# 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.

Source code: prob026-shlomif.pl

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";