Given two numbers represented as strings, return multiplication of the numbers as a string.

Note:

  • The numbers can be arbitrarily large and are non-negative.
  • Converting the input string to integer is NOT allowed.
  • You should NOT use internal library such as BigInteger.
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public class Solution {
    public String multiply(String num1, String num2) {
        if (num1 == null || num2 == null) {
            return null;
        }
        int m = num1.length(), n = num2.length();
        int[] sums = new int[m + n];
        
        for (int i = m - 1; i >= 0; i--) {
            for (int j = n - 1; j >=0; j--) {
                int left = i + j, right = i + j + 1;
                int sum = (num1.charAt(i) - '0') * (num2.charAt(j) - '0') + sums[right];
                sums[right] = sum % 10;
                sums[left] += sum / 10;
            }
        }
        
        StringBuilder res = new StringBuilder();
        for (int i = 0; i < sums.length; i++) {
            if (!(res.length() == 0 && sums[i] == 0)) {
                res.append(sums[i]);
            }
        }
        return res.length() == 0 ? "0" : res.toString();
    }
}