function Generate($level)
{
if ($level <= 3) {
$num1 = rand(2, 4);
$num2 = rand(5, 9);
} elseif ($level <= 6) {
$num1 = rand(4, 9);
$num2 = rand(10, 20);
} else {
$num1 = rand(10, 20);
$num2 = rand(10, 20);
}
// // Original exercise
// $num1 = 6;
// $num2 = 8;
$mult = $num1 * $num2;
$lcm = lcm($num1, $num2);
$correct = $mult == $lcm ? 0 : 1;
$options = ['Igaz', 'Hamis'];
$solution = $options[$correct];
$question = 'Adja meg az alábbi állítás logikai értékét (igaz vagy hamis)!<br />' . 'Ha egy szám osztható $' . $num1 . '$-' . With($num1) . ' és $' . $num2 . '$-' . With($num2) . ', akkor osztható $' . $mult . '$-' . With($mult) . ' is.';
$page[] = 'Tudjuk, hogy ha egy szám osztható $a$-val, és osztható $b$-vel is, akkor $a$ és $b$ <b>legkisebb közös többszörösével</b> is osztható, amit $[a;b]$-vel jelölünk.';
$page[] = 'Két szám legkisebb közös többszöröséhez először írjuk fel mindkét szám prímtényezős felbontását!';
$hints[] = $page;
$hints[][] = 'Az első szám prímtényezős felbontása: $' . $num1 . '=' . implode('\\cdot', $this->CanonicForm($num1)) . '$, ugyanis:' . $this->Factorization($num1);
$hints[][] = 'A második szám prímtényezős felbontása: $' . $num2 . '=' . implode('\\cdot', $this->CanonicForm($num2)) . '$, ugyanis:' . $this->Factorization($num2);
$page = [];
$page[] = 'Most gyűjtsünk össze minden prímtényezőt a hozzátartozó kitevővel (ha mindkét számban előfordul, akkor a nagyobb kitevőt nézzük): $$[' . $num1 . ';' . $num2 . ']=' . implode('\\cdot', $this->CanonicForm($lcm)) . '=' . $lcm . '$$';
$page[] = 'Mivel a legkisebb közös többszörös ' . ($lcm == $mult ? 'megegyezik' : 'nem egyezik meg') . ' ' . The($mult) . ' $' . $mult . '$-' . With($mult) . ', ezért az állítás <span class="label label-success">' . strtolower($solution) . '</span>.';
$hints[] = $page;
return array('question' => $question, 'correct' => $correct, 'solution' => $solution, 'options' => $options, 'hints' => $hints);
}
function lcm_arr($items)
{
//Input: An Array of numbers
//Output: The LCM of the numbers
while (count($items) >= 2) {
array_push($items, lcm(array_shift($items), array_shift($items)));
}
return reset($items);
}
function lcm_nums($ar)
{
if (count($ar) > 1) {
$ar[] = lcm(array_shift($ar), array_shift($ar));
return lcm_nums($ar);
} else {
return $ar[0];
}
}
/**
* Finds the LCM of an array of integers
* @param array $integers
* @return int
*/
function lcm(array $integers) {
if (count($integers) > 1) {
$a = array_shift($integers);
$b = array_shift($integers);
$integers[] = ($a / gcf($a, $b) * $b);
return lcm($integers);
}
else {
return $integers[0];
}
}
/**
* GI that generates data in clusters, using a specified distribution for each
* cluster.
*
* This GI requires the following template arguments:
* - 'n' or 0
* The number of tuples to generate. Note: this value is per task.
* The total number of tuples generated will be n_tasks * n
* - 'centers' or 1
* A list of configuration for the centers.
*
* The following template arguments are optional:
* - 'outputs'
* If the outputs of the GI are not given implicitly, they can be
* specified in this template argument. The number of dimensions will
* be determined by the number of outputs.
*
* All output types must be numeric real types. The default type for
* outputs is DOUBLE.
* - 'dist.lib' = 'std'
* Which library to use for generating distributions.
* Valid options are:
* - std
* - boost
* - 'seed' = null
* The seed to be used for the random number generator. This seed will
* be used to generate the seed for each task, and different runs with
* the same seed will produce the same data.
* - 'compute.sets' = 1
* The number of sets of tuples to compute at once.
*
* Each center configuration is a functor with the form:
* dist_name(args)
*
* The following distributions are supported:
* { Uniform Distributions }
* - uniform(a = 0, b = 1)
*
* { Normal Distributions }
* - normal(mean = 0.0, std_dev = 1.0) [ synonyms: gaussian ]
* - inverse_gaussian(mean = 1, shape = 1) [ synonyms: inverse_normal ]
*
* { Bernoulli Distributions }
* - binomial(t = 1, p = 0.5)
* - negative_binomial(k = 1, p = 0.5)
*
* { Poisson Distributions }
* - exponential( lambda = 1 )
* - gamma(alpha = 1, beta = 1) [ synonyms: Gamma ]
*/
function ClusterGen(array $t_args, array $outputs)
{
$sys_headers = ['array', 'cinttypes'];
$user_headers = [];
$libraries = [];
if (\count($outputs) == 0) {
grokit_assert(array_key_exists('outputs', $t_args), 'ClusterGen: No outputs specified');
$count = 0;
foreach ($t_args['outputs'] as $type) {
if (is_identifier($type)) {
$type = lookupType($type);
}
grokit_assert(is_datatype($type), 'ClusterGen: Non data-type ' . $type . ' given as output');
$name = 'output' . $count++;
$outputs[$name] = $type;
}
}
foreach ($outputs as $name => &$type) {
if (is_null($type)) {
$type = lookupType('base::DOUBLE');
} else {
grokit_assert($type->is('real'), 'ClusterGen: Non-real datatype ' . $type . ' given as output');
}
}
$myOutputs = [];
foreach ($outputs as $name => $type) {
$myOutputs[$name] = $type;
}
$tSize = \count($outputs);
$seed = get_default($t_args, 'seed', null);
if ($seed !== null) {
grokit_assert(is_int($seed), 'ClusterGen: Seed must be an integer or null.');
} else {
$user_headers[] = 'HashFunctions.h';
}
$distLib = get_default($t_args, 'dist.lib', 'std');
$distNS = '';
switch ($distLib) {
case 'std':
$sys_headers[] = 'random';
$distNS = 'std';
break;
case 'boost':
$sys_headers[] = 'boost/random.hpp';
$distNS = 'boost::random';
$libraries[] = 'boost_random-mt';
if ($seed === null) {
// Need random_device
$sys_headers[] = 'boost/random/random_device.hpp';
$libraries[] = 'boost_system-mt';
}
break;
default:
grokit_error('ClusterGen: Unknown RNG library ' . $distLib);
}
$distRNG = 'mt19937';
$RNGtype = $distNS . '::' . $distRNG;
$nTuples = get_first_key($t_args, ['n', '0']);
grokit_assert(is_int($nTuples), 'ClusterGen: the number of tuples to be produced must be an integer.');
$centers = get_first_key($t_args, ['centers', 1]);
grokit_assert(is_array($centers), 'ClusterGen: centers must be an array of functors');
$handleDist = function ($name, $args, $oType) use($distNS) {
$distName = '';
$distArgs = [];
switch ($name) {
case 'gaussian':
case 'normal':
$distName = $distNS . '::' . 'normal_distribution<' . $oType . '>';
grokit_assert(\count($args) <= 2, 'ClusterGen: Normal distribution takes at most 2 arguments, ' . \count($args) . ' given');
$mean = get_default($args, ['mean', 0], 0.0);
$sigma = get_default($args, ['std_dev', 'sigma', 1], 1.0);
grokit_assert(is_numeric($mean), 'ClusterGen: mean parameter of binomial distribution must be a real number.');
grokit_assert(is_numeric($sigma), 'ClusterGen: sigma parameter of binomial distribution must be a real number.');
$mean = floatval($mean);
$sigma = floatval($sigma);
$distArgs = [$mean, $sigma];
break;
case 'binomial':
$distName = $distNS . '::' . 'binomial_distribution<' . $oType . '>';
grokit_assert(\count($args) <= 2, 'ClusterGen: Binomial distribution takes at most 2 arguments, ' . \count($args) . ' given');
$t = get_default($args, ['t', 0], 1);
$p = get_default($args, ['p', 1], 0.5);
grokit_assert(is_int($t), 'ClusterGen: t parameter of binomial distribution must be an integer.');
grokit_assert(is_numeric($p), 'ClusterGen: p parameter of binomial distribution must be a real number.');
$p = floatval($p);
grokit_assert($p >= 0 && $p <= 1, 'ClusterGen: p parameter of binomial distribution must be in the range [0, 1]');
grokit_assert($t >= 0, 'ClusterGen: t parameter of binomial distribution must be in the range [0, +inf)');
$distArgs = [$t, $p];
break;
case 'negative_binomial':
$distName = $distNS . '::' . 'negative_binomial_distribution<' . $oType . '>';
grokit_assert(\count($args) <= 2, 'ClusterGen: Negative Binomial distribution takes at most 2 arguments, ' . \count($args) . ' given');
$k = get_default($args, ['k', 0], 1);
$p = get_default($args, ['p', 1], 0.5);
grokit_assert(is_int($k), 'ClusterGen: k parameter of binomial distribution must be an integer.');
grokit_assert(is_numeric($p), 'ClusterGen: p parameter of binomial distribution must be a real number.');
$p = floatval($p);
grokit_assert($p > 0 && $p <= 1, 'ClusterGen: p parameter of negative binomial distribution must be in the range (0, 1]');
grokit_assert($k > 0, 'ClusterGen: k parameter of negative binomial distribution must be in the range (0, +inf)');
$distArgs = [$k, $p];
break;
case 'inverse_gaussian':
case 'inverse_normal':
grokit_assert(\count($args) <= 2, 'ClusterGen: Inverse Gaussian distribution takes at most 2 arguments, ' . \count($args) . ' given');
$mean = get_default($args, ['mean', 0], 1);
$shape = get_default($args, ['shape', 1], 1);
grokit_assert(is_numeric($mean), 'ClusterGen: mean parameter of inverse gaussian distribution must be a real number.');
grokit_assert(is_numeric($shape), 'ClusterGen: shape parameter of inverse gaussian distribution must be a real number.');
$mean = floatval($mean);
$shape = floatval($shape);
grokit_assert($mean > 0, 'ClusterGen: mean of inverse gaussian distribution must be in range (0, inf)');
grokit_assert($shape > 0, 'ClusterGen: shape of inverse gaussian distribution must be in range (0, inf)');
$gen_args = ['output' => $oType, 'ns' => $distNS];
$distName = strval(lookupResource('datagen::InverseGaussianGen', $gen_args));
$distArgs = [$mean, $shape];
break;
case 'uniform':
$distName = $distNS . '::' . 'uniform_real_distribution<' . $oType . '>';
grokit_assert(\count($args) <= 2, 'ClusterGen: Uniform distribution takes at most 2 arguments, ' . \count($args) . ' given');
$a = get_default($args, ['a', 0], 0.0);
$b = get_default($args, ['b', 1], 1.0);
grokit_assert(is_numeric($a), 'ClusterGen: `a` parameter of uniform distribution must be a real number.');
grokit_assert(is_numeric($b), 'ClusterGen: `b` parameter of uniform distribution must be a real number.');
$a = floatval($a);
$b = floatval($b);
grokit_assert($b >= $a, 'ClusterGen: `b` parameter of uniform distribution must be >= the `a` parameter.');
$distArgs = [$a, $b];
break;
case 'exponential':
$distName = $distNS . '::' . 'exponential_distribution<' . $oType . '>';
grokit_assert(\count($args) <= 1, 'ClusterGen: Exponential distribution takes at most 1 argument.');
$lambda = get_default($args, ['lambda', 0], 1.0);
grokit_assert(is_numeric($lambda), 'ClusterGen: `lambda` parameter of exponential distribution must be a real number.');
$lambda = floatval($lambda);
grokit_assert($lambda > 0, 'ClusterGen: `lambda` parameter of exponential distribution must be in range (0, +inf).');
$distArgs = [$lambda];
break;
case 'gamma':
case 'Gamma':
$distName = $distNS . '::' . 'gamma_distribution<' . $oType . '>';
grokit_assert(\count($args) <= 2, 'ClusterGen: Gamma distribution takes at most 2 arguments.');
$alpha = get_default($args, ['alpha', 0], 1.0);
$beta = det_default($args, ['beta', 1], 1.0);
grokit_assert(is_numeric($alpha), 'ClusterGen: `alpha` parameter of gamma distribution must be a real number.');
grokit_assert(is_numeric($beta), 'ClusterGen: `beta` parameter of gamma distribution must be a real number.');
$alpha = floatval($alpha);
$beta = floatval($beta);
$distArgs = [$alpha, $beta];
break;
default:
grokit_error('ClusterGen: Unknown distribution ' . $name . ' given for center');
}
return [$distName, $distArgs];
};
$dists = [];
$distArgs = [];
$count = 0;
$oType = '';
$nCenters = 1;
reset($outputs);
foreach ($centers as $val) {
$cluster = $val;
if (is_functor($val)) {
$cluster = [$val];
} else {
if (is_array($val)) {
$nCenters = lcm($nCenters, \count($val));
} else {
grokit_error('ClusterGen: center descriptions must be functors or list of functors');
}
}
$curDist = [];
$curDistArgs = [];
$curDistName = 'distribution' . $count++;
$oType = strval(current($outputs));
$iCount = 0;
foreach ($cluster as $functor) {
grokit_assert(is_functor($functor), 'ClusterGen: center description must be a functor');
$vName = $curDistName . '_' . $iCount++;
$ret = $handleDist($functor->name(), $functor->args(), $oType);
$curDist[$vName] = $ret[0];
$curDistArgs[$vName] = $ret[1];
}
next($outputs);
$dists[$curDistName] = $curDist;
$distArgs[$curDistName] = $curDistArgs;
}
// Determine the default number of sets to compute at a time.
// We want to generate either $nTuples or 10,000 tuples, depending on which
// is less.
$defaultSetsTarget = min($nTuples, 10000);
$setsToTarget = intval(ceil($defaultSetsTarget / $nCenters));
$computeSets = get_default($t_args, 'compute.sets', $setsToTarget);
grokit_assert(is_int($computeSets) && $computeSets > 0, 'ClusterGen: compute.sets must be a positive integer, ' . $computeSets . ' given');
$className = generate_name('ClusterGen');
// For some BIZZARE reason, the $outputs array was getting modified while
// traversing over the $dists array. Making a deep copy of the outputs and
// then reassigning it seems to fix the issue.
$outputs = $myOutputs;
?>
class <?php
echo $className;
?>
{
// The number of tuples to produce per task
static constexpr size_t N = <?php
echo $nTuples;
?>
;
static constexpr size_t CacheSize = <?php
echo $computeSets * $nCenters;
?>
;
// Typedefs
typedef std::tuple<<?php
echo array_template('{val}', ', ', $outputs);
?>
> Tuple;
typedef std::array<Tuple, CacheSize> TupleArray;
typedef TupleArray::const_iterator TupleIterator;
typedef <?php
echo $RNGtype;
?>
RandGen;
// Number of tuples produced.
uintmax_t count;
// Cache a number of outputs for efficiency
TupleArray cache;
TupleIterator cacheIt;
// Random number generator
RandGen rng;
// Distributions
<?php
// This is the section causing issues.
foreach ($dists as $name => $list) {
foreach ($list as $vName => $type) {
?>
<?php
echo $type;
?>
<?php
echo $vName;
?>
;
<?php
}
// foreach distribution
}
// foreach cluster set
?>
// Helper function to generate tuples.
void GenerateTuples(void) {
<?php
$tIndex = 0;
foreach ($dists as $name => $list) {
$lCenters = \count($list);
// $nCenters has been defined to be the LCM of the number of centers in
// any column, so $lCenter is guaranteed to divide evenly into
// CacheSize
?>
for( size_t index = 0; CacheSize > index; index += <?php
echo $lCenters;
?>
) {
<?php
$index = 0;
foreach ($list as $vName => $type) {
?>
std::get<<?php
echo $tIndex;
?>
>(cache[index + <?php
echo $index;
?>
]) = <?php
echo $vName;
?>
(rng);
<?php
$index++;
}
// foreach value in tuple
?>
}
<?php
$tIndex++;
}
// foreach distribution
?>
cacheIt = cache.cbegin();
}
public:
// Constructor
<?php
echo $className;
?>
( GIStreamProxy & _stream ) :
cache()
, cacheIt()
, count(0)
, rng()
<?php
foreach ($dists as $name => $list) {
foreach ($list as $vName => $type) {
?>
, <?php
echo $vName;
?>
(<?php
echo implode(', ', $distArgs[$name][$vName]);
?>
)
<?php
}
// foreach distribution
}
// foreach cluster set
?>
{
<?php
if (is_null($seed)) {
?>
<?php
echo $distNS;
?>
::random_device rd;
<?php
}
// if seed is null
?>
RandGen::result_type seed = <?php
echo is_null($seed) ? 'rd()' : "CongruentHash({$seed}, _stream.get_id() )";
?>
;
rng.seed(seed);
cacheIt = cache.cend();
}
// Destructor
~<?php
echo $className;
?>
(void) { }
bool ProduceTuple(<?php
echo typed_ref_args($outputs);
?>
) {
if( N > count ) {
if( cacheIt == cache.cend() ) {
GenerateTuples();
}
<?php
$tIndex = 0;
foreach ($outputs as $name => $type) {
?>
<?php
echo $name;
?>
= std::get<<?php
echo $tIndex;
?>
>(*cacheIt);
<?php
$tIndex++;
}
// foreach output
?>
++cacheIt;
++count;
return true;
}
else {
return false;
}
}
};
<?php
return array('kind' => 'GI', 'name' => $className, 'output' => $outputs, 'system_headers' => $sys_headers, 'user_headers' => $user_headers, 'libraries' => $libraries);
}
public static function carmichael_of_factorized($f_list)
{
if (extension_loaded('gmp') && USE_EXT == 'GMP') {
if (count($f_list) < 1) {
return 1;
}
$result = self::carmichael_of_ppower($f_list[0]);
for ($i = 1; $i < count($f_list); $i++) {
$result = lcm($result, self::carmichael_of_ppower($f_list[$i]));
}
return $result;
} elseif (extension_loaded('bcmath') && USE_EXT == 'BCMATH') {
if (count($f_list) < 1) {
return 1;
}
$result = self::carmichael_of_ppower($f_list[0]);
for ($i = 1; $i < count($f_list); $i++) {
$result = lcm($result, self::carmichael_of_ppower($f_list[$i]));
}
return $result;
} else {
throw new ErrorException("Please install BCMATH or GMP");
}
}
function Hints($l, $r, $x)
{
$lcm = lcm($r[1], $r[3]);
if (abs($r[1]) != abs($r[3])) {
$page[] = 'Hozzuk közös nevezőre az egyenlet jobb oldalát (a közös nevező $' . $lcm . '$ lesz):' . $this->Equation($l, $r, 1);
}
$page[] = 'Szorozzuk meg mindkét oldalt $' . $lcm . '$-' . With($lcm) . '!' . $this->Equation($l, $r, 2);
$page[] = 'Bontsuk fel a zárójeleket mindkét oldalon!' . $this->Equation($l, $r, 3);
$page[] = 'Vonjuk össze az egynemű tagokat!' . $this->Equation($l, $r, 4);
$page[] = 'Gyűjtsük össze az $x$-et tartalmazó tagokat jobb oldalra, a többit pedig balra!' . $this->Equation($l, $r, 5);
$page[] = 'Ha mindkét oldalt leosztjuk az $x$ együtthatójával, azt kapjuk, hogy a megoldás <span class="label label-success">$' . $x . '$</span>.';
$hints[] = $page;
return $hints;
}
function chem_makeioniccompound($cation, $anion)
{
if (!is_array($cation)) {
global $chem_cations;
$found = false;
foreach ($chem_cations as $c) {
if ($c[0] == $cation) {
$cation = $c;
$found = true;
break;
}
}
if (!$found) {
echo "Cation not found.";
}
}
if (!is_array($anion)) {
global $chem_anions;
$found = false;
foreach ($chem_anions as $c) {
if ($c[0] == $anion) {
$anion = $c;
$found = true;
break;
}
}
if (!$found) {
echo "Anion not found.";
}
}
$lcm = lcm($cation[1], $anion[1]);
$catsub = $lcm / $cation[1];
if ($catsub == 1) {
$formula = $cation[0];
} else {
if (strpos($cation[0], ' ') !== false) {
$formula = '(' . $cation[0] . ')';
$formula .= '_' . $catsub;
} else {
if (strpos($cation[0], '_') !== false) {
//this is Hg_2 only
$pts = explode('_', $cation[0]);
$formula = $pts[0] . '_' . $pts[1] * $catsub;
} else {
$formula = $cation[0];
$formula .= '_' . $catsub;
}
}
}
$ansub = $lcm / $anion[1];
if ($ansub == 1) {
$formula .= ' ' . $anion[0];
} else {
if (strpos($anion[0], ' ') !== false) {
$formula .= ' (' . $anion[0] . ')';
$formula .= '_' . $ansub;
} else {
if (strpos($anion[0], '_') !== false) {
$pts = explode('_', $anion[0]);
$formula .= ' ' . $pts[0] . '_' . $ansub * $pts[1];
} else {
$formula .= ' ' . $anion[0];
$formula .= '_' . $ansub;
}
}
}
$name = $cation[2] . ' ' . $anion[2];
return array($formula, $name);
}
