/*
This program computes factorials greater than 20 without BCMath.
It uses a simple big‑integer implementation based on string multiplication.
*/
/*
Multiply two non‑negative integers represented as strings.
Classic grade‑school multiplication adapted for PHP strings.
*/
function multiply_strings(string $a, string $b): string
{
$a = strrev($a);
$b = strrev($b);
$result = array_fill(0, strlen($a) + strlen($b), 0);
for ($i = 0; $i < strlen($a); $i++) {
for ($j = 0; $j < strlen($b); $j++) {
$result[$i + $j] += (int)$a[$i] * (int)$b[$j];
}
}
// Handle carries
for ($i = 0; $i < count($result); $i++) {
if ($result[$i] >= 10) {
$carry = intdiv($result[$i], 10);
$result[$i] %= 10;
if (!isset($result[$i + 1])) {
$result[$i + 1] = 0;
}
$result[$i + 1] += $carry;
}
}
// Convert back to string
while (end($result) === 0 && count($result) > 1) {
array_pop($result);
}
return implode('', array_reverse($result));
}
/*
Compute factorial using string‑based big‑integer arithmetic.
*/
function factorial_big(int $n): string
{
$result = "1";
for ($i = 2; $i <= $n; $i++) {
$result = multiply_strings($result, (string)$i);
}
return $result;
}
/*
Main entry point: read input, compute factorial, print result.
*/
echo "Enter a number greater than 20: ";
$n = intval(trim(fgets(STDIN)));
$result = factorial_big($n);
echo "\nFactorial of {$n} is:\n\n";
echo $result . "\n";
/*
run:
Enter a number greater than 20: 25
Factorial of 25 is:
15511210043330985984000000
*/
