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#! /opt/local/bin/perl
#
# embrace_the_power.pl
#
# TASK #2 › Power Integers
# Submitted by: Mohammad S Anwar
#
# You are given an integer $N.
#
# Write a script to check if the given number can be expressed as
# mn where m and n are positive integers. Otherwise print 0.
#
# Please make sure m > 1 and n > 1.
#
# BONUS: If there are more than one ways to express the given
# number then print all possible solutions.
#
# Example 1:
# For given $N = 9, it should print 32 or 3^2.
#
# Example 2:
# For given $N = 45, it should print 0.
#
# Example 3:
# For given $N = 64, it should print all or one of 8^2 or 2^6 or 4^3.
#
#
#
#
# 2020 colin crain
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
use warnings;
use strict;
use feature ":5.26";
## ## ## ## ## MAIN:
my $input = shift @ARGV;
my $maxprime = int( sqrt($input) );
my @primes = make_prime_list($maxprime);
my %decomp;
%decomp = map { $_, ++$decomp{$_} } decompose($input, \@primes);
my ($power, $base_factors) = get_powers( \%decomp );
if (defined $base_factors) {
my $base = 1;
for (keys $base_factors->%*) {
$base *= $_ ** $base_factors->{$_};
}
say "$input = $base^$power";
}
else {
say 0;
}
## ## ## ## ## SUBS:
sub get_powers {
## divides a hash of factors and their incidence into a power and a hash of factors with new incidences,
## or returns undef if impossible
my %decomp = $_[0]->%*;
my @factors = sort { $decomp{$a} <=> $decomp{$b}
|| $a <=> $b
} keys %decomp ;
return unless @factors;
my $power = $decomp{$factors[0]};
return if $power == 1;
my %base_factors = map { $decomp{$_} % $power == 0 ? ($_, $decomp{$_} / $power)
: return
} @factors;
return ($power, \%base_factors);
}
sub make_prime_list {
## creates a list of all primes less than or equal to a given number
my $max = shift;
my @output = (2);
CANDIDATE: for( my $candidate = 3; $candidate <= $max; $candidate += 2 ) {
my $sqrt_candidate = sqrt( $candidate );
for( my $test = 3; $test <= $sqrt_candidate; $test += 2 ) {
next CANDIDATE if $candidate % $test == 0;
}
push @output, $candidate;
}
return @output;
}
sub decompose {
## given a number and a list of primes less than n/2,
## returns an array list of prime decomposition factors of the number
my ($num, $primes) = @_;
my @decomp;
my @primelist = $primes->@*;
my $prime = shift @primelist;
while ( $prime <= $num ) {
while ($num % $prime == 0) {
$num = $num / $prime;
push @decomp, $prime;
}
last if scalar @primelist == 0;
$prime = shift @primelist;
}
return @decomp;
}
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