<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) 
    {
        string& st1 = num1.size() > num2.size() ? num1 : num2;
        string& st2 = st1 == num1 ? num2 : num1;

        uint8_t** buffers = new uint8_t*[st2.size()];
        int nc = st1.size() + st2.size() + 1;
        for(int i = 0; i < st2.size(); ++i)
        {
            buffers[i] = new uint8_t[nc]();
        }

        for(int i = st2.size()-1; i >= 0; --i)
        {
            uint8_t d1 = st2[i] - '0';
            for(int j = st1.size()-1; j >= 0; j--)
            {
                uint8_t d2 = st1[j] - '0';
                uint8_t prod = d2*d1;

                int cell1 = buffers[st2.size()-1-i][nc-1-(st1.size()-1-j)-(st2.size()-1-i)] + prod;
                buffers[st2.size()-1-i][nc-1-(st1.size()-1-j)-(st2.size()-1-i)] = (cell1 % 10);
                buffers[st2.size()-1-i][nc-1-(st1.size()-1-j)-(st2.size()-1-i)-1] += (uint8_t)floor((double)cell1 / 10.0);
            }
        }

        string result = "";
        int carry = 0;
        for(int c = nc-1; c >= 0; --c)
        {
            int currSum = carry;
            for(int r = 0; r < st2.size(); ++r)
            {
                currSum += buffers[r][c];
            }
            result += '0' + (currSum % 10);
            carry = (int)floor((double)currSum/10.0);
        }

        while(*result.rbegin() == '0')
        {
            result.pop_back();
        }
        reverse(result.begin(), result.end());

        for(int i = 0; i < st2.size(); ++i)
        {
            delete[] buffers[i];
        }
        delete[] buffers;

        return result.size() == 0 ? "0" : result;;    
    }
};
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