updatead notes

1 files changed, 24 insertions, 0 deletions

diff --git a/challenge-169/james-smith/perl/ch-2.pl b/challenge-169/james-smith/perl/ch-2.pl
index d385b4239a..6588e57cce 100644
--- a/challenge-169/james-smith/perl/ch-2.pl
+++ b/challenge-169/james-smith/perl/ch-2.pl
@@ -11,8 +11,29 @@ my $time = time;
 open my $fh, '>', 'achilles.txt';
 
 for( my( $n, $c, $MAX ) = ( 2, 0, @ARGV ? $ARGV[0] : 1e2 ); $c<$MAX; $n++ ) {
+
+  ## Factorise $n into prime factors, and count for each factor...
+  ##
+  ## e.g. 10800 has factors ( 2, 2, 2, 2, 3, 3, 3, 5, 5 ) or 2^4 3^3 5^2
+  ##
+  ## So %factors = ( 2 => 4, 3 => 3, 5 => 2 );
+  ##
+
   my %factors;
   $factors{$_}++ for factor $n;
+
+  ## If any of the values in this hash are 1 then we skip to the next number
+  ## as it isn't brilliant..
+  ##
+  ## To rule out perfect numbers we find the gcd of the values and if it is
+  ## greater than 1 we have a perfect number and skip to the next number
+  ##
+  ## We have a brilliant imperfect (or archilles) number.... so display it..
+  ##
+  ## To pretty print the archilles numbers - we have a counter so that we
+  ## know which achilles number it is, we display the number AND the
+  ## factorisation.
+
   say {$fh} sprintf '%6d: %15d = %s', ++$c, $n,
       join ' . ',
       map  { "$_^$factors{$_}" }
@@ -20,6 +41,9 @@ for( my( $n, $c, $MAX ) = ( 2, 0, @ARGV ? $ARGV[0] : 1e2 ); $c<$MAX; $n++ ) {
       keys  %factors
     if 1 == gcd( grep { $_ < 2 ? next : 1 } values %factors )
     ## Any of the factors is not squared we try the next number in the loop!
+
+    ## The `next` out of grep jumps to the next loop of the foor loop...
+
 }
 close $fh;
 warn 'Time taken: ', time-$time, "\n";