# Random shuffle

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(Difference between revisions)

(drawing without replacement) |
m (removed need for scoped variables, etc) |

## Revision as of 04:45, 23 October 2008

## Contents |

## 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:

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.

## 3 Other implemenations

### 3.1 Purely functional

### 3.2 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"]