Project Euler #103 - Inelegant and slow.pl

$|=1;

for ($n=1;$n<=7;$n++) {
    print "-\n"; $answer="";
    @set=();
    %bad=(); %good=();
    $max=10**10;
    for ($i=1;$i<=$n;$i++) {push @set,$i;}
    while ($count<$max) {
        increment();
        if (check()) {
            print "N=$n : ";
            $sum=0;
            foreach (@set) {
                print "$_ ";
                $sum+=$_;
            }
            print "\n";
            if ($sum<$max) {$max=$sum;}
        }
        $count=$set[-1];
        for ($i=0;$i+1<scalar @set;$i++) {
            $count+=int(@set[-1]/2)+$i;
#            print "$count $max\n";
        }
    }

#    print "N=$n : $answer\n";
}

sub increment() {
    @set=sort {$a<=>$b} @set;
    @set[0]++;
    for (my $i=0;$i<scalar @set;$i++) {
        for (my $j=1+$i;$j<scalar @set;$j++) {
           if ($set[$i]==$set[$j]) {
               $set[$j]++;
               if ($j==$n-1) {print @set[-1]."\n";}
               for (my $k=0;$k<$j;$k++) {
                   $set[$k]=$k+1;
               }
           }
        }
    }
    @set=sort {$a<=>$b} @set;
}

sub check() {
    $depth++;

    if (1==scalar @set) {
        $depth--;
        return 1;
    }
    $string=join " ",sort {$a<=>$b} @set;
    if (2<scalar @set) {
        @taco=sort {$a<=>$b} @set;
        if (@taco[0]+@taco[1]<@taco[-1]) {
            $depth--;
            $bad{$string}=1;
            return 0;
        }
    if (4<scalar @set) {
        if (@taco[0]+@taco[1]+@taco[2]<@taco[-2]+@taco[-1]) {
            $depth--;
            $bad{$string}=1;
            return 0;
        }
    }
    }
    if (4<=scalar @set) {
        for ($i=0;$i+3<scalar @set;$i++) {
            if ($set[$i]+$set[$i+3]==$set[$i+1]+$set[$i+2]) {
                $depth--;
                $bad{$string}=1;
                return 0;
            }
        }
    }
    if ($good{$string}) {
        $depth--;
        return 1;
    }
    if ($bad{$string}) {
        $depth--;
        return 0;
    }
    my $sum=0; foreach (@set) { $sum+=$_;}
    if ($sum>=$max) {
        $depth--;
            $string=join " ",sort {$a<=>$b} @set;$bad{$string}=1;return 0;
    }

    if ($n==scalar @set) {
    @taco=sort {$a<=>$b} @set;
    for (my $i=1;$i<scalar @taco;$i++) {
        if ($taco[$i-1] *2 < $taco[$i]) {
            $depth--;
            $string=join " ",sort {$a<=>$b} @set;$bad{$string}=1;return 0;
            return 0;
        }
    }
    }
#    print "$answer";
#    foreach (1..$depth) {print "    ";}
#    foreach (sort {$a<=>$b} @set) {print "$_ ";}
#    print "\n";
    for (my $i=1;$i<2**(scalar @set)-1;$i++) {
#        print "$i\n";
        my @left=(); my @right=();
        my $sumleft=0; my $sumright=0;
        for (my $j=0;$j<(scalar @set);$j++) {
#            print "$j ";
            if ($i&(2**$j)) {
                push @left,$set[$j];
#                print "<- ".$set[$j]."\n";
                $sumleft+=$set[$j];
            } else {
                push @right,$set[$j];
#                print "-> ".$set[$j]."\n";
                $sumright+=$set[$j];
            }
        }
        if ($sumright==$sumleft) {
            $depth--;
                $string=join " ",sort {$a<=>$b} @set;$bad{$string}=1;return 0;
        }
        if ((scalar @left)>(scalar @right) & ($sumright>$sumleft)) {
            $depth--;
                $string=join " ",sort {$a<=>$b} @set;$bad{$string}=1;return 0;
        }
        if ((scalar @left)<(scalar @right) & ($sumright<$sumleft)) {
            $depth--;
                $string=join " ",sort {$a<=>$b} @set;$bad{$string}=1;return 0;
        }
        for (my $i=0;$i<scalar @set;$i++) {
            my $temp=shift @set;
            if (!check()) {
                unshift @set,$temp;
                @set=sort {$a<=>$b} @set;
                $depth--;
                    $string=join " ",sort {$a<=>$b} @set;$bad{$string}=1;return 0;
            }
            push @set,$temp;
        }
    }
    $string=join " ",sort {$a<=>$b} @set;
    if ($n==scalar @set) {
        my $sum=0;
        foreach (@set) {
            $sum+=$_;
        }
        if ($sum<$max) {$max=$sum;$answer=$string;}
    } else {
        $good{$string}=1;
    }
    $depth--;
    return 1;
}