From 6e98239f9d7df539606d6f6412d9aae8002851ae Mon Sep 17 00:00:00 2001
From: Jörg Sommrey <28217714+jo-37@users.noreply.github.com>
Date: Mon, 3 Apr 2023 23:06:58 +0200
Subject: Solution to task 1

---
 challenge-211/jo-37/perl/ch-1.pl | 85 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100755 challenge-211/jo-37/perl/ch-1.pl

diff --git a/challenge-211/jo-37/perl/ch-1.pl b/challenge-211/jo-37/perl/ch-1.pl
new file mode 100755
index 0000000000..586b91905e
--- /dev/null
+++ b/challenge-211/jo-37/perl/ch-1.pl
@@ -0,0 +1,85 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0 '!float';
+use PDL;
+
+our ($tests, $examples);
+
+run_tests() if $tests || $examples;	# does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [-tests] [Matrix]
+
+-examples
+    run the examples from the challenge
+ 
+-tests
+    run some tests
+
+Matrix
+    a string representation of a matrix as accepted by the PDL constructor,
+    e.g. "[3 2 1] [4 3 2]"
+
+EOS
+
+
+### Input and Output
+
+say is_toeplitz("@ARGV") ? 'true' : 'false';
+
+
+### Implementation
+
+# A NxM matrix (N,M > 1) has N + M - 3 diagonals having more than one
+# element.  Creating a set of NxN matrices where each of them have one
+# of the orignal matrix' diagonals as its main diagonal.  Then take the
+# diagonal of these matrices and re-arrange them into a new matrix
+# having the main diagonals of the matrix series as rows. Taking minimum
+# and maximum over the rows.  If min and max equals for every row, the
+# matrix is Toeplitz.
+# Note: Utilizing BAD values in incomplete diagonals that do not account
+# for minimum or maximum.
+sub is_toeplitz {
+	(my $m = pdl @_)->badflag(1);
+    my ($min, $max) = (
+        cat map $_->diagonal(0, 1),
+        $m->range($m->dim(0) - 2 - sequence(indx, 1, $m->shape->sum - 3),
+            $m->dim(1), 't')
+        ->reorder(1,2,0)->dog
+    )->minmaximum;
+
+    all $min == $max;
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    SKIP: {
+        skip "examples" unless $examples;
+        
+        ok is_toeplitz(
+            [4, 3, 2, 1],
+            [5, 4, 3, 2],
+            [6, 5, 4, 3]), 'example 1';
+
+        ok !is_toeplitz(
+            [1, 2, 3],
+            [3, 2, 1]), 'example 2';
+    }
+
+    SKIP: {
+        skip "tests" unless $tests;
+
+        ok is_toeplitz(sequence(4) + 5 - sequence(5)->dummy(0)), '4 x 5';
+        ok is_toeplitz(sequence(5) + 4 - sequence(4)->dummy(0)), '5 x 4';
+
+        my $nt = sequence(4) + 5 - sequence(5)->dummy(0);
+        $nt->set(1, 4, 0);
+        ok !is_toeplitz($nt), 'one element failing';
+	}
+
+    done_testing;
+    exit;
+}
-- 
cgit 


From 2bcb7ffce5bfbf0c9f1e23ef714c678f9f992a8a Mon Sep 17 00:00:00 2001
From: Jörg Sommrey <28217714+jo-37@users.noreply.github.com>
Date: Tue, 4 Apr 2023 22:31:34 +0200
Subject: Solution to task 2

---
 challenge-211/jo-37/perl/ch-2.pl | 73 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100755 challenge-211/jo-37/perl/ch-2.pl

diff --git a/challenge-211/jo-37/perl/ch-2.pl b/challenge-211/jo-37/perl/ch-2.pl
new file mode 100755
index 0000000000..dd2c6b03fb
--- /dev/null
+++ b/challenge-211/jo-37/perl/ch-2.pl
@@ -0,0 +1,73 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0;
+use Math::Prime::Util qw(forcomb lastfor);
+use List::Util qw(sum);
+use experimental qw(signatures);
+
+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...
+    list of numbers
+
+EOS
+
+
+### Input and Output
+
+say same_average(@ARGV) ? 'true' : 'false';
+
+
+### Implementation
+
+# It can easily be shown that if two partitions of the list have the
+# same average, this common average equals the average of the whole
+# list.  Thus all we need to do is find a nonempty true subset of the
+# list having the same average as the list.  The complement will have
+# the same average.
+
+sub same_average (@list) {
+    state $delta = 1e-6;
+    my $avg = sum(@list) / @list;
+    my $res;
+    # Loop over all subsets.
+    forcomb {
+        # Skip non true subsets.
+        return unless @_ && @_ != @list;
+        $res = 1, lastfor if abs($avg - sum(@list[@_]) / @_) < $delta;
+    } @list;
+
+    $res;
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    SKIP: {
+        skip "examples" unless $examples;
+
+        ok same_average(1, 2, 3, 4, 5, 6, 7, 8), 'example 1';
+        ok !same_average(1, 3), 'example 2';
+    }
+
+    SKIP: {
+        skip "tests" unless $tests;
+        ok same_average(1, 1, 1, 1, 5, 9,), '(1 5), (1 1 1 9)';
+	}
+
+    done_testing;
+    exit;
+}
-- 
cgit