# Question

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Example 1:

Input: num1 = "2", num2 = "3"
Output: "6"


Example 2:

Input: num1 = "123", num2 = "456"
Output: "56088"


Note:

1. The length of both num1 and num2 is < 110.
2. Both num1 and num2 contain only digits 0-9.
3. Both num1 and num2 do not contain any leading zero, except the number 0 itself.
4. You must not use any built-in BigInteger library or convert the inputs to integer directly.

# Solution

class Solution:
def multiply(self, num1, num2):
"""
:type num1: str
:type num2: str
:rtype: str
"""
if num1 == "0" or num2 == "0":
return "0"
num1 = list(num1)
num2 = list(num2)
num1.reverse()
num2.reverse()
factor = 1
total_sum = [0] * (len(num2) + len(num1))
for i in range(len(num2)):
for j in range(len(num1)):
position = i + j
product = int(num1[j]) * int(num2[i]) + total_sum[position]
digit = product % 10
carry = product // 10
total_sum[position] = digit
while carry > 0:
position += 1
product = carry + total_sum[position]
digit = product % 10
carry = product // 10
total_sum[position] = digit

while total_sum[-1] == 0:
total_sum.pop()

total_sum.reverse()
return "".join([str(x) for x in total_sum])