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Hey kiat,
I noticed that your algorithm skips the "1 1" row. I made some changes to fix that bug:
```sub pascal {
my (\$rows) = @_;
print "1\n";
for (my \$outer = 1; \$outer < \$rows; \$outer++) {
my \$inner = \$outer;
print "1";
for (\$i = 1; \$i < \$inner; \$i++) {
my \$denominator = factorial(\$i)*(factorial(\$inner-\$i));
my \$pascalnum = factorial(\$inner)/\$denominator if (\$denominator
+!= 0);
print " \$pascalnum" if (\$outer > 1);
}
print " 1\n";
}
}
I also think that using the Binomial Theorem when printing out an entire Pascal's triangle is inefficient. I would rather add numbers from the previous row, as this is much, much faster for large numbers of rows. So I wrote up some code to do this:
```sub ton_pascal
{
my \$rows = shift;
my \$last_row = [ ];
my \$this_row = [ 1 ];

last unless (\$rows > 0);
print "1\n";
for (my \$i = 1; \$i < \$rows; ++\$i) {
\$last_row = \$this_row;
\$this_row = [ 1 ];
for (my \$j = 1; \$j < \$i; \$j++) {
push(@\$this_row, \$last_row->[\$j - 1] + \$last_row->[\$j]);
}
push(@\$this_row, 1);
print join(' ', @\$this_row) . "\n";
}
}
I'm using array references instead of arrays for extra speed (when we copy the results of \$this_row into \$last_row), but the references could be removed without affecting the algorithm.

Hope this was helpful... I had fun coding up ton_pascal, so thanks for the problem!

-Ton
-----
Be bloody, bold, and resolute; laugh to scorn
The power of man...

In reply to Re: Pascal triange... by ton
in thread Pascal's triangle... by kiat

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