function q34()
{
// The maximum value the sum of factorial function can reach is ceil(log(n, 10)) * 9!, where n is any number
// for example, if n = 399, then ceil(log(399, 10)) = ceil(2.6) = 3 (3 digits) and thus the max for 3 digits is
// 3 * 9! or 3 * 362880
// ceil(log(n, 10)) * 9! < n
// If we ignore the ceil and solve for log(n, 10) * 9! < n, n > 74482
$n = 3;
$total = 0;
for ($n = 3; $n < 74482; ++$n) {
$parts = str_split($n);
$sum = 0;
foreach ($parts as $part) {
$factorial = Math::factorial($part);
$sum += $factorial;
}
if ($sum === $n) {
$total += $sum;
}
}
return $total;
}
/**
* @param array $lexemes ordered from smallest to biggest
* @param int $permutationIndex
*/
function q24(array $lexemes, $permutationIndex)
{
$lexemesCount = count($lexemes);
$size = Math::factorial($lexemesCount);
if ($permutationIndex > $size) {
throw new LogicException('Index is superior to the size of the generatable permutations.');
}
$output = '';
while ($lexemesCount !== 0) {
$x = Math::factorial($lexemesCount - 1);
foreach ($lexemes as $index => $lexeme) {
if ($permutationIndex <= $x) {
$output .= $lexemes[$index];
unset($lexemes[$index]);
break;
}
$permutationIndex -= $x;
}
--$lexemesCount;
}
echo $output;
}
/**
* @param int $n
* @param int $k
* @return int
*/
public static function combination($n, $k)
{
return Math::factorial($n) / (Math::factorial($k) * Math::factorial($n - $k));
}
