43. Multiply Strings

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Note: You must not use any built-in BigInteger library or convert the inputs to integer directly.

两个字符串的位数做乘法，每次计算进位。
当前位等于自身加上计算结果的个位（由于有之前的进位存在。），下一位等于计算结果的十位。

class Solution {
    public String multiply(String num1, String num2) {
        int m = num1.length();
        int n = num2.length();
        if( num1.equals("0") || num2.equals("0")){
            return "0";
        }
        int[] product = new int[m+n];
        
        char[] arr1 = num1.toCharArray();
        char[] arr2 = num2.toCharArray();
        
        for(int i = m-1; i >= 0; i--){
            for(int j = n-1; j >=0; j--){
                int sum = product[i+j+1] + (arr1[i] - '0') * (arr2[j] - '0');
                int curr = sum % 10;
                int carry = sum / 10;
            
                product[i+j] += carry;
                product[i+j+1] = curr;
            }
        }
        StringBuffer sb = new StringBuffer();
        for(int k = 0; k < m+n; k++ ){
            if(k == 0 && product[k] == 0 ) continue;
            sb.append(product[k]);
        }
        return sb.toString();
    }
}