Merge pull request #3900 from drbaggy/master

Solutions with doc notes about bell number calculation.

2 files changed, 85 insertions, 0 deletions

diff --git a/challenge-108/james-smith/perl/ch-1.pl b/challenge-108/james-smith/perl/ch-1.pl
new file mode 100644
index 0000000000..8aa29eb291
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+++ b/challenge-108/james-smith/perl/ch-1.pl
@@ -0,0 +1,24 @@
+#!/usr/local/bin/perl
+
+use strict;
+
+use warnings;
+use feature qw(say);
+use Test::More;
+
+my $scalar = 1;
+my @array  = (1);
+my %hash   = (1=>1);
+my $arrayref = \@array;
+my $hashref  = \%hash;
+my $scalarref  = \$scalar;
+
+say "Scalar ", get_loc( \$scalar );
+say "Scalarref ", get_loc( \$scalarref );
+say "Array ", get_loc( \@array );
+say "Arrayref ", get_loc( \$arrayref );
+
+sub get_loc {
+  return $_[0] =~ s{(?:.*\(|\))}{}rg;
+}
+
diff --git a/challenge-108/james-smith/perl/ch-2.pl b/challenge-108/james-smith/perl/ch-2.pl
new file mode 100644
index 0000000000..9e6d8006f9
--- /dev/null
+++ b/challenge-108/james-smith/perl/ch-2.pl
@@ -0,0 +1,61 @@
+#!/usr/local/bin/perl
+
+use strict;
+
+use warnings;
+use feature qw(say);
+use Test::More;
+
+my $ANSWER_10 = '1 1 2 5 15 52 203 877 4140 21147';
+my $ANSWER_20 = '1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 82864869804 682076806159 5832742205057';
+
+is( "@{ bell_numbers(10) }", $ANSWER_10 );
+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;                 #1
+  while(1) {
+    push @res, my @b = $a[-1];         #2
+    return \@res if @res >= $N;        #3
+    push @b, $b[-1] + $_ foreach @a;   #4
+    @a = @b;                           #5
+  }
+}
+
+