Does j change for each set, or do you want to print the same number of lines for each set? It sounds like the amount of lines for each set is the same. Assuming that you want to print the same amount of lines for each set, than do the following
-read an entire set, let $m = the number of lines read
-let $j = int(rand($m))+1
-print out $j lines of the first set that you've already read
-now read the file line by line, buffering the input, and after you've read out $m lines, print out
the first $j lines for each set, and throw away the remaining ($m-$j) lines.
j random lines from each set. Then you can throw away your buffer and start over.
As for the size of the file, just don't slurp the entire file into memory, read it line by line.
Have I answered your question? I have a feeling that I'm oversimplifying it. If so, please give a few more details.
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