Solutions to challenge-133

2 files changed, 124 insertions, 0 deletions

diff --git a/challenge-133/wanderdoc/perl/ch-1.pl b/challenge-133/wanderdoc/perl/ch-1.pl
new file mode 100644
index 0000000000..e34281b960
--- /dev/null
+++ b/challenge-133/wanderdoc/perl/ch-1.pl
@@ -0,0 +1,45 @@
+#!perl
+use strict;
+use warnings FATAL => qw(all);
+
+=prompt
+You are given a positive integer $N. Write a script to calculate the integer square root of the given number $N. Please avoid using built-in function.
+=cut
+
+
+
+
+
+
+
+use List::Util qw(reduce);
+
+
+
+sub nthroot # newton algorithm ch.105
+{
+     my ( $n, $k, $precision ) = @_;
+
+     $precision //= 5;
+
+     my $x0 = $k / $n;
+     my $x1; 
+          
+     while (1)
+     {
+          $x1 = (1 / $n) * 
+               ( ( $n - 1 ) * $x0 + $k / ( reduce { $a * $b } ($x0) x ($n - 1) ) );
+          last if sprintf("%.${precision}f", $x0) == sprintf("%.${precision}f", $x1);
+          $x0 = $x1;
+     }
+     return sprintf("%.${precision}f", $x1) + 0;
+}
+sub int_sqrt { return nthroot(2, $_[0], 0) }
+
+
+
+print int_sqrt(10), $/;
+print int_sqrt(27), $/;
+print int_sqrt(85), $/;
+print int_sqrt(101), $/;
+print int_sqrt(333), $/;
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diff --git a/challenge-133/wanderdoc/perl/ch-2.pl b/challenge-133/wanderdoc/perl/ch-2.pl
new file mode 100644
index 0000000000..69631e2506
--- /dev/null
+++ b/challenge-133/wanderdoc/perl/ch-2.pl
@@ -0,0 +1,79 @@
+#!perl
+use strict;
+use warnings FATAL => qw(all);
+
+=prompt
+Write a script to generate first 10 Smith Numbers.
+According to Wikipedia:
+In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base.
+=cut
+
+
+
+
+
+
+
+
+
+use List::Util qw(sum);
+use ntheory qw(is_prime);
+use Memoize;
+use Mojo::UserAgent;
+
+
+memoize('sum_of_digits');
+
+my $URL = 'https://oeis.org/A006753/b006753.txt';
+my $ua = Mojo::UserAgent->new;
+my $res = $ua->get( $URL )->res;
+my %SMITH;
+do 
+{ 
+     my ($key, $value) = split(/\s/, $_, 2);
+     $SMITH{$key} = $value if ( length($key) > 0 );
+} for split(/\n/,$res->dom);
+
+my $number = 2;
+my $counter = 1;
+
+
+while ( $counter < 1_001 ) # 10_001 )
+{
+     $number++ and next if is_prime($number);
+
+     my $sum_of_digits_of_factors = 
+          sum(map sum_of_digits($_), prime_factors($number), 0);
+
+
+
+     if ( $sum_of_digits_of_factors == sum_of_digits($number) )
+     {
+          die "Something wrong with ${number}$/" if $SMITH{$counter} != $number;
+          print join(": ", $counter++, $number), $/;
+     }
+     $number++;
+}
+
+
+sub prime_factors
+{
+     my $num = $_[0];
+     my $half = $num / 2;
+     my @factors;
+
+     for my $cand ( 2 .. $half )
+     {
+
+          if ( $num % $cand == 0 )
+          {
+               push @factors, $cand;
+               $num /= $cand;
+               redo;
+          }
+     }
+     return @factors;
+
+}
+
+sub sum_of_digits { return $_[0] < 10 ? $_[0] : sum(split(//,$_[0]));}
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