I'm a little afraid of answering this 'cause it looks a bit like homework. That said...

The first question I have is "how did you get the string in the first place?" The answer to this might present a better solution (e.g., don't concatenate blank lines to $str in the firs place).

To answer your original question, though:

use strict;
use warnings;
use diagnostics;

print "START: '$str'";
$str =~ s/\n\n+/\n/g;
print "\nEND: '$str'";
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