From 8450f8839063870ddad1911c3b2f7d3724fdba24 Mon Sep 17 00:00:00 2001
From: Jörg Sommrey <28217714+jo-37@users.noreply.github.com>
Date: Mon, 2 May 2022 21:53:42 +0200
Subject: Solution to task 1

---
 challenge-163/jo-37/perl/ch-1.pl | 85 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100755 challenge-163/jo-37/perl/ch-1.pl

diff --git a/challenge-163/jo-37/perl/ch-1.pl b/challenge-163/jo-37/perl/ch-1.pl
new file mode 100755
index 0000000000..ce90fd33d6
--- /dev/null
+++ b/challenge-163/jo-37/perl/ch-1.pl
@@ -0,0 +1,85 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0 '!float';
+use PDL;
+use List::Util 'uniqnum';
+use Math::Prime::Util qw(fromdigits todigits);
+
+our ($tests, $examples);
+
+run_tests() if $tests || $examples;	# does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [-tests] [N...]
+
+-examples
+    run the examples from the challenge
+ 
+-tests
+    run some tests
+
+N...
+    Calculate the sum over pairwise and'ed values.
+
+EOS
+
+
+### Input and Output
+
+# The term "for all unique pairs" is a bit vague.  Taking unordered
+# pairs of different numbers here.
+say sum_bit_pair_wise(uniqnum @ARGV);
+
+
+### Implementation
+
+# There is no need to loop over pairs to solve this task.  Taking the
+# numbers' binary representation and adding the digits at a specific
+# position gives the count C of numbers having this bit set.  Then the
+# number of pairs having this bit set is C * (C - 1) / 2.  Taking a
+# pseudo-binary number from these "digits" gives the requested sum.
+# Here PDL comes handy for several reasons:
+# - Missing/undefined values on piddle creation are taken as zero by
+#   default.
+# - There is a simple transpose operation.
+# - There are projections over one dimension, e.g. sumover.
+# - The data in any dimension can easily be reversed.
+# - Piddle values can be transformed "simultaneously".
+
+sub sum_bit_pair_wise {
+    # By reversing the digits, these become aligned at the least
+    # significant position even if the binary representations (without
+    # leading zeros) have different lengths.  Missing digits will be
+    # taken as zeros by the PDL constructor.  Then sum over each bit
+    # position and revert the reverse operation.
+    my $sum = (long map [reverse todigits $_, 2], @_)
+        ->xchg(0, 1)->sumover->slice('-1:0');
+    # Calculate the number of pairs having a certain bit in common and
+    # build the requested sum from these "binary" digits.  'fromdigits'
+    # is not limited to digits below the base and is thus able to handle
+    # these.
+    fromdigits +($sum * ($sum - 1) / 2)->unpdl, 2;
+}
+
+### Examples and tests
+
+sub run_tests {
+    SKIP: {
+        skip "examples" unless $examples;
+        
+        is sum_bit_pair_wise(1, 2, 3), 3, 'example 1';
+        is sum_bit_pair_wise(2, 3, 4), 2, 'example 2';
+    }
+
+    SKIP: {
+        skip "tests" unless $tests;
+
+        is sum_bit_pair_wise(0 .. 7), 42,
+            'Ultimate Question to Life, the Universe, and Everything';
+        is sum_bit_pair_wise(1, 4, 9, 13), 15, 'asymmetric';
+	}
+
+    done_testing;
+    exit;
+}
-- 
cgit 


From fe3f63d53074a27740ac314212da59eb4b1fbf8e Mon Sep 17 00:00:00 2001
From: Jörg Sommrey <28217714+jo-37@users.noreply.github.com>
Date: Tue, 3 May 2022 14:23:43 +0200
Subject: Solution to task 2

---
 challenge-163/jo-37/perl/ch-2.pl | 50 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100755 challenge-163/jo-37/perl/ch-2.pl

diff --git a/challenge-163/jo-37/perl/ch-2.pl b/challenge-163/jo-37/perl/ch-2.pl
new file mode 100755
index 0000000000..fbf230e7c9
--- /dev/null
+++ b/challenge-163/jo-37/perl/ch-2.pl
@@ -0,0 +1,50 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0;
+use List::Util 'reductions';
+use experimental 'signatures';
+
+our $examples;
+
+run_tests() if $examples;	# does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [N...]
+
+-examples
+    run the examples from the challenge
+ 
+N...
+    Calculate the "triangular sum" over the given numbers.
+
+EOS
+
+
+### Input and Output
+
+say triangular_sum(@ARGV);
+
+
+### Implementation
+
+sub triangular_sum (@n) {
+    # Calculate the running sums over the array starting with the second
+    # element until the array becomes a singleton.
+    @n = reductions {$a + $b} @n[1 .. $#n] while @n > 1;
+
+    $n[0];
+}
+
+
+### Examples and tests
+
+sub run_tests {
+
+    # Meeting Slartibartfast, again.
+    is triangular_sum(1, 2, 3, 4, 5), 42, 'example 1';
+    is triangular_sum(1, 3, 5, 7, 9), 70, 'example 2';
+
+    done_testing;
+    exit;
+}
-- 
cgit