Task — Unique fraction generator

Given a positive integer N, generate all unique fractions you can create using integers from 1 to N and follow the rules below:

• Use numbers 1 through N only (no zero).
• Create fractions like numerator/denominator.
• List them in ascending order (from smallest to largest).
• If two fractions have the same value (like 1/2 and 2/4) only show the one with the smallest numerator.

Examples

Example 1
Input: $int = 3
Output: 1/3, 1/2, 2/3, 1/1, 3/2, 2/1, 3/1

Example 2
Input: $int = 4
Output: 1/4, 1/3, 1/2, 2/3, 3/4, 1/1, 4/3, 3/2, 2/1, 3/1,
   4/1

Example 3
Input: $int = 1
Output: 1/1

Example 4
Input: $int = 6
Output: 1/6, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4,
        4/5, 5/6, 1/1, 6/5, 5/4, 4/3, 3/2, 5/3, 2/1,
        5/2, 3/1, 4/1, 5/1, 6/1

Example 5
Input: $int = 5
Output: 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1,
        5/4, 4/3, 3/2, 5/3, 2/1, 5/2, 3/1, 4/1, 5/1

Analysis

This is another challenge which is solved more or less by translating the description into Perl.

The fractions are generated by iterating over numerator and denominator from 1 to N. I save each decimal value in a hash key, unless it already exists (which willl be with a smaller numerator), and use the textual fraction as the hash value.

It's then just a case of sorting by the hash key.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2026-01-19
use utf8;     # Week 357 - task 2 - Unique fraction generator
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

unique_fraction_generator(3);
unique_fraction_generator(4);
unique_fraction_generator(1);
unique_fraction_generator(6);
unique_fraction_generator(5);
unique_fraction_generator(10);

sub unique_fraction_generator {
    
    my ($n, $i, $j, $q, %quotient, $result);
    
    # initialise
    $n = $_[0];
    
    # generate fractions
    for $i (1 .. $n) {
        for $j (1 .. $n) {
            $q = $i / $j;
            
            # save result unless an equal earlier one
            $quotient{$q} .= qq[$i/$j] unless $quotient{$q};
        }
    }
    
    # sort them by value
    $result = '';
    for $q (sort {$a <=> $b} keys %quotient) {
        $result .= qq[$quotient{$q}, ];
    }
    
    say qq[\nInput:  $n];
    say qq[Output: ] . substr($result, 0, -2);
}

Output

Input:  3
Output: 1/3, 1/2, 2/3, 1/1, 3/2, 2/1, 3/1

Input:  4
Output: 1/4, 1/3, 1/2, 2/3, 3/4, 1/1, 4/3, 3/2, 2/1, 3/1,
   4/1

Input:  1
Output: 1/1

Input:  6
Output: 1/6, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5,
   5/6, 1/1, 6/5, 5/4, 4/3, 3/2, 5/3, 2/1, 5/2, 3/1, 4/1,
   5/1, 6/1

Input:  5
Output: 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1,
   5/4, 4/3, 3/2, 5/3, 2/1, 5/2, 3/1, 4/1, 5/1

Input:  10
Output: 1/10, 1/9, 1/8, 1/7, 1/6, 1/5, 2/9, 1/4, 2/7,
   3/10, 1/3, 3/8, 2/5, 3/7, 4/9, 1/2, 5/9, 4/7, 3/5, 5/8,
   2/3, 7/10, 5/7, 3/4, 7/9, 4/5, 5/6, 6/7, 7/8, 8/9,
   9/10, 1/1, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3,
   7/5, 10/7, 3/2, 8/5, 5/3, 7/4, 9/5, 2/1, 9/4, 7/3, 5/2,
   8/3, 3/1, 10/3, 7/2, 4/1, 9/2, 5/1, 6/1, 7/1, 8/1, 9/1,
   10/1