Haskell中的纯Knuth / Fisher-Yates混洗

Question

在执行过程中，我可以编写如下函数：

func pureFisherYates(s []int, swaps []int) []int {
    newS := copy(s)
    for i, _ := range newS {
            for _, j := range swaps {
                    newS[i], newS[j] = newS[j], newS[i]
            }
    }
}

对我来说，这似乎是一个纯粹的功能。在给定相同输入的情况下，它总是返回相同的输出，并且不会改变世界的状态（严格意义上讲，它与其他任何函数都一样，占用cpu资源，产生热能，等等）。然而，每当我寻找如何进行纯随机转换时，我都会发现类似这样的东西，每当我寻找特定的Haskell实现Fisher-Yates时，我就可以0^2使用列表或[a] -> IO [a]实现来实现Fisher-Yates 。是否存在[a] -> [a] O(n)改组，如果没有，我的上述实现为何不正确。

Answer 1

该ST单子允许正是这样封装的可变性，以及Data.Array.ST包含能够在被突变阵列ST，然后一个不可变的版本返回外部。

https://wiki.haskell.org/Random_shuffle使用给出了两种Fisher-Yates混编的实现ST。它们不是字面上的[a] -> [a]，而是因为还需要处理随机数的生成：

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

和

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 <- forM [0..(l-2)] $ \i -> getRandomR (i, l-1)
    let ar = runSTArray $ do
        ar <- thawSTArray $ listArray (0, l-1) xs
        forM_ (zip [0..] 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]

编辑：与swaps您的Go代码中的参数一样，该代码非常简单

{-# LANGUAGE ScopedTypeVariables #-}

import Data.Array.ST
import Data.Foldable
import Control.Monad.ST

shuffle :: forall a. [a] -> [Int] -> [a]
shuffle xs swaps = runST $ do
    let n = length xs
    ar <- newListArray (1,n) xs :: ST s (STArray s Int a)
    for_ [1..n] $ \i ->
        for_ swaps $ \j -> do
            vi <- readArray ar i
            vj <- readArray ar j
            writeArray ar j vi
            writeArray ar i vj
    getElems ar

但我不确定您是否可以合理地称其为Fisher-Yates洗牌。