<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) {
        int n1 = num1.size();
        int n2 = num2.size();
        
        // Edge case: If either number is "0", the result is "0"
        if (num1 == "0" || num2 == "0") return "0";
        
        // Result array to store multiplication results
        vector<int> result(n1 + n2, 0);

        // Perform multiplication digit by digit
        for (int i = n1 - 1; i >= 0; --i) {
            for (int j = n2 - 1; j >= 0; --j) {
                int digit1 = num1[i] - '0'; // Convert char to int
                int digit2 = num2[j] - '0'; // Convert char to int

                int mul = digit1 * digit2;
                int sum = mul + result[i + j + 1];

                result[i + j + 1] = sum % 10;          // Place the unit value at the current position
                result[i + j] += sum / 10;             // Carry to the next position
            }
        }
        
        // Convert result array to string
        string product = "";
        for (int num : result) {
            if (!(product.empty() && num == 0)) { // Avoid leading zeros
                product.push_back(num + '0');     // Convert int to char
            }
        }
        
        return product.empty() ? "0" : product;
    }
};

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