RabbitFarm

The examples used here are from The Weekly Challenge problem statement and demonstrate the working solution.

Part 1

Write a script to find lowest 10 positive integers having exactly 8 divisors

Solution

use strict;
use warnings;
sub factor{
    my($n) = @_;
    my @factors = (1, $n);
    foreach my $j (2..sqrt($n)){
        push @factors, $j if $n % $j == 0;
        push @factors, ($n / $j) if $n % $j == 0 && $j ** 2 != $n;
    }    
    return @factors;  
}

sub first_ten_with_eight{
    my $i = 0;
    my @first_ten;  
    do{
        my @factors = factor($i);
        push @first_ten, $i if @factors == 8;   
        $i++; 
    }while(@first_ten != 10); 
    return @first_ten;
}

MAIN:{
    print join(", ", first_ten_with_eight()) . "\n";   
}  

Sample Run

$ perl perl/ch-1.pl
24, 30, 40, 42, 54, 56, 66, 70, 78, 88

Notes

I have re-used that factor() function quite a bit for these challenges, especially recently. My blog writing has been fairly terse recently and as much as I'd like to be a bit more verbose I really am not sure if there all that much more to say about this code that hasn't been said before!

Part 2

You are given positive integers, $m and $n. Write a script to find total count of integers created using the digits of $m which is also divisible by $n.

Solution

use strict;
use warnings;
##
# You are given positive integers, $m and $n.
# Write a script to find total count of integers 
# created using the digits of $m which is also 
# divisible by $n.
##
use Data::PowerSet q/powerset/;

sub like_numbers{
    my($m, $n) = @_; 
    my @divisible; 
    for my $subset (@{powerset(split(//, $m))}){
        my $i = join("", @$subset);
        push @divisible, $i if $i && $i != $m && $i % $n == 0;
    }  
    return @divisible;
}

MAIN:{
    print like_numbers(1234, 2) . "\n";
    print like_numbers(768, 4) . "\n";
}

Sample Run

$ perl perl/ch-2.pl
9
3

Notes

I've been making more use of Data::PowerSet recently that I would have expected! If anyone is interested in seeing an implementation of the Power Set calculations see my C++ solution links below. While not Perl the code is quite readable and should be adaptable easy to other languages. There is also a Rosetta Code entry for Power Set but, frankly, many of the submissions there, especially the C++ and Perl ones are overly convoluted in my opinion. Or at least much more so than the way I implemented it, which I would think would be the more common method but I guess not!

References

Challenge 141

Power Set Defined

Data::PowerSet

Rosetta Code Entry: Power Set

C++ Solutions: Part 1

C++ Solutions: Part 2