A big problem I see in your program is that you are reading the whole file into an array first and then are assigning that to a scalar so you have TWO copies of the whole file in memory. It would be more memory efficient just to read the file directly into a scalar.
use warnings;
use strict;
system 'clear';
print "Palindrome - gamma version\n";
print "--------------------------\n\n";
print 'Please enter DNA filename: ';
chomp( my $filename = <STDIN> );
open DNASEQ, $filename or die "Cannot open $filename: $!";
( my $dna = do { local $/; <DNASEQ> } ) =~ tr/atcgATCG//cd;
my $count_of_2 = () = $dna =~ /a(?=t)|t(?=a)|c(?=g)|g(?=c)/ig;
print "Number of 2bp palindromes: ", $count_of_2, "\n";
__END__
See if that produces the same result as your friend's C++ code.
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