' .
getFractionOperationDisplayTable($b[$pos1 - 1], $o[$op], $b[$pos2 - 1]) .
'';
}
function getFractionOperationDisplayTable($fraction1, $operation, $fraction2) {
$t = '';
$t .= '';
$t .= '| ' .
$fraction1[0] . ' | ' . $operation . ' | ' .
'' . $fraction2[0] . ' |
';
$t .= '| ' .$fraction1[1] . ' | ' .
'' .$fraction2[1] . ' |
';
$t .= '
';
return $t;
}
function getFractionDisplayTable($fraction) {
if ($fraction[0] == 0) {
$t = '0';
}
elseif ($fraction[0] == $fraction[1]) {
$t = '1';
}
elseif ($fraction[1] == 1) {
$t = $fraction[0];
}
else {
$t = '';
$t .= '';
if ($fraction[0] > 0)
{
$t .= '| ' .
$fraction[0] . ' |
';
}
else {
$t .= ''
. '| − | '
. ''
. (-1 * $fraction[0]) . ' |
';
}
$t .= '| ' . $fraction[1] . ' |
';
$t .= '
';
}
return $t;
}
function shortenFraction(&$fraction) {
$lessi = abs($fraction[0]);
if ($fraction[1] < $lessi) $lessi = abs($fraction[1]);
for ($c=2; $c<=$lessi; $c++)
{
while (($c * floor($fraction[0]/$c) == $fraction[0])
&& ($c * floor($fraction[1]/$c) == $fraction[1]))
{
$fraction[0] /= $c;
$fraction[1] /= $c;
}
}
}
function solution($number) {
$b = Array (
Array(1,2), Array(1,3), Array(1,4),
Array(2,3), Array(3,2), Array(3,4),
Array(3,4), Array(3,2), Array(2,3),
Array(1,4), Array(1,3), Array(1,2)
);
$o = Array (
'+', '−', '·', ':'
);
$op = ($number - 1) % 4;
$numb = floor(($number - 1) / 4) + 1;
$block = floor(sqrt(2*$numb - 7/4)-1/2);
$start = 0.5 * $block * $block + 0.5 * $block + 1;
$pos1 = $numb - $start + 1;
$pos2 = $block + 2 - $pos1;
$b1 = $b[$pos1 - 1];
$b2 = $b[$pos2 - 1];
switch ($op)
{
case 0:
if ($b1[1] != $b2[1]) {
$e1 = $b2[1];
$e2 = $b1[1];
$b1[0] *= $e1; $b1[1] *= $e1;
$b2[0] *= $e2; $b2[1] *= $e2;
}
$r = Array($b1[0] + $b2[0], $b1[1]);
shortenFraction($r);
break;
case 1:
if ($b1[1] != $b2[1]) {
$e1 = $b2[1];
$e2 = $b1[1];
$b1[0] *= $e1; $b1[1] *= $e1;
$b2[0] *= $e2; $b2[1] *= $e2;
}
$r = Array($b1[0] - $b2[0], $b1[1]);
shortenFraction($r);
break;
case 2:
$r = Array($b1[0] * $b2[0], $b1[1] * $b2[1]);
shortenFraction($r);
break;
case 3:
$r = Array($b1[0] * $b2[1], $b1[1] * $b2[0]);
shortenFraction($r);
break;
}
return '' . getFractionDisplayTable($r) . '
';
}
?>