43_Multiply Strings

Given two non-negative integersnum1andnum2represented as strings, return the product ofnum1andnum2, 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 num1and num2is < 110.

2. Both num1and num2contain only digits0-9.

3. Both num1and 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

Variant of multiply two integers.

Time complexity: $O(mn)$, where $m, n$ are length of inputs.

def multiply(num1, num2):
    """
    :type num1: str
    :type num2: str
    :rtype: str
    """
    # deal with corner case
    if num1 == '0' or num2 == '0':
        return '0'

    result = [0] * (len(num1) + len(num2))
    for i in range(len(num1)-1, -1, -1):
        for j in range(len(num2)-1, -1, -1):
            result[i+j+1] += int(num1[i]) * int(num2[j])
            result[i+j] += result[i+j+1] // 10
            result[i+j+1] %= 10
    result = result[next(i for i, x in enumerate(result) if x != 0):]
    return ''.join(str(e) for e in result)