/**
* Return the factorial (n!) of the parameter $wanted.
*
* If GMP is installed, GMP will be used to calculate the factorial,
* If libbcmath is installed, bcmath will be used for all mathematics operation.
*
* If none of previous library is available, then basic php functions will be used,
* so the function could result in an error or php can return INF.
*
* If GMP is not installed, be aware of the "Maximum function nesting level" value.
*
* @param int|string $wanted The wanted factorial base
*
* @return int|string
*
* @throws \InvalidArgumentException if [$wanted] is not a positive number
*/
public static function factorial($wanted)
{
// Check input data
if (!is_numeric($wanted) || $wanted < 0) {
throw new \InvalidArgumentException('The [wanted] parameter MUST be a positive number');
}
// Use GMP extension if available
if (function_exists('gmp_fact')) {
return gmp_strval(gmp_fact($wanted));
}
// Use cache if exist (for performance)
if (array_key_exists($wanted, self::$factorialCache)) {
return self::$factorialCache[$wanted];
}
if ($wanted === 1 || $wanted === 0) {
$value = 1;
} else {
if (function_exists('gmp_mul')) {
$value = gmp_strval(gmp_mul($wanted, self::factorial($wanted - 1)));
} elseif (function_exists('bcmul')) {
$value = bcmul($wanted, self::factorial($wanted - 1));
} else {
$value = $wanted * self::factorial($wanted - 1);
}
}
// Save in cache for later use
self::$factorialCache[$wanted] = $value;
return $value;
}
public static function combinations($num, $repetitions)
{
if ($num >= $repetitions) {
return gmp_strval(gmp_fact($num)) / (gmp_strval(gmp_fact($repetitions)) * gmp_strval(gmp_fact($num - $repetitions)));
} else {
exit('Error you could, not second parameter that is greater than the first one.');
}
}
/**
* Gets the probaibiliy using the pmf function of a certain outcome
* @param float $x Outcome
* @return float
* @throws UnexpectedValueException if x is not an int
*/
public function get_probability($x)
{
if (is_int($x)) {
return gmp_fact($this->n) / (gmp_fact($x) * gmp_fact($this->n - $x)) * exp($this->p, $x) * exp(1 - $this->p, $this->n - $x);
} else {
throw new UnexpectedValueException('UnexpectedValueException occured because BionomailDistribution is not continous so x cannot be a non-integer');
}
}
public function get_probability($x)
{
if (is_numeric($x)) {
return exp($this->lambda, $x) * exp(M_E, $this->lambda * -1) / gmp_fact($x);
} else {
throw new UnexpectedValueException();
}
}
function solve($reader)
{
fscanf($reader, "%d\n", $number);
for ($i = 0; $i < $number; $i++) {
fscanf($reader, "%d\n", $N);
$fac = gmp_strval(gmp_fact($N));
$sum = 0;
while ($fac != 0) {
$sum += bcmod($fac, 10);
$fac = bcdiv($fac, 10);
}
echo $sum . "\n";
}
}
function CantorExpand($n, $x)
{
//參數說明
// $n - 排列的位數
// $x - 第幾個 (必須要是字串)
//1. $x 先減1
$x = gmp_sub($x, "1");
$str = "";
for ($i = 1; $i <= $n; $i++) {
//2. 先算($n-$i)階乘
$fac = gmp_strval(gmp_fact($n - $i));
//3. 再算 $x / ($n-$i) 的商跟餘數
$res = gmp_div_qr($x, $fac);
$quotient = gmp_strval($res[0]);
$remainder = gmp_strval($res[1]);
//4. 比這個位數小的數目總共有 $quotient 個，所以開始找出這個位數
$str .= findMax($quotient);
//5. 把餘數設為 $x，下次要使用
$x = $remainder;
}
return $str;
}
<?php
// Name ( Cost, Damage, Armor )
$weapons = array("Dagger" => array(8, 4, 0), "Shortsword" => array(10, 5, 0), "Warhammer" => array(25, 6, 0), "Longsword" => array(40, 7, 0), "Greataxe" => array(74, 8, 0));
$armor = array("Leather" => array(13, 0, 1), "Chainmail" => array(31, 0, 2), "Splintmail" => array(53, 0, 3), "Bandedmail" => array(75, 0, 4), "Platemail" => array(102, 0, 5));
$rings = array("Damage +1" => array(25, 1, 0), "Damage +2" => array(50, 2, 0), "Damage +3" => array(100, 3, 0), "Defense +1" => array(20, 0, 1), "Defense +2" => array(40, 0, 2), "Defense +3" => array(80, 0, 3));
$everything = array_values(array_merge($weapons, $armor, $rings));
$boss = array("Hit Points" => 104, "Damage" => 8, "Armor" => 1);
$hero = array("Hit Points" => 100, "Damage" => 0, "Armor" => 0);
$gold_spent = false;
$permutations = gmp_strval(gmp_fact(count($everything)) / gmp_fact(count($everything) - 3));
// 3 types of items
function permute($items, $perms = array())
{
if (empty($items)) {
var_dump($perms);
} else {
for ($i = count($items) - 1; $i >= 0; --$i) {
$newitems = $items;
$newperms = $perms;
list($foo) = array_splice($newitems, $i, 1);
array_unshift($newperms, $foo);
permute($newitems, $newperms);
}
}
}
permute($everything);
while ($boss['Hit Points'] > 0 & $hero['Hit Points'] > 0) {
$damage_to_hero = $boss["Damage"] - $hero["Armor"];
$damage_to_boss = $hero["Damage"] - $boss["Armor"];
$boss["Hit Points"] -= $damage_to_boss > 0 ? $damage_to_boss : 1;
private function _fact($num)
{
$num = (int) $num;
if (0 > $num) {
return NAN;
}
if (function_exists('gmp_fact')) {
$fact = gmp_strval(gmp_fact("{$num}"));
} else {
$fact = 1;
for ($i = 2; $i <= $num; ++$i) {
$fact = $fact * $i;
}
}
return $fact;
}
<?php
$totsum = 0;
// the maximum for a digit is 9! = 362880
// the maximum total for a 7 digit number is 2,540,160
// the maximum total for a 8 digit number is 2,903,040
// our ceiling will have to be 7 digits and no more than 2.9 million
for ($num = 10; $num < 2903040; $num++) {
$num = (string) $num;
$sum = 0;
for ($i = 0; $i < strlen((string) $num); $i++) {
$sum = gmp_add(gmp_fact($num[$i]), $sum);
}
$sum = gmp_strval($sum);
if ($sum == $num) {
$totsum += $sum;
echo "{$sum}\n";
}
}
echo "total: {$totsum}\n";
function extraLongFactorial($n)
{
$fact1 = gmp_fact($n);
// 5 * 4 * 3 * 2 * 1
return gmp_strval($fact1) . "\n";
}
/**
* Calculates factorial of this value.
*
* @return BigInteger
*/
public function factorial() : BigInteger
{
$calculatedValue = gmp_fact($this->getValue());
return $this->assignValue($calculatedValue);
}
<?php
$fact = gmp_strval(gmp_fact(100));
$sum = 0;
for ($a = 0; $a < strlen($fact); $a++) {
$sum += $fact[$a];
}
echo "{$sum}\n";
<?php
/**
* Lattice paths
*
* Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
*
* How many such routes are there through a 20×20 grid?
*/
$steps_left = 20;
$steps_down = 20;
$possible = 1;
$steps = $steps_left + $steps_down;
while ($steps > $steps_left) {
$possible = $possible * $steps;
$steps--;
}
$paths = $possible / gmp_strval(gmp_fact($steps_down));
echo $paths;
public function factorial($a)
{
$result = null;
$aa = gmp_fact($a);
$result = gmp_strval($aa);
// $this->op = "!";
return $result;
}
var_dump($res);
printf("Result is: q - %s, r - %s" . PHP_EOL, gmp_strval($res[0]), gmp_strval($res[1]));
// gmp_div_r
$div = gmp_div_r("105", "20");
echo gmp_strval($div) . "\n";
// gmp_div
$div1 = gmp_div("100", "5");
echo gmp_strval($div1) . "\n";
// gmp_divexact
$div1 = gmp_divexact("10", "2");
echo gmp_strval($div1) . "\n";
// gmp_fact
$fact1 = gmp_fact(5);
// 5 * 4 * 3 * 2 * 1
echo gmp_strval($fact1) . "\n";
$fact2 = gmp_fact(50);
// 50 * 49 * 48, ... etc
echo gmp_strval($fact2) . "\n";
// gmp_gcd
$gcd = gmp_gcd("12", "21");
echo gmp_strval($gcd) . "\n";
// gmp_gcdext
$a = gmp_init(12);
$b = gmp_init(21);
$g = gmp_gcd($a, $b);
$r = gmp_gcdext($a, $b);
$check_gcd = gmp_strval($g) == gmp_strval($r['g']);
$eq_res = gmp_add(gmp_mul($a, $r['s']), gmp_mul($b, $r['t']));
$check_res = gmp_strval($g) == gmp_strval($eq_res);
if ($check_gcd && $check_res) {
$fmt = "Solution: %d*%d + %d*%d = %d\n";
<?php
var_dump(gmp_strval(gmp_fact(0)));
var_dump(gmp_strval(gmp_fact("")));
var_dump(gmp_strval(gmp_fact("0")));
var_dump(gmp_strval(gmp_fact("-1")));
var_dump(gmp_strval(gmp_fact(-1)));
var_dump(gmp_strval(gmp_fact(1.1)));
var_dump(gmp_strval(gmp_fact(20)));
var_dump(gmp_strval(gmp_fact("50")));
var_dump(gmp_strval(gmp_fact("10")));
var_dump(gmp_strval(gmp_fact("0000")));
$n = gmp_init(12);
var_dump(gmp_strval(gmp_fact($n)));
$n = gmp_init(-10);
var_dump(gmp_strval(gmp_fact($n)));
var_dump(gmp_fact());
var_dump(gmp_fact(1, 1));
var_dump(gmp_fact(array()));
var_dump(gmp_strval(gmp_fact(array())));
echo "Done\n";
<?php
/**
* Factorial digit sum
*
* n! means n × (n − 1) × ... × 3 × 2 × 1
*
* For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
* and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
*
* Find the sum of the digits in the number 100!
*/
$factorial = gmp_strval(gmp_fact(100));
$numbers_arr = array();
while ($factorial > 0) {
$numbers_arr[] = gmp_strval(gmp_mod($factorial, 10));
$factorial = gmp_strval(gmp_div_q($factorial, 10));
}
echo array_sum($numbers_arr);
