[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 18:04:48 CEST 2011

```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):

```