<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:
    std::string multiply(std::string num1, std::string num2) {
        if (num1 == "0" || num2 == "0") return "0";  // Edge case where one of the numbers is zero

        int n1 = num1.size();
        int n2 = num2.size();

        vector<string> ans;

        for(int i = n2 - 1; i >= 0; i--){
            int x = num2[i] - '0';
            int carry = 0;
            string res = "";
            
            for(int j = n1 - 1; j >= 0; j--){
                int y = num1[j] - '0';
                int product = (x * y) + carry;
                res = to_string(product % 10) + res;
                carry = product / 10;
            }
            
            if(carry != 0){
                res = to_string(carry) + res;
            }
            
            // Append the required number of zeros
            res.append(n2 - 1 - i, '0');
            ans.push_back(res);
        }

        // Now sum up all the partial results
        string finalResult = "";
        int carry = 0;
        int maxLength = ans[ans.size() - 1].size();

        for(int i = 0; i < maxLength; i++){
            int sum = carry;
            for(int j = 0; j < ans.size(); j++){
                if (i < ans[j].size()) {
                    sum += ans[j][ans[j].size() - 1 - i] - '0';
                }
            }
            finalResult = to_string(sum % 10) + finalResult;
            carry = sum / 10;
        }

        if(carry != 0){
            finalResult = to_string(carry) + finalResult;
        }

        return finalResult;
    }
};
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