Reciprocal cycles
AUTHOR
Shlomi Fish
https://projecteuler.net/problem=26
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.
use v6;
sub find_cycle_len(Int $n) returns Int {
my %states;
my $r = 1;
my $count = 0;
while ! ( %states{$r}:exists ) {
# $*ERR.say( "Trace: N = $n ; R = $r" );
%states{$r} = $count++;
($r *= 10) %= $n;
}
return $count - %states{$r};
}
my $max_cycle_len = -1;
my $max_n;
for (2 .. 999) -> $n {
if ((my $cycle_len = find_cycle_len($n)) > $max_cycle_len) {
$max_n = $n;
$max_cycle_len = $cycle_len;
}
}
say "The recurring cycle is $max_n, and the cycle length is $max_cycle_len";
# vim: expandtab shiftwidth=4 ft=perl6