Restructuring

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2024-07-01 13:49:44 +00:00
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commit 8d60e1b905
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title: Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
url: http://projecteuler.net/problem=26
desc: |
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.
solution: Bruteforce
solutions:
solve.php:
desc: Basic Solution - needs BCMath
language: php

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<?php
define('MAX',1000);
$max_len = 0;
for($div = MAX; $div > 2; $div--) {
$result = bcdiv('1',(string)$div,2000);
for($len = 2; $len < 1000; $len++) {
if(substr($result,10,$len) === substr($result,10+$len,$len)) {
if($len > $max_len) {
echo "Div: ".$div. " Len: ".$len."\n";
$max_len = $len;
$max_div = $div;
}
break;
}
}
}
echo $max_div;

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DIGITS = 1000
max = 10 ** (DIGITS-1)
fcurrent = 1
fprev = 1
term = 2
while fcurrent < max do
term = term + 1
fnext = fcurrent + fprev
fprev = fcurrent;
fcurrent = fnext;
end
puts term