function q53()
{
$count = 0;
for ($n = 1; $n <= 100; ++$n) {
for ($k = 0; $k <= $n; ++$k) {
$numberOfCombinations = Math::combination($n, $k);
if ($numberOfCombinations > 1000000) {
++$count;
}
}
}
return $count;
}
function q21($from, $to)
{
$integerToSum = [];
for ($i = $from; $i < $to; ++$i) {
$primeDecomposition = IntegerFactorization::solve($i);
$sumOfDivisors = Math::divisorsSum($primeDecomposition);
$sumOfProperDivisors = $sumOfDivisors - $i;
$integerToSum[$i] = $sumOfProperDivisors;
}
$sumOfAmicableNumbers = 0;
foreach ($integerToSum as $integer => $sum) {
if ($integer !== $sum && isset($integerToSum[$sum]) && $integerToSum[$sum] === $integer) {
$sumOfAmicableNumbers += $integerToSum[$integer] + $integerToSum[$sum];
unset($integerToSum[$integer]);
unset($integerToSum[$sum]);
}
}
return $sumOfAmicableNumbers;
}
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;
}
<?php use tomzx\ProjectEuler\Math; require_once 'vendor/autoload.php'; echo Math::combination(40, 20);
/**
* @param int $n
* @param int $k
* @return int
*/
public static function combination($n, $k)
{
return Math::factorial($n) / (Math::factorial($k) * Math::factorial($n - $k));
}
function q5($number)
{
$numbers = range(1, $number);
return Math::leastCommonMultiple($numbers);
}
