None

- Can we assume this fits memory?
- Yes

* None input -> TypeError * 5, 7 -> 12 * -5, -7 -> -12 * 5, -7 -> -2

We'll look at the following example, adding a and b:

a 0111 b 0101

First, add a and b, without worrying about the carry (0+0=0, 0+1=1, 1+1=0):

result = a ^ b = 0010

Next, calculate the carry (1+1=2). We'll need to left shift one to prepare for the next iteration when we move to the next most significant bit:

carry = (a&b) << 1 = 1010

If the carry is not zero, we'll need to add the carry to the result. Recursively call the function, passing in result and carry.

Below are the values of a, b, and the carry of a = 7 and b = 5, producing the result of 12.

a 0111 b 0101 ----- c 0101 a 0010 b 1010 ----- c 0010 a 1000 b 0100 ----- c 0000 a 1100 b 0000 c = carry = 0, return the result 1100

Complexity:

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

In [1]:

```
class Solution(object):
def sum_two(self, a, b):
if a is None or b is None:
raise TypeError('a or b cannot be None')
result = a ^ b;
carry = (a&b) << 1
if carry != 0:
return self.sum_two(result, carry)
return result;
```

In [2]:

```
%%writefile test_sum_two.py
import unittest
class TestSumTwo(unittest.TestCase):
def test_sum_two(self):
solution = Solution()
self.assertRaises(TypeError, solution.sum_two, None)
self.assertEqual(solution.sum_two(5, 7), 12)
self.assertEqual(solution.sum_two(-5, -7), -12)
self.assertEqual(solution.sum_two(5, -7), -2)
print('Success: test_sum_two')
def main():
test = TestSumTwo()
test.test_sum_two()
if __name__ == '__main__':
main()
```

In [3]:

```
%run -i test_sum_two.py
```