Introduction

In this blog post, we will explore how to solve the LeetCode problem "43" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string. Note: You must not use any built-in BigInteger library or convert the inputs to integer directly. Example 1: Input: num1 = "2", num2 = "3" Output: "6" Example 2: Input: num1 = "123", num2 = "456" Output: "56088" Constraints: 1 <= num1.length, num2.length <= 200 num1 and num2 consist of digits only. Both num1 and num2 do not contain any leading zero, except the number 0 itself.

Explanation

Here's the breakdown of the approach, complexity, and the Python code for multiplying two non-negative integers represented as strings without using built-in BigInteger libraries.

• High-Level Approach:

  • Simulate manual multiplication: Multiply each digit of num1 with each digit of num2.
  • Store intermediate products: Accumulate the products at the correct positions in a result array (similar to how you'd do it on paper).
  • Handle carries: Propagate carries through the result array to get the final product.

• Complexity:

  • Runtime: O(m*n), where 'm' and 'n' are the lengths of num1 and num2 respectively. Storage: O(m+n) to store the result.

• Python Code:

Code

    def multiply_strings(num1, num2):
    """
    Multiplies two non-negative integers represented as strings.

    Args:
        num1: The first number as a string.
        num2: The second number as a string.

    Returns:
        The product of num1 and num2 as a string.
    """

    if num1 == "0" or num2 == "0":
        return "0"

    m, n = len(num1), len(num2)
    product = [0] * (m + n)

    for i in range(m - 1, -1, -1):
        carry = 0
        for j in range(n - 1, -1, -1):
            product[i + j + 1] += int(num1[i]) * int(num2[j]) + carry
            carry = product[i + j + 1] // 10
            product[i + j + 1] %= 10
        product[i] += carry

    result = "".join(map(str, product))
    # Remove leading zeros
    while result[0] == '0' and len(result) > 1:
        result = result[1:]
    return result