Pascal's triangle, Perl, and homework

Frequently, an evil professor gives to his students homework and sometimes it may be a request to write code which prints Pascal's triangle. Naturally, the student cranks up Firefox (that is synonym for web browser) and goes googling around for examples. A nice elegant solution comes up in the form of:

sub pascal { 
   my @row; 
   foreach (1 .. shift) { 
      push @row => 1; 
      $row [$_] += $row [$_ - 1] for reverse 1 .. @row - 2; 
      print "@row\n"; 
   } 
}

I picked up that one on http://www.perlmonks.org/?node=175586, naturally very few students will understand, right away, what is happening in this code. In order to make the code shorter the author did some Perl tricks, which made it difficult to read and understand the code. In the first transformation I will introduce one unnecessary variable and also make function call more C or Java like.

sub pascal {
   my $size = shift();
   my @row;
   foreach (1 .. $size) {
      push (@row, 1);
      $row [$_] += $row [$_ - 1] for reverse 1 .. @row - 2;
      print "@row\n";
   }
}

Already looks better. Inner loop still looks odd and we are not quite sure what it does and which $_ is used, one from foreach or one from for reverse. In order to see, let us add one debug loop:

sub pascal {
   my $size = shift();
   my @row;
   foreach (1 .. $size) {
      push (@row, 1);
      for (reverse 1 .. @row - 2){
          print $row [$_]," + ",$row [$_ - 1]," store in \$row[$_]\n";
       }
      $row [$_] += $row [$_ - 1] for reverse 1 .. @row - 2;
      print "@row\n";
   }
}

Output will look like this:

1 
1 1 
1 + 1 store in $row[1] 
1 2 1 
1 + 2 store in $row[2] 
2 + 1 store in $row[1] 
1 3 3 1 
1 + 3 store in $row[3] 
3 + 3 store in $row[2] 
3 + 1 store in $row[1] 
1 4 6 4 1 

Now it is obvious that outer loop just pushes ones and inner loop does all difficult work.
One small thing is left, printout doesn't look nice, it is somehow skew. To remedy that we add some pretty printing:

sub pascal {
    my $size = shift;
    my $count;
    my $margin;
    my @row;
    foreach (1 .. $size) {
       push (@row, 1);
       $row [$_] += $row [$_ - 1] for reverse 1 .. @row - 2;
       $margin = "   " x ($size - $count - 1);
       print "$margin";
       $count++;
       foreach (@row){
           printf "%6d",$_;
        }
       print "\n";
}

If we call it and pass 16 as parameter it will print this:

                                                 1
                                              1     1
                                           1    2     1
                                        1    3    3     1
                                     1    4    6    4     1
                                  1    5    10   10    5     1
                               1    6    15   20   15    6     1
                            1    7    21   35    35   21    7     1
                         1    8    28   56    70   56   28    8     1
                      1    9    36   84   126  126    84   36    9     1
                   1    10   45   120   210  252   210  120    45   10     1
                1    11   55   165   330  462   462   330  165    55  11     1
             1    12   66   220   495  792   924   792  495   220   66   12     1
          1    13   78   286   715 1287  1716  1716  1287  715   286   78   13     1
       1    14   91   364  1001  2002 3003  3432  3003  2002 1001   364   91   14     1
    1    15  105   455  1365  3003 5005  6435  6435  5005 3003  1365   455  105   15     1 

Not quite equilateral, one would say.