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26.php
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<!--
A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Find the value of d 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
-->
<?php $startTime = microtime(true);
function isMulRec($input)//is recursive of multiple nums
{
$numerator = 1;
$numText = "0.";
$leftover = 1;
while ($leftover>0) {
$number = floor(($numerator*10)/$input);
$leftover = ($numerator*10)%$input;
$currentText = ".".$number."-".$leftover.".";
$numText .= $currentText;
$testText = "";
for ($i=0; $i < 4; $i++) {
$testText .= $currentText;
}
if (substr_count($numText, $currentText)>1) {
//this isn't the exact number due to adding "." and "-" in but the offset is exact across all numbers, it's roughly x5 plus leading values that don't reoccur
//this returns 5 for any single digit cycle
return strripos($numText, $currentText)-stripos($numText, $currentText);
}
$numerator = $leftover;
}
return 0;
}
$HighestVal = 0;
$HighestNum = 0;
for ($i=999; $i > 1; $i--) {
$iRecValue = isMulRec($i);
if ($iRecValue>$HighestVal) {
$HighestVal = $iRecValue;
$HighestNum = $i;
}
}
$answer = $HighestNum;
$endTime = microtime(true);
echo "Answer: ",$answer,"\nTime: ",($endTime - $startTime),"\n";
// Answer: 983
// Time: 0.46s