Random shuffle

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:

{-# 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

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

Other implemenations

• Purely functional O(n log n) random shuffle algorithm.