It’s (Perl) Weekly Challenge #156! 156 is a Harshad number, which means that it is divisible by the sum of it’s digits. Harshad is from Sanskrit and it means it gives joy. I think that means D. R. Kaprekar is the Marie Kondo of number theory. It’s nice to have a repeatable, algorithmic answer to the question “Does this spark joy?”

### Hey, It’s Pi Day!

I’m pulling back out some code from eight years ago where I demonstrate

• how to estimate pi in a few different ways
• that you can use the character π as part of your variable names

There’s no Pi-related tasks in this one. Maybe one will come around when we get to Tau Day.

``````#!/usr/bin/env perl

use feature qw{ say } ;
use strict ;
use warnings ;
use utf8 ;

my \$π = 3.14159 ;

my \$est2  = estimate_2() ;
my \$diff2 = sprintf '%.5f',abs \$π - \$est2 ;
say qq{Estimate 2: \$est2 - off by \$diff2} ;

my \$est1  = estimate_1() ;
my \$diff1 = sprintf '%.5f',abs \$π - \$est1 ;
say qq{Estimate 1: \$est1 - off by \$diff1} ;

exit ;

# concept here is that the area of a circle = π * rsquared
# if r == 1, area = π. If we just take the part of the circle
# where x and y are positive, that'll be π/4. So, take a random
# point between 0,0 and 1,1 see if the distance between it and
# 0,0 is < 1. If so, we increment, and the count / the number
# so far is an estimate of π.

# because randomness, this will change each time you run it

sub estimate_1 {
srand ;
my \$inside = 0.0 ;
my \$pi ;
for my \$i ( 1 .. 1_000_000 ) {
my \$x = rand ;
my \$y = rand ;
\$inside++ if \$x * \$x + \$y * \$y < 1.0 ;
\$pi = sprintf '%.5f', 4 * \$inside / \$i ;
}
return \$pi ;
}

# concept here is that π can be estimated by 4 ( 1 - 1/3 + 1/5 - 1/7 ...)
# so we get closer the further we go
sub estimate_2 {
my \$pi = 0;
my \$c  = 0;
for my \$i ( 0 .. 1_000_000 ) {
my \$j = 2 * \$i + 1 ;
if ( \$i % 2 == 1 ) { \$c -= 1 / \$j ; }
else               { \$c += 1 / \$j ; }
\$pi = sprintf '%.5f', 4 * \$c ;
}
return \$pi ;
}
``````

### TASK #1 › Pernicious Numbers

Write a script to permute first 10 Pernicious Numbers.

A pernicious number is a positive integer which has prime number of ones in its binary representation.

The first pernicious number is 3 since binary representation of 3 = (11) and 1 + 1 = 2, which is a prime.

Expected Output
`3, 5, 6, 7, 9, 10, 11, 12, 13, 14 `

In reverse order:

• binary representation: `sprintf '%b' \$n`
• number of ones: `sum0 split //, \$n`
• is_prime: I’ve shown that one a lot recently

So, `push @pernicious, \$n if is_prime(count_ones(to_binary(\$n)))` does the trick.

#### Show Me The Code!

``````#!/usr/bin/env perl

use strict;
use warnings;
use feature qw{ say postderef signatures state };
no warnings qw{ experimental };

use List::Util qw{ product sum0 uniq };

my @pernicious;
my \$i = 0;
while ( scalar @pernicious < 10 ) {
\$i++;
if ( is_prime( count_ones( to_binary(\$i) ) ) ) {
push @pernicious, \$i;
}
}
say join ', ', @pernicious;

sub count_ones( \$n ) {
return sum0 split //, \$n;
}

sub to_binary( \$n ) {
return sprintf '%b', \$n;
}

sub is_prime (\$n) {
return 0 if \$n == 0 || \$n == 1;
for ( 2 .. sqrt \$n ) { return 0 unless \$n % \$_ }
return 1;
}
``````
``````\$ ./ch-1.pl
3, 5, 6, 7, 9, 10, 11, 12, 13, 14
``````

### TASK #2 › Weird Number

Submitted by: Mohammad S Anwar You are given number, `\$n > 0`.

Write a script to find out if the given number is a Weird Number.

According to Wikipedia, it is defined as:

The sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.

So, a number is Weird if

• sum of the proper divisors is greater than the number, but
• there’s no combination of the proper divisors whose sum equals the number

So, we go back to List::Util and `sum0`. (Reminder: `sum0` and not `sum` because `sum0()` is `0` and `sum()` is `undef`. Always use `sum0` would be my Perl Best Practice.) Otherwise, finding the factors is a functional one-liner: `grep { \$n % \$_ == 0 } 1 .. \$n - 1`.

The “sum of combination of proper divisors” part, well…

THIS looks like a JOB for RECURSION!

So, there’s the necessary values: the number and an arrayref of divisors of the number. Then there’s the index of the list, and the current set, which is an array, not an arrayref, which makes moving forward easy.

``````    # appends the current factor to @values
return 1 if subset_sum( \$n, \$factors, \$i + 1, @values, \$factors->[\$i] );

# appends the 0 to @values
return 1 if subset_sum( \$n, \$factors, \$i + 1, @values, 0 );
``````

And then, when we’re at the end, we see if the sum equals the number.

``````    if ( !defined \$factors->[\$i] ) {
my \$sum = sum0 @values;
return \$n == \$sum ? 1 : 0;
}
``````

Plus, of course, the usefulness of Getopt::Long.

#### Show Me The Code!

``````#!/usr/bin/env perl

use strict;
use warnings;
use feature qw{ say postderef signatures state };
no warnings qw{ experimental };

use Carp;
use Getopt::Long;
use List::Util qw{ sum0 };
use Scalar::Util qw{ looks_like_number };

my \$n = 12;
GetOptions( 'number=i' => \\$n );
croak "Not Greater than 0" unless \$n > 0;

my \$w = is_weird(\$n);
say <<"END";
Input:  \\$n = \$n
Output: \$w
END

sub is_weird ( \$n ) {
my \$m       = \$n;
my @factors = grep { \$n % \$_ == 0 } 1 .. \$n - 1;
my \$sum     = sum0 @factors;
my \$w       = subset_sum( \$n, \@factors );
return ( \$sum > \$n && !\$w ) ? 1 : 0;
}

sub subset_sum ( \$n, \$factors, \$i = 0, @values ) {
if ( !defined \$factors->[\$i] ) {
my \$sum = sum0 @values;
return \$n == \$sum ? 1 : 0;
}
my @o;
return 1 if subset_sum( \$n, \$factors, \$i + 1, @values, \$factors->[\$i] );
return 1 if subset_sum( \$n, \$factors, \$i + 1, @values, 0 );
return 0;
}
``````
``````\$ ./ch-2.pl -n 12
Input:  \$n = 12
Output: 0

\$ ./ch-2.pl -n 70
Input:  \$n = 70
Output: 1

\$ ./ch-2.pl -n 5830
Input:  \$n = 5830
Output: 1

\$ ./ch-2.pl -n 5831
Input:  \$n = 5831
Output: 0
``````