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

<p><strong>Note:</strong>&nbsp;You must not use any built-in BigInteger library or convert the inputs to integer directly.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> num1 = "2", num2 = "3"
<strong>Output:</strong> "6"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> num1 = "123", num2 = "456"
<strong>Output:</strong> "56088"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num1.length, num2.length &lt;= 200</code></li>
	<li><code>num1</code> and <code>num2</code> consist of digits only.</li>
	<li>Both <code>num1</code> and <code>num2</code>&nbsp;do not contain any leading zero, except the number <code>0</code> itself.</li>
</ul>

class Solution {
public:
    string addStrings(string num1, string num2) {
        string result(max(num1.size() , num2.size()) + 1, '0');
        int i = num1.size() - 1, carry = 0 , j = num2.size() - 1;
        int k = result.size() - 1;
        while(i >= 0 || j >= 0 || carry != 0){
            int x = (i >= 0) ? num1[i] - '0' : 0;
            int y = (j >= 0) ? num2[j] - '0' : 0;
            int sum = x + y + carry;
            carry = sum / 10;
            result[k--] = (sum % 10) + '0';
            i--;
            j--;
        }
        if(result[0] == '0'){
            result.erase(0,1);
        }
        return result;
    }
    string multiply(string num1, string num2) {
        if(num1 == "0" || num2 == "0") return "0";
        string res = "0";
        int power = 0;
        for(int i = num2.size() - 1 ; i >= 0 ; i--){
            string temp = "";
            int carry = 0;
            for(int j = num1.size() - 1 ; j >= 0 ; j--){
                int n1 = (j >= 0) ? (num1[j] - '0') : 0;
                int n2 = (i >= 0) ? (num2[i] - '0') : 0;
                int mult = n1 * n2 + carry;
                carry = mult / 10;
                mult = mult % 10;
                temp = char(mult + '0') + temp;
            }
            if(carry > 0){
                temp = char(carry + '0') + temp;
            }
            for(int k = 0 ; k < power ; k++){
                temp += '0';
            }
            res = addStrings(res,temp);
            power++;
        }
        return res;
    }
};
28123