I have written something similar to what you are trying to achieve, I rewrote an old script that had a very inefficient algorithm, with a new script with an efficient algorithm. The algorithm I used was similar to Corion's but different in detail. The algorithm is as follows:

1. 1st pass through the file, build an array structure that records the position of the line number in the file, with the line number as the array index.
2. randomize the line numbers, generate a new randomized list with line numbers in the new sequence.
3. for each line number in the new sequence, look up the @linepos->[$line_number] => position in the array structure, seek to the desired position in the source file, read the line, and output the line in the new file.

This algorithm is very fast, I once have reduced the time of processing of a file from 15+ minutes using the old and clumsy algorithm, to just under 3 seconds using the new efficient algorithm.

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