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/**
 * 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.
 */
 
public class Solution {
    public String multiply(String num1, String num2) {
        if(num1.equals("0") || num2.equals("0"))
            return "0";
        int l1 = num1.length(), l2 = num2.length();
        int[] n1 = new int[l1];
        int[] n2 = new int[l2];
        // convert num1 to number array reversely
        for (int i = 0; i < l1; i++) {
            n1[l1 - i - 1] = num1.charAt(i) - '0';
        }
        // convert num2 to number array reversely
        for (int i = 0; i < l2; i++) {
            n2[l2 - i - 1] = num2.charAt(i) - '0';
        }
        int sum = 0;
        StringBuilder ss = new StringBuilder();
        for (int i = 0; i < l1 + l2 - 1; i++) {
            for (int j = 0; j <= i; j++) {
                if(j < l1 && i - j < l2) {
                    sum += n1[j] * n2[i - j];
                }
            }
            ss.append((char) (sum % 10 + '0'));
            sum /= 10;
        }
        if (sum > 0) 
            ss.append((char) (sum + '0'));
        String s = ss.reverse().toString();
        return s.isEmpty() ? "0" : s;
    }
    
    public String multiply(String num1, String num2) {
        String n1 = new StringBuilder(num1).reverse().toString();
        String n2 = new StringBuilder(num2).reverse().toString();
     
        int[] d = new int[num1.length()+num2.length()];
     
        //multiply each digit and sum at the corresponding positions
        for(int i=0; i<n1.length(); i++){
            for(int j=0; j<n2.length(); j++){
                d[i+j] += (n1.charAt(i)-'0') * (n2.charAt(j)-'0');
            }
        }
     
        StringBuilder sb = new StringBuilder();
     
        //calculate each digit
        for(int i=0; i<d.length; i++){
            int mod = d[i]%10;
            int carry = d[i]/10;
            if(i+1<d.length){
                d[i+1] += carry;
            }
            sb.insert(0, mod);
        }
     
        //remove front 0's
        while(sb.charAt(0) == '0' && sb.length()> 1){
            sb.deleteCharAt(0);
        }
     
        return sb.toString();
    }
}