#!/usr/bin/perl -w
#
# add fractions and display partial results
#

use re 'eval'; #use recursive regex for parsing
use strict;

our $num = qr{\d+(?:/\d+)?};
our $op  = qr{[+*/\-]};
# an expression is a fraction or a pair of expressions separated by
# an operator, enclosed in parens.
our $exp;
    $exp = qr{$num|\(\s*(??{$exp})\s*$op\s*(??{$exp})\s*\)}s;

# Something to test the evaluator with
my @tests = ("(1/2+2/3)","(1/2+(2/3+4/5))","((5/3+7/13)+(5/2+3/7))");
for my $t (@tests)
{
    print "$t\n";
    print simplify($t,"","");
    print "\n\n";
}   
    
sub simplify
{       
    my ($e, $pre, $post) = @_;
    
    if($e =~ /^($num)$/s)
    {
        return $1;
    }
    elsif ($e =~ /^\(($exp)\+($exp)\)$/s)
    {
       my ($l, $r) = ($1,$2);
       my $left  = simplify($l,"","");
       print "$pre($left+$r)$post\n" if $l!~m/^$num$/;
       my $right = simplify($r,"($left+",")");
       print "$pre($left+$right)$post\n" if $r!~m/^$num$/;
       my $sum   = add_frac($left, $right);

       return "$sum";
    }
    elsif ($e =~ /^\(($exp)-($exp)\)$/s)
    {
        #subtraction 
    }
    elsif ($e =~ /^\(($exp)\*($exp)\)$/s)
    {
       #multiplication 
    }
    elsif ($e =~ /^\(($exp)\/($exp)\)$/s)
    {
        #division
    }
    else
    {
        die "Syntax error\n";
    }
}
sub add_frac
{
    my ($l, $r) = @_;

    my ($l_num, $l_denom) = $l =~ m{(\d+)/(\d+)};
    my ($r_num, $r_denom) = $r =~ m{(\d+)/(\d+)};

    my $denom = $l_denom * $r_denom;
    my $ans   = $l_num * $r_denom + $r_num * $l_denom;
    return "$ans/$denom";
}
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