Solution.php

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;
    }
}