Task 2 via Brute Force

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+#!/usr/bin/perl
+# The Weekly Challenge - 121
+# Task 2 The Travelling Salesman
+# a brute-force solution via permutations again
+# Usage: $ ch-2.pl
+use strict;
+use warnings;
+use Algorithm::Combinatorics qw/permutations/;
+use feature qw/say/;
+
+my $M;
+
+my $M04 = [
+    [0, 5, 2, 7],
+    [5, 0, 5, 3],
+    [3, 1, 0, 6],
+    [4, 5, 4, 0]
+];
+
+my $M09 = [
+    [0,2,3,9,4,1,8,5,2],
+    [8,0,6,4,6,5,2,8,8],
+    [8,4,0,9,4,9,6,8,9],
+    [3,4,5,0,5,8,6,3,1],
+    [1,4,2,5,0,4,7,2,9],
+    [5,8,8,9,1,0,7,7,1],
+    [4,5,8,2,5,3,0,9,2],
+    [6,6,1,7,9,6,9,0,8],
+    [3,1,4,3,9,7,3,3,0]
+];
+
+my $M15 = [
+[ 0 , 1 , 3 ,11 , 9 ,13 , 2 ,15 ,10 ,10 ,13 , 9 , 3 ,15 , 8],
+[15 , 0 , 7 ,13 , 6 , 3 , 7 , 7 , 3 , 6 , 1 , 1 ,11 , 2 ,12],
+[ 9 , 7 , 0 ,16 , 5 ,14 ,12 , 2 , 6 ,16 ,10 , 9 , 8 ,13 , 3],
+[ 1 , 4 , 5 , 0 , 9 ,14 , 3 ,10 , 2 ,11 , 4 ,12 , 5 , 9 , 7],
+[11 , 2 , 8 , 8 , 0 , 8 ,16 , 1 , 1 , 7 , 6 , 8 ,15 , 4 , 3],
+[ 1 , 4 , 8 ,13 , 7 , 0 ,13 ,13 , 6 , 4 ,12 , 5 , 1 , 7 , 9],
+[ 6 , 8 , 6 ,13 , 3 ,11 , 0 , 7 , 1 ,14 , 2 ,12 , 1 , 7 , 5],
+[ 2 ,12 , 2 ,11 ,14 ,13 , 2 , 0 , 8 , 7 , 2 , 2 , 2 , 9 , 2],
+[14 ,14 ,15 , 8 ,16 , 5 ,14 ,15 , 0 , 9 ,14 , 3 ,11 , 3 ,13],
+[11 , 8 , 2 ,12 ,12 , 1 ,11 ,11 , 2 , 0 , 3 , 4 , 2 ,10 , 5],
+[12 , 4 , 2 , 8 , 6 ,10 , 7 ,15 ,16 , 4 , 0 ,12 , 1 , 5 ,10],
+[13 ,13 , 7 , 8 ,16 ,10 , 9 ,14 , 9 ,11 , 6 , 0 , 8 ,10 , 6],
+[15 ,14 , 4 ,15 , 5 ,16 ,14 , 6 , 4 ,16 , 4 , 3 , 0 , 2 , 2],
+[ 2 , 2 , 9 ,12 , 8 , 8 ,13 ,15 , 1 , 5 ,16 , 1 , 1 , 0 ,12],
+[14 , 6 ,14 , 6 , 9 , 1 ,11 ,12 ,11 , 5 , 9 , 9 , 6 , 4 , 0]
+];
+
+# $M09 and $M15 are produced by:
+# https://onlinemathtools.com/generate-random-matrix
+# manually edit the diagonal afterwards 
+# (but they won't be referenced actually)
+
+$M = $M09;
+my $N = $ARGV[0] || scalar @{$M};
+
+# $M = $M04, $N = 4 (Task Example)
+# (0 2 1 3 0)
+# length: 10
+
+# $M = $M15, $N = 11
+# Z A E I J B G F D H C Z
+# length: 30
+
+# $M = $M15, $N = 12
+# Z A E I J B G F D H K C Z
+# length: 33
+
+my $min = 10000;
+my @arr_min = ();
+
+my $v = chr(ord("A")+$N-2);
+my $iter = permutations(['A'..$v]);
+while (my $c = $iter->next) {
+    my $d = calc_dist($c);
+    if (defined($d) && $d <= $min) {  #related to the improvement A
+        if ($d < $min) {
+            @arr_min = ();
+            $min = $d;
+            say "new shorter circuit found: @{$c}"; #facilitate testing
+        }
+        push @arr_min, $c;
+    }
+}
+
+say "";
+say "length = $min";
+say ('tour = (0 ', (join " ", map {alp2n($_)} @{$arr_min[0]}) , ' 0)' ) ;
+
+
+sub alp2n {
+    return ord($_[0])-ord("A")+1;
+}
+
+
+sub calc_dist {
+    my @seq = @{$_[0]};
+    my $dist = 0;
+    $dist += $M->[0][ alp2n($seq[0]) ];
+    for my $i (0..$#seq-1) {
+        $dist += $M->[ alp2n($seq[$i]) ][ alp2n($seq[$i+1]) ];
+        return undef if $dist >= $min;    # a slightly improvement A 
+    }
+    $dist += $M->[alp2n($seq[-1])][0];
+}
+