# [Haskell-cafe] Acquiring a random set of a specific size (w/o dups) from a range of Ints

Patrick Perry patperry at gmail.com
Tue Jun 14 18:09:21 CEST 2011

Correction: the version in monte-carlo takes time O(n), but it only consumes k random numbers.  The streaming algorithm consumes n random numbers.

On Jun 14, 2011, at 12:04 PM, Patrick Perry wrote:

> There are time/space tradeoffs in sampling without replacement.  The version in monte-carlo takes space O(n) and time O(k), for all k.  I chose this algorithm instead of a streaming algorithm, with takes space O(k) and time O(n).
>
> If k is much less than n, you can improve a bit.  Here is a version taking space O(k) and time O(k^2), *provided k << n*;  when k is large relative to n, the time increases to roughly O(n log n).
>
> import Data.List( nub )
>
> sampleSmallIntSubset :: MonadMC m => Int -> Int -> m [Int]
> sampleSmallIntSubset n k = (take k . nub) `liftM` repeatMC (sampleInt n)
>
> sampleSmallSubset :: MonadMC m => [a] -> Int -> m [a]
> sampleSmallSubset xs k = (map (xs !!)) `liftM` sampleSmallIntSubset (length xs) k
>
> -- strict version of the above
> sampleSmallSubset' :: MonadMC m => [a] -> Int -> m [a]
> sampleSmallSubset' xs k = do
>    ys <- sampleSmallSubset xs k
>    (length ys) `seq` return ys -- by forcing the length, we make sure we are done with the RNG when we return
>
>
> If you're wondering about the strict version, the following example should be instructive:
>
> Let's note the first three numbers generated by the RNG with seed 0:
>
>    ghci> (replicateM 3 \$ uniform 0 1) `evalMC` mt19937 0
>    [0.999741748906672,0.16290987539105117,0.28261780529282987]
>
> Now, let's look at the first number we get after a call to sampleSmallSubset, if we don't evaluate the subset:
>
>    ghci> sampleSmallSubset [1..10000] 2 >> uniform 0 1) `evalMC` mt19937 0
>    0.999741748906672
>
> Apparently, the call to sampleSmallSubset doesn't consume any random numbers.  Now, let's try the strict version:
>
>    ghci> (sampleSmallSubset' [1..10000] 2 >> uniform 0 1) `evalMC` mt19937 0
>    0.28261780529282987
>
> This time, the call to sampleSmallSubset' consumes two random numbers, even if we throw away the result.
>
> Since you're just starting out, I recommend using the strict versions of the functions.  They are less space-efficient than the lazy versions, but they are guaranteed to be safe.
>
>
>
>
>> From: Jonas Almström Duregård <jonas.duregard at chalmers.se>
>
>> Subject: Re: [Haskell-cafe] Acquiring a random set of a specific size (w/o dups) from a range of Ints
>> To: "michael rice" <
>> nowgate at yahoo.com
>>>
>> Cc: "Felipe Almeida Lessa" <
>>
>> Date: Tuesday, June 14, 2011, 5:17 AM
>>
>>>
>> Shuffle [1..20], then take 5?
>>
>>>
>> Yes, so simple, I'm embarrassed I didn't think of it.
>>
>>
>> That works well for small numbers, but I'm guessing it will evaluate the entire list so it should not be used for large inputs. If you have a large interval and use a relatively small part of it, the following function should be significantly faster (it builds a random permutation lazily):