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"""

Multiply Strings

Given two non-negative integers represented as strings, return their product

as a string without using built-in BigInteger or direct integer conversion.

Reference: https://leetcode.com/problems/multiply-strings/

Complexity:

Time: O(m * n) where m, n are the lengths of the two numbers

Space: O(m + n)

"""

from __future__ import annotations

def multiply(num1: str, num2: str) -> str:

"""Multiply two numbers represented as strings.

Args:

num1: The first number as a string.

num2: The second number as a string.

Returns:

The product of the two numbers as a string.

Examples:

>>> multiply("23", "23")

'529'

"""

intermediate: list[int] = []

zero = ord("0")

position_i = 1

for digit_i in reversed(num1):

position_j = 1

accumulator = 0

for digit_j in reversed(num2):

product = (

(ord(digit_i) - zero) * (ord(digit_j) - zero) * position_j * position_i

)

position_j *= 10

accumulator += product

position_i *= 10

intermediate.append(accumulator)

return str(sum(intermediate))

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