Practice/Meta/Leetcode 43. Multiply Strings

Leetcode 43. Multiply Strings

CodingMust

Problem

Given two non-negative integers represented as strings, return their product as a string. You must implement the multiplication algorithm without converting the entire strings to integer or floating-point types, and without using any built-in big integer libraries.

The challenge is to simulate manual multiplication the way you learned in elementary school: multiply each digit of one number by each digit of the other, properly manage the place values and carries, and construct the final result digit by digit.

Requirements

1. Implement multiplication using only string manipulation and basic digit operations
2. Return the result as a string with no leading zeros (except when the result is "0")
3. Do not use built-in conversion functions like int() to convert the entire string
4. Do not use big integer libraries or classes
5. Handle the zero case correctly

Constraints

• 1 ≤ num1.length, num2.length ≤ 200
• Both strings contain only digits (0-9)
• Both strings do not contain any leading zeros except for the number 0 itself
• Time complexity should be O(m × n) where m and n are the lengths of the input strings
• Space complexity should be O(m + n) for the result storage

Examples

Example 1:

Input: num1 = "2", num2 = "3" Output: "6" Explanation: Simple single-digit multiplication: 2 × 3 = 6

Example 2:

` Input: num1 = "123", num2 = "456" Output: "56088" Explanation: 123 × 456

738 (123 × 6) 6150 (123 × 5, shifted one position) 49200 (123 × 4, shifted two positions)

56088 `

Example 3:

Input: num1 = "0", num2 = "999" Output: "0" Explanation: Anything multiplied by zero is zero