Multiply Strings

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.

For example:

reverse the input numbers,

then calculate {[0,0]-16}, {[0,1],[1,0] - 24}, {[1,2],[2,1] - 17}, {[2,2],[3,1] - 10}, {[3,2] - 3}

append digit%10, carryon digit/10

1234 * 34

  4321              
    43   
------------     
  16           
   24             
    17         
     10
      3
------------
65914 -> 41956

public String multiply(String num1, String num2) {
        if (num1==null||num2==null||num1.isEmpty()||num2.isEmpty()) {
            return null;
        }

        String n1 = new StringBuilder(num1).reverse().toString();
        String n2 = new StringBuilder(num2).reverse().toString();

        int[] results = new int[n1.length()+n2.length()];

        for (int i=0; i<n1.length(); i++) {
            for (int j=0; j<n2.length(); j++) {
                results[i+j] += (n1.charAt(i)-'0') * (n2.charAt(j)-'0');
            }
        }

        StringBuilder product = new StringBuilder();
        for (int i=0; i<results.length; i++) {
            int digit = results[i]%10;
            int carryOn = results[i]/10;

            if (i+1<results.length) {
                results[i+1] += carryOn;
            }
            product.insert(0, digit);
        }

        //if we allocate a larger results array, then clear all leading 0
        while (product.charAt(0)=='0' && product.length()>1) {
            product.deleteCharAt(0);
        }

        return product.toString();
    }