Multiply Two Strings

class Solution:
    # UNRELATED TO SOLVE -- THIS IS JUST IN CASE INTERVIEWER ASKS
    def multiply_number_with_single_digit(self, num: str, digit: str) -> list[str]:
        from collections import deque
        answers = deque([])

        remainder = 0
        for i in range(len(num) - 1, -1, -1):
            total = int(num[i]) * int(digit) + remainder
            next_digit, remainder = total % 10, total // 10 # max = 81
            answers.appendleft(str(next_digit))
        # Post for processing
        if remainder > 0:
            answers.append_left(str(remainder))

        return answers

    def solve(self, num1: str, num2: str) -> str:
        """
        The idea is we compute in reversed order of num1 and num2
        to get reversed order of our answer so that we can
        allocate the number of zeros and distribute the remainder

        Time Complexity: O(len(num1) * len(num2))
        Space Complexity: O(len(num1) + len(num2))
        """

        if num1 == "0" or num2 == "0":
            return "0"
        answer = [0] * (len(num1) + len(num2))

        for i2 in range(len(num2) - 1, -1, -1):
            digit2 = num2[i2]
            # multiply 'digit2' by all digits in num1.
            for i1 in range(len(num1) - 1, -1, -1):
                digit1 = num1[i1]

                # e.g 45 * 23 = 45 * 3 * 10^0 + 45 * 3 * 10^1
                dist_from_last1 = len(num1) - 1 - i1
                dist_from_last2 = len(num2) - 1 - i2
                num_zeros = dist_from_last1 + dist_from_last2

                # The digit currently at position numZeros in the answer string
                # is carried over and summed with the current result.
                remainder = answer[num_zeros]
                multiplication = int(digit1) * int(digit2) + remainder
                answer[num_zeros] = multiplication % 10

                # remainder the tens place of the multiplication result by
                # adding it to the next position in the answer array.
                answer[num_zeros + 1] += multiplication // 10

        # Pop the excess 0 from the end of answer.
        if answer[-1] == 0:
            answer.pop(-1)

        return "".join(str(digit) for digit in reversed(answer))