Worst case: Millions of lines, and the only two lines that are equal are the first and last ones.

I'm surpised that no one has yet mentioned an on disk database, given the constraint on memory.

use DB_File ;

tie %h, "DB_File", $dbFname ;

while( <$f> ) {
   if( exists $h{$_} ) {
      # equal lines in file
   }
   $h{$_} = 1 ; # or some piece of data

}
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It's painful, and probably not nearly so fast as an in-mem hash, but it should work. However, now the next question is how much disk space have you got? The indexes that DB_File generates can get to be VERY large.

As for speed, there are quite a few options to DB_File and you may spend some time 'tuning' it. Sensitize oneself to the concept of "fast" vs "fastest" vs "working at all".