[your code here]
a at a.com
Fri Feb 17 23:33:45 PST 2012
> Assuming that by "any" you mean "any particular", you would
> have to read all the lines first. Otherwise, if the code
> selects the first line with probability 1/K, then I can just
> input some other number of lines.
I'm not sure if I understood your post correctly, but it seems to
me that you didn't read the code carefully. The code selects the
last read line with probability 1/n, where n is the number of
strings already read, not the number of all strings. Say you have
have already read n strings and they are all selected with
probability 1/n. Now you read a new string and select it with
probability 1 / (n+1). The probability that you didn't select
the new string is then n / (n + 1) and the first n strings are
selected with probability 1 / n * n / (n + 1) = 1 / (n + 1), so
you now have n+1 lines all selected with probability 1 / (n + 1).
So if the property that input strings are all selected with equal
probability holds for n, it must also hold for n+1. Since it
obviously holds for n = 1 (we just select the only string with
probability 1 in that case), it must hold for all n.
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