# RabbitFarm

### 2020-11-08

#### Perl Weekly Challenge 085

## Part 1

*You are given an array of real numbers greater than zero. Write a script to find if there exists a triplet (a,b,c) such that 1 < a+b+c < 2. Print 1 if you succeed otherwise 0.*

### Solution

```
use strict;
use warnings;
##
# You are given an array of real numbers greater than zero.
# Write a script to find if there exists a triplet (a,b,c)
# such that 1 < a+b+c < 2. Print 1 if you succeed otherwise 0.
##
use boolean;
use Math::Combinatorics;
sub build_constraints{
my @constraints;
my $a_not_equal_b = sub { $_[0] != $_[1] };
my $a_not_equal_c = sub { $_[0] != $_[2] };
my $b_not_equal_c = sub { $_[1] != $_[2] };
my $sum_greater_than_1 = sub { 1 < ($_[0] + $_[1] + $_[2]) };
my $sum_less_than_2 = sub { 2 > ($_[0] + $_[1] + $_[2]) };
return (
$a_not_equal_b,
$a_not_equal_c,
$b_not_equal_c,
$sum_greater_than_1,
$sum_less_than_2
);
}
MAIN:{
my $combinations = Math::Combinatorics->new(
count => 3,
data => [@ARGV],
);
my $found;
while(my @combination = $combinations->next_combination()){
$found = true;
for my $constraint (build_constraints()){
if(!$constraint->(@combination)){
$found = false;
last;
}
}
do{ print "1\n"; last; } if($found);
}
print "0\n" if(!$found);
}
```

### Sample Run

```
$ perl perl/ch-1.pl 0.1 1.2 3.4 0.2
1
$ perl perl/ch-1.pl 1.1 1.2 3.4 0.2
0
```

### Notes

I decided to try a *constraint programming* approach for this. While there are several modules for doing this available on CPAN I didnâ€™t want to quite go so deep down that rabbithole. Instead I took the simpler path of implementing each constraint as a subroutine stored in an array. For each candidate combination the constraints are tests. Since all constraints must be satisfied if any one returns a false value then we can move immediately to the next combination.

## Part 2

*You are given a positive integer $N. Write a script to find if it can be expressed as a ** b where a > 0 and b > 1. Print 1 if you succeed otherwise 0.*

### Solution

```
use strict;
use warnings;
##
# You are given a positive integer $N.
# Write a script to find if it can be expressed
# as a ^ b where a > 0 and b > 1.
# Print 1 if you succeed otherwise 0.
##
use boolean;
sub log_a{
my($a, $n) = @_;
return log($n)/log($a);
}
MAIN:{
my $N = $ARGV[0];
my $found = false;
for my $a (2 .. $N){
my $b = log_a($a, $N);
if($b =~ /^[-]?\d+$/ && $b > 1){
print "1\n";
$found = true;
last;
}
}
print "0\n" if(!$found);
}
```

### Sample Run

```
$ perl perl/ch-2.pl 7
0
$ perl perl/ch-2.pl 9
1
```

### Notes

I was tempted to repeat roughly the same design as Part 1 and use constraints but that really would be over engineering it! Instead here we just loop over all possible values `$a`

and test using logarithms to see if `$b`

holds an integer value. There seems to be a number of ways to do the test to determine if a scalar holds an integer but a regex seems maybe the most idiomatically Perlish way.

posted at: 16:20 | path: /perl | permanent link to this entry