[LeetCode] 43. Multiply Strings

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2.
Note:
  1. The length of both num1 and num2 is < 110.
  2. Both num1 and num2 contains only digits 0-9.
  3. Both num1 and num2 does not contain any leading zero.
  4. You must not use any built-in BigInteger library or convert the inputs to integer directly.

Thought process:
Use an array to keep track of the products of each pair of digits and add them together. When doing multiplication, I need to align the numbers to the right. So I need to iterate through the product array from right to left.

 Solution:

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class Solution {
    public String multiply(String num1, String num2) {
        int[] products = new int[num1.length() + num2.length() - 1];
        for (int i = num1.length() - 1; i >= 0; i--) {
            for (int j = num2.length() - 1; j >= 0; j--) {
                products[i + j] += (num1.charAt(i) - '0') * (num2.charAt(j) - '0');
            }
        }
        
        int i = products.length - 1;
        int carry = 0;
        StringBuilder sb = new StringBuilder();
        
        while (i >= 0 || carry > 0) {
            int sum = i >= 0 ? products[i] + carry : carry;
            sb.append(sum % 10);
            carry = sum / 10;
            i--;
        }
        while (sb.length() > 0 && sb.charAt(sb.length() - 1) == '0') {
            sb.deleteCharAt(sb.length() - 1);
        }
        
        return sb.length() == 0 ? "0" : sb.reverse().toString();
    }
}

Time complexity:
Say num1.length = a and num2.length = b. The overall time complexity is O(ab).
Location: Philadelphia, PA, USA

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