[OT] shuffling lines in a stream

[Andrei Alexandrescu]

Sergey Gromov wrote:
> Fri, 10 Oct 2008 15:54:18 -0500,
> Andrei Alexandrescu wrote:
>> Sean Kelly wrote:
>>> It would be slower than the seeking option, but something like a 
>>> randomized mergesort would work as well.  If the program can buffer k 
>>> lines in a file containing n lines, then read the first k lines into 
>>> memory, shuffle them, and write them out to a temporary file.  Repeat 
>>> until the input is exhausted.  Now randomly pick two of the temporary 
>>> files and randomly merge them.  Repeat until two temporary files remain, 
>>> then output the result of the final random merge to the screen.
>>>
>>> For small files (ie. where n<k) the file would be read, shuffled in 
>>> memory, and printed to the screen, assuming the proper checks were in 
>>> place.
>> I think I found a problem with your solution. Consider you break the 
>> file in three chunks: a, b, c. Then you pick at random b and c and 
>> randomly merge them. The problem is, you make early the decision that 
>> nothing in a will appear in the first two thirds of the result. So the 
>> quality of randomness suffers. How would you address that?
> 
> After merging b and c you end up with a and bc.  Then you randomly merge 
> these two files and lines from a have all the chances to appear anywhere 
> within result.
> 
> When randomly merging, the probability of picking a line from a file 
> should be proportional to a number of lines left in that file.

How do you "randomly merge"? Describe the process.

Andrei