Merge pull request #6212 from jaldhar/challenge-167

Challenge 167 by Jaldhar H. Vyas.

5 files changed, 167 insertions, 0 deletions

diff --git a/challenge-167/jaldhar-h-vyas/blog.txt b/challenge-167/jaldhar-h-vyas/blog.txt
new file mode 100644
index 0000000000..401873b45e
--- /dev/null
+++ b/challenge-167/jaldhar-h-vyas/blog.txt
@@ -0,0 +1 @@
+https://www.braincells.com/perl/2022/06/perl_weekly_challenge_week_167.html
\ No newline at end of file
diff --git a/challenge-167/jaldhar-h-vyas/perl/ch-1.pl b/challenge-167/jaldhar-h-vyas/perl/ch-1.pl
new file mode 100755
index 0000000000..1f5b9007a9
--- /dev/null
+++ b/challenge-167/jaldhar-h-vyas/perl/ch-1.pl
@@ -0,0 +1,46 @@
+#!/usr/bin/perl
+use 5.030;
+use warnings;
+
+sub isPrime {
+    my ($n) = @_;
+
+    if ($n < 2) {
+        return undef;
+    }
+
+    if ($n == 2) {
+        return 1;
+    }
+
+    for my $i (2 .. sqrt($n)) {
+        if ($n % $i == 0) {
+            return undef;
+        }
+    }
+
+    return 1;
+}
+
+my @circularPrimes;
+my $n = 99;
+
+outer: while (scalar @circularPrimes < 10) {
+    $n++;
+
+    unless ($n =~ /^[1379]+$/) {
+        next;
+    }
+
+    my $rotated = $n;
+    for (0 .. length $n) {
+        unless (isPrime($rotated) && ! grep { $_ == $rotated } @circularPrimes) {
+            next outer;
+        }
+
+        $rotated = substr($rotated, 1) . substr($rotated, 0, 1);
+    }
+    push @circularPrimes, $n;
+}
+
+say join q{, }, @circularPrimes;
diff --git a/challenge-167/jaldhar-h-vyas/perl/ch-2.pl b/challenge-167/jaldhar-h-vyas/perl/ch-2.pl
new file mode 100755
index 0000000000..de90de30ea
--- /dev/null
+++ b/challenge-167/jaldhar-h-vyas/perl/ch-2.pl
@@ -0,0 +1,49 @@
+#!/usr/bin/perl
+use 5.030;
+use warnings;
+use utf8;
+use Math::Complex qw/ Im Re pi /;
+use Math::Round qw/ nearest /;
+use constant ε => 1e-7;
+
+sub dropImaginary {
+    my ($z) = @_;
+
+    if (abs(Im($z)) < ε) {
+        $z = Re($z);
+    }
+
+    return $z;
+}
+
+sub Γ {
+    my ($z) = @_;
+    $z = Math::Complex->new($z);
+
+    if (Re($z) <  .5) {
+        return pi / sin(pi * $z) / Γ(1 - $z);
+    } else {
+        my @coefficients = qw/
+            676.5203681218851
+            -1259.1392167224028
+            771.32342877765313
+            -176.61502916214059
+            12.507343278686905
+            -0.13857109526572012
+            9.9843695780195716e-6
+            1.5056327351493116e-7
+        /;
+        $z -= 1;
+        my $sum = 0.99999999999980993;
+        my $i =  0;
+        for my $c (@coefficients) {
+            $sum += $c / ($z + 1 + $i++);
+        }
+        my $t = $z + scalar @coefficients - 0.5;
+        return dropImaginary(sqrt(2 * pi) * $t ** ($z + 0.5) * exp(-$t) * $sum);
+    }
+}
+
+for my $i (3, 5, 7) {
+    say nearest(0.01, Γ($i)); 
+}
diff --git a/challenge-167/jaldhar-h-vyas/raku/ch-1.raku b/challenge-167/jaldhar-h-vyas/raku/ch-1.raku
new file mode 100755
index 0000000000..90f8adb86b
--- /dev/null
+++ b/challenge-167/jaldhar-h-vyas/raku/ch-1.raku
@@ -0,0 +1,26 @@
+#!/usr/bin/raku
+
+sub MAIN() {
+    my @circularPrimes;
+    my $n = 99;
+
+    outer: while @circularPrimes.elems < 10 {
+        $n++;
+
+        unless $n ~~ /^ <[1379]>+ $/ {
+            next;
+        }
+
+        my $rotated = $n;
+        for 0 ..^ $n.chars {
+            unless $rotated.is-prime && $rotated.Int ∉ @circularPrimes {
+                next outer;
+            }
+
+            $rotated = $rotated.substr(1 .. *) ~ $rotated.substr(0, 1);
+        }
+        @circularPrimes.push($n);
+    }
+
+    @circularPrimes.join(q{, }).say;
+}
\ No newline at end of file
diff --git a/challenge-167/jaldhar-h-vyas/raku/ch-2.raku b/challenge-167/jaldhar-h-vyas/raku/ch-2.raku
new file mode 100755
index 0000000000..add7e1e8bd
--- /dev/null
+++ b/challenge-167/jaldhar-h-vyas/raku/ch-2.raku
@@ -0,0 +1,45 @@
+#!/usr/bin/raku
+
+sub Γ(Real $n) {
+    my $z = Complex.new($n, 0);
+
+    if $z.re <  0.5 {
+        return pi / sin(pi * $z) / Γ(1 - $z);
+    } else {
+        my @coefficients = <
+            676.5203681218851
+            -1259.1392167224028
+            771.32342877765313
+            -176.61502916214059
+            12.507343278686905
+            -0.13857109526572012
+            9.9843695780195716e-6
+            1.5056327351493116e-7
+        >;
+        $z -= 1;
+        my $sum = 0.99999999999980993;
+        my $i =  0;
+        for @coefficients -> $c {
+            $sum += $c / ($z + 1 + $i++);
+        }
+        my $t = $z + @coefficients.elems - 0.5;
+        return dropImaginary(sqrt(2 * pi) * $t ** ($z + 0.5) * exp(-$t) * $sum);
+    }
+}
+
+sub dropImaginary(Complex $n) {
+    constant ε = 1e-7;
+    my $z = $n;
+
+    if $z.im.abs < ε {
+        $z = $z.re;
+    }
+
+    return $z;
+}
+
+sub MAIN() {
+    for (3, 5, 7) -> $i {
+        say Γ($i).round(0.01); 
+    }
+}
\ No newline at end of file