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Knuth's algorithm S: Difference between revisions
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;The algorithm:
:* Select the first n items as the sample as they become available;
:* For the i-th item where i > n, have a random chance of n/i of keeping it. If failing this chance, the sample remains the same. If not, have it randomly (1/n) replace one of the previously selected n items of the sample.
:* Repeat #2 for any subsequent items.
;The Task:
:* Create a function <code>s_of_n_creator</code> that given <math>n</math> the maximum sample size, returns a function <code>s_of_n</code> that takes one parameter, <code>item</code>.
:* Function <code>s_of_n</code> when called with successive items returns an equi-weighted random sample of up to n of its items so far, each time it is called, calculated using Knuths Algorithm S.
:* Test your functions by printing and showing the frequency of occurrences of the selected digits from 100,000 repetitions of:
:::# Use the s_of_n_creator with n == 3 to generate an s_of_n.
:::# call s_of_n with each of the digits 0 to 9 in order, keeping the returned three digits of its random sampling from its last call with argument item=9.
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