added some docs

1 files changed, 38 insertions, 5 deletions

diff --git a/challenge-108/james-smith/perl/ch-2.pl b/challenge-108/james-smith/perl/ch-2.pl
index 524cde283d..9e6d8006f9 100644
--- a/challenge-108/james-smith/perl/ch-2.pl
+++ b/challenge-108/james-smith/perl/ch-2.pl
@@ -14,14 +14,47 @@ is( "@{ bell_numbers(20) }", $ANSWER_20 );
 
 done_testing();
 
+## Bell numbers can be computed by using a bell triangle.
+## The bell numbers are the last cell of each row of the table.
+##
+## To get one row from the next.
+##  * We copy the previous "bell number" the last cell in
+##    the previous row.
+##  * Each other element of the row is computed by adding the number
+##    to the left of it in this row and the element about (and to the
+##    left of it)
+##
+## The solution...
+##
+## * We will use 2 arrays to represent the previous row and
+##   the current row of the table. @a & @b;
+##   We initialise the first row to just contain the number 1   #1
+##
+## * And at each iteration we remember this last element.       #2
+##
+## * When we have enough elements in our results array we       #3
+##   return. We don't need to do last and then return outside
+##   the loop as we can just return from the subroutine from
+##   inside the loop!
+##
+## * In each iteration we initialise the row to contain the
+##   previous last value...                                     #1
+##   and then loop through all the elements in the previous     #4
+##   array accumulating the total - the ability to get the
+##   value of the last element of the array with [-1] is
+##   very useful perl feature here...
+##
+## * Finally we copy the new row into the previous row and      #5
+##   continue around the loop....
+
 sub bell_numbers {
   my $N = shift;
-  my @res = my @a = 1;
+  my @res = my @a = 1;                 #1
   while(1) {
-    push @res, my @b = $a[-1];
-    return \@res if @res >= $N;
-    push @b, $b[-1] + $_ foreach @a;
-    @a = @b;
+    push @res, my @b = $a[-1];         #2
+    return \@res if @res >= $N;        #3
+    push @b, $b[-1] + $_ foreach @a;   #4
+    @a = @b;                           #5
   }
 }