<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 multiply(string num1, string num2) {
        
        if(num1 == "0" || num2 == "0")
            return "0";
        
        if(num2.size() > num1.size())
            swap(num1, num2);
        
        int ptrOne = num1.size() - 1;
        int ptrTwo = num2.size() - 1;
        int zeroes = 0;

        string result;

        while(ptrTwo >= 0)
        {
            string temp;
            smul(num1, num2, ptrTwo, temp);
            for(int i = 0; i<zeroes; i++)
            {
                temp+="0";
            }
            sadd(result, temp);
            ptrTwo--;
            zeroes++;
        }

        return result;
    }
    void smul(string& num1, string& num2, int ptrTwo, string& temp)
    {
        int ptrOne = num1.size()-1;
        int carry = 0;
        while(ptrOne >= 0)
        {
            int digit = carry;
            digit += (num1[ptrOne] - '0') * (num2[ptrTwo] - '0');
            if(digit > 9)
            {
                carry = digit/10;
                digit %= 10;
            }
            else
            {
                carry = 0;
            }
            temp = to_string(digit) + temp;
            ptrOne--;
        }
        if(carry > 0)
        {
            temp = to_string(carry) + temp;
        }
    }
    void sadd(string& result, string& temp)
    {
        //ensuring result is larger than temp
        if(result.size() < temp.size())
            swap(result,temp);
        
        int ptrOne = temp.size()-1;
        int ptrTwo = result.size() - 1;
        int carry = 0;
        while(ptrTwo >= 0)
        {
            int digit = carry;
            if(ptrOne >=0)
            {
                digit += temp[ptrOne] - '0';
            }
            digit += result[ptrTwo] - '0';
            
            if(digit>9)
            {
                carry = digit/10;
                digit = digit % 10;
            }
            else
            {
                carry = 0;
            }
           
            result[ptrTwo] = digit + '0';
            ptrTwo--;
            ptrOne--;
        }
        if(carry > 0)
        {
            result = to_string(carry) + result;
        }
    }
};
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