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#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl
#
# fareys-wear-boots.pl
#
# Farey Sequence
# Submitted by: Mohammad S Anwar
# You are given a positive number, $n.
#
# Write a script to compute Farey Sequence of the order $n.
#
# Example 1:
# Input: $n = 5
# Output: 0/1, 1/5, 1/4, 1/3, 2/5,
# 1/2,
# 3/5, 2/3, 3/4, 4/5, 1/1
#
# Example 2:
# Input: $n = 7
# Output: 0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7,
# 1/2,
# 4/7, 3/5, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 1/1
#
# Example 3:
# Input: $n = 4
# Output: 0/1, 1/4, 1/3,
# 1/2,
# 2/3, 3/4, 1/1
#
# method:
#
# The Fahey sequence or a given order n is a list of all
# subunary fractions with denominators up to the value of the
# order, reduced to their lowest terms and placed in ascending
# order. One interesting property of this sequence is that for
# any triplet of successive terms selected, the central term
# will be the mediant of the two outer, which is to say we can
# obtain the ratio of the intermediate value by summing the two
# numerators and two denominators of the outside terms: for the
# two terms in example 2 above 2/7 and 2/5 the intermediate
# numerator is 2+2 and denominator is 7+5, yielding 4/12, wich
# can be reduced to 1/3. This can be seen to be the case by
# examination of the example.
#
# Two algorithms suggest themselves to produce the Fahey
# sequence for a given order: we can either construct all the
# fractions exhaustively, reduce them to their lowest terms,
# remove duplicates and sort them; or alternately we can bisect
# each set of adjacent fractions in the the previous order to
# construct the next, reducing them as possible along the way,
# until we arrive at the order requested.
#
# As it
# © 2022 colin crain
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
use warnings;
use strict;
use utf8;
use feature ":5.26";
use feature qw(signatures);
no warnings 'experimental::signatures';
package Rat;
{
use Moo;
use feature qw(signatures);
no warnings 'experimental::signatures';
has n => ( is => 'ro');
has d => ( is => 'ro');
has num => ( is => 'rw');
has den => ( is => 'rw');
has val => ( is => 'rw');
around BUILDARGS => sub {
my ( $orig, $class, @args ) = @_;
return { n => $args[0],
d => $args[1] };
};
sub BUILD ($self, $args) {
my $gcd = gcd( $self->n, $self->d );
$self->num( $self->n / $gcd );
$self->den( $self->d / $gcd );
$self->val( $self->n / $self->d );
};
sub gcd ($m, $n) {
return $n if $m == 0; ## gcd of (0,n) is n
while ( $n != 0 ) {
$n > $m and ($m, $n) = ($n, $m);
my $r = $m - $n * ( int ($m/$n));
return $n if $r == 0;
($m, $n) = ($n, $r);
}
}
sub string ($self) {
return $self->num . "/" . $self->den;
};
}
package main;
my $order = shift @ARGV // 7;
my @rats;
for my $den (1..$order) {
for my $num ( 0..$den) {
push @rats, new Rat($num, $den);
}
}
my %farey = map { $_->string => $_->val } @rats;
say join ' ', sort { $farey{$a} <=> $farey{$b} } keys %farey;
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