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"""

Add Binary

Given two binary strings, return their sum as a binary string.

Reference: https://leetcode.com/problems/add-binary/

Complexity:

Time: O(max(m, n)) where m, n are lengths of the two strings

Space: O(max(m, n))

"""

from __future__ import annotations

def add_binary(first: str, second: str) -> str:

"""Add two binary strings and return their binary sum.

Args:

first: A string representing a binary number.

second: A string representing a binary number.

Returns:

A string representing the binary sum of the two inputs.

Examples:

>>> add_binary("11", "1")

'100'

"""

result = ""

carry, index_a, index_b = 0, len(first) - 1, len(second) - 1

zero = ord("0")

while index_a >= 0 or index_b >= 0 or carry == 1:

if index_a >= 0:

carry += ord(first[index_a]) - zero

index_a -= 1

if index_b >= 0:

carry += ord(second[index_b]) - zero

index_b -= 1

result = chr(carry % 2 + zero) + result

carry //= 2

return result

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