# Difference between revisions of "Random shuffle"

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m (removed need for scoped variables, etc) |
(Add a variation on the ST-based implementation) |
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This is a lot simpler than the purely functional algorithm linked below. |
This is a lot simpler than the purely functional algorithm linked below. |
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+ | |||

+ | Here's a variation using the MonadRandom package: |
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+ | |||

+ | <haskell> |
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+ | import Control.Monad |
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+ | import Control.Monad.ST |
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+ | import Control.Monad.Random |
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+ | import System.Random |
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+ | import Data.Array.ST |
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+ | import GHC.Arr |
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+ | |||

+ | shuffle :: RandomGen g => [a] -> Rand g [a] |
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+ | shuffle xs = do |
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+ | let l = length xs |
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+ | rands <- take l `fmap` getRandomRs (0, l-1) |
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+ | let ar = runSTArray $ do |
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+ | ar <- thawSTArray $ listArray (0, l-1) xs |
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+ | forM_ (zip [0..(l-1)] rands) $ \(i, j) -> do |
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+ | vi <- readSTArray ar i |
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+ | vj <- readSTArray ar j |
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+ | writeSTArray ar j vi |
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+ | writeSTArray ar i vj |
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+ | return ar |
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+ | return (elems ar) |
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+ | |||

+ | *Main> evalRandIO (shuffle [1..10]) |
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+ | [6,5,1,7,10,4,9,2,8,3] |
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+ | </haskell> |
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== Other implemenations == |
== Other implemenations == |

## Revision as of 12:37, 16 May 2009

## The problem

Shuffling a list, i.e. creating a random permutation, is not easy to do correctly. Each permutation should have the same probability.

## Imperative algorithm

The standard imperative algorithm can be implemented as follows:

```
import System.Random
import Data.Array.IO
import Control.Monad
-- | Randomly shuffle a list
-- /O(N)/
shuffle :: [a] -> IO [a]
shuffle xs = do
ar <- newArray n xs
forM [1..n] $ \i -> do
j <- randomRIO (i,n)
vi <- readArray ar i
vj <- readArray ar j
writeArray ar j vi
return vj
where
n = length xs
newArray :: Int -> [a] -> IO (IOArray Int a)
newArray n xs = newListArray (1,n) xs
```

Or one can use ST to avoid needing IO:

```
import System.Random
import Data.Array.ST
import Control.Monad
import Control.Monad.ST
import Data.STRef
-- | Randomly shuffle a list without the IO Monad
-- /O(N)/
shuffle' :: [a] -> StdGen -> ([a],StdGen)
shuffle' xs gen = runST (do
g <- newSTRef gen
let randomRST lohi = do
(a,s') <- liftM (randomR lohi) (readSTRef g)
writeSTRef g s'
return a
ar <- newArray n xs
xs' <- forM [1..n] $ \i -> do
j <- randomRST (i,n)
vi <- readArray ar i
vj <- readArray ar j
writeArray ar j vi
return vj
gen' <- readSTRef g
return (xs',gen'))
where
n = length xs
newArray :: Int -> [a] -> ST s (STArray s Int a)
newArray n xs = newListArray (1,n) xs
```

And if you are using IO's hidden StdGen you can wrap this as usual:

```
shuffleIO :: [a] -> IO [a]
shuffleIO xs = getStdRandom (shuffle' xs)
```

This is a lot simpler than the purely functional algorithm linked below.

Here's a variation using the MonadRandom package:

```
import Control.Monad
import Control.Monad.ST
import Control.Monad.Random
import System.Random
import Data.Array.ST
import GHC.Arr
shuffle :: RandomGen g => [a] -> Rand g [a]
shuffle xs = do
let l = length xs
rands <- take l `fmap` getRandomRs (0, l-1)
let ar = runSTArray $ do
ar <- thawSTArray $ listArray (0, l-1) xs
forM_ (zip [0..(l-1)] rands) $ \(i, j) -> do
vi <- readSTArray ar i
vj <- readSTArray ar j
writeSTArray ar j vi
writeSTArray ar i vj
return ar
return (elems ar)
*Main> evalRandIO (shuffle [1..10])
[6,5,1,7,10,4,9,2,8,3]
```

## Other implemenations

### Purely functional

### Drawing without replacement

- uses New_monads/MonadRandom
- allows you to not shuffle the entire list but only part of it (drawing elements without replacement)
- allows you to take multiple drawings/shufflings at once, which can save some array building

```
{- | @grabble xs m n@ is /O(m*n')/, where @n' = min n (length xs)@
Chooses @n@ elements from @xs@, without putting back,
and that @m@ times. -}
grabble :: MonadRandom m => [a] -> Int -> Int -> m [[a]]
grabble xs m n = do
swapss <- replicateM m $ forM [0 .. min (maxIx - 1) n] $ \i -> do
j <- getRandomR (i, maxIx)
return (i, j)
return $ map (take n . swapElems xs) swapss
where
maxIx = length xs - 1
grabbleOnce :: MonadRandom m => [a] -> Int -> m [a]
grabbleOnce xs n = head `liftM` grabble xs 1 n
swapElems :: [a] -> [(Int, Int)] -> [a]
swapElems xs swaps = elems $ runSTArray (do
arr <- newListArray (0, maxIx) xs
mapM_ (swap arr) swaps
return arr)
where
maxIx = length xs - 1
swap arr (i,j) = do
vi <- readArray arr i
vj <- readArray arr j
writeArray arr i vj
writeArray arr j vi
```

So e.g.

```
*Main MonadRandom Random> evalRand (grabble "abcdef" 6 3) (mkStdGen 0)
["fbd","efb","bef","adc","cef","eac"]
*Main MonadRandom Random> grabble "abcdef" 6 3
["fce","dfa","ebf","edb","cea","dbc"]
*Main MonadRandom Random> grabble "abcdef" 6 3
["cbf","dec","edb","fae","bda","cde"]
```