Multiply Strings
<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>
Math; String; Simulation
class Solution {
    /**
     * @param string $num1
     * @param string $num2
     * @return string
     */

    function multiply($num1, $num2) {
        $length1 = strlen($num1);
        $length2 = strlen($num2);
        $product = array_fill(0, $length1 + $length2, 0);

        for ($i = $length1 - 1; $i >= 0; $i--) {
            for ($j = $length2 - 1; $j >= 0; $j--) {
                $digit1 = intval($num1[$i]);
                $digit2 = intval($num2[$j]);

                $temp = $digit1 * $digit2 + $product[$i + $j + 1];
                $product[$i + $j + 1] = $temp % 10;

                $carry = intval($temp / 10);
                $product[$i + $j] += $carry;
            }
        }
        $result = implode('', $product);
        $result = ltrim($result, '0');
        return $result === '' ? '0' : $result;
    }
}