# Random shuffle

### From HaskellWiki

(Difference between revisions)

(Random shuffle algorithm) |
(Add pure version using ST) |
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writeArray ar j vi | writeArray ar j vi | ||

return vj | return vj | ||

+ | </haskell> | ||

+ | |||

+ | Or one can use ST to avoid needing IO: | ||

+ | |||

+ | <haskell> | ||

+ | -- | 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 | ||

+ | </haskell> | ||

+ | |||

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

+ | |||

+ | <haskell> | ||

+ | shuffleIO :: [a] -> IO [a] | ||

+ | shuffleIO xs = getStdRandom (shuffle' xs) | ||

</haskell> | </haskell> | ||

## Revision as of 20:49, 18 October 2007

## 1 The problem

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

## 2 Imperative algorithm

The standard imperative algorithm can be implemented as follows:

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

Or one can use ST to avoid needing IO:

-- | 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.