<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";
        int carry = 0, temp = 0, length1 = num1.length() - 1, length2 = num2.length() - 1;
        string output;
        vector<string> outputlist;
        for (int i = 0; i <= length1; i++) {
            outputlist.push_back({});
            carry = 0;
            for (int j = 0; j < i; j++) outputlist[i] += "0";
            for (int j = 0; j <= length2; j++) {
                temp = (num1[length1 - i] - '0') * (num2[length2 - j] - '0') + carry;
                outputlist[i] += '0' + (temp%10);
                carry = temp/10;
            }
            if (carry != 0) outputlist[i] += '0' + carry;
        }
        temp = carry = 0;
        length1 = outputlist.size();
        for (int i = 0; i < outputlist.back().length(); i++) {
            temp = 0;
            for (int j = 0; j < length1; j++) {
                if (outputlist[j].length() > i) temp += (outputlist[j][i] - '0');
            }
            temp += carry;
            output += '0' + (temp%10);
            carry = temp / 10;
        }
        if (carry != 0) output += '0' + carry;
        reverse(output.begin(), output.end());
        return output;
    }
};
11759