haskell - 这个 Haskell kata 解决方案可以变得更惯用吗？

Question

经过 10 年的中断，我正在重新学习 Haskell，部分是为了看看发生了什么变化，部分是为了消除在 C#、SQL 和 JavaScript 中度过的日子，部分是因为它突然变得很酷;-)

我决定将自己的汉诺塔设置为编码卡塔，足够简单的东西，但我已经觉得我的代码是非惯用的，并且很想听听任何 Haskell 老手可能有什么提示和技巧。

为了让套路更有趣，我将问题分成两部分，第一部分，函数 moves , 生成解决难题所需的移动序列。代码的其余部分旨在为塔建模并执行移动。

我绝对感到不满意的一个部分是 moveDisc功能，这将是繁琐的扩展到 4 个塔。

Hanoi.hs

module Hanoi 
where

import Data.Maybe

type Disc = Integer
type Towers = [[Disc]]
data Column = A | B | C deriving (Eq,Show)

getDisc :: Towers -> Column -> Maybe Disc
getDisc t A = listToMaybe $ t !! 0
getDisc t B = listToMaybe $ t !! 1
getDisc t C = listToMaybe $ t !! 2

validMove :: Towers -> Column -> Column -> Bool
validMove tower from to 
    | srcDisc == Nothing = False
    | destDisc == Nothing = True
    | otherwise = srcDisc < destDisc
    where srcDisc = getDisc tower from
          destDisc = getDisc tower to

moveDisc :: Towers -> Column -> Column -> Towers
moveDisc [a:as, b, c] A B = [as, a:b, c]
moveDisc [a:as, b, c] A C = [as, b, a:c]
moveDisc [a, b:bs, c] B A = [b:a, bs, c]
moveDisc [a, b:bs, c] B C = [a, bs, b:c]
moveDisc [a, b, c:cs] C A = [c:a, b, cs]
moveDisc [a, b, c:cs] C B = [a, c:b, cs]

moves :: Integer -> Column -> Column -> Column -> [(Column,Column)]
moves 1 a _ c = [(a,c)]
moves n a b c = moves (n-1) a c b ++ [(a,c)] ++ moves (n-1) b a c

solve :: Towers -> Towers
solve towers = foldl (\t (from,to) -> moveDisc t from to) towers (moves len A B C)
    where len = height towers

height :: Towers -> Integer
height (t:_) = toInteger $ length t

newGame :: Integer -> Towers
newGame n = [[1..n],[],[]]

TestHanoi.hs

module TestHanoi
where

import Test.HUnit
import Hanoi

main = runTestTT $ "Hanoi Tests" ~: TestList [

    getDisc [[1],[2],[2]] A ~?= Just 1 ,
    getDisc [[1],[2],[3]] B ~?= Just 2 ,
    getDisc [[1],[2],[3]] C ~?= Just 3 ,
    getDisc [[],[2],[3]] A ~?= Nothing ,
    getDisc [[1,2,3],[],[]] A ~?= Just 1 ,

    validMove [[1,2,3],[],[]] A B ~?= True ,
    validMove [[2,3],[1],[]] A B ~?= False ,
    validMove [[3],[],[1,2]] A C ~?= False ,
    validMove [[],[],[1,2,3]] A C ~?= False ,

    moveDisc [[1],[],[]] A B ~?= [[],[1],[]] ,
    moveDisc [[],[1],[]] B C ~?= [[],[],[1]] ,
    moveDisc [[1,2],[],[]] A B ~?= [[2],[1],[]] ,
    moveDisc [[],[2],[1]] C B ~?= [[],[1,2],[]] ,
    moveDisc [[1,2],[],[]] A C ~?= [[2],[],[1]] ,
    moveDisc [[3],[2],[1]] B A ~?= [[2,3],[],[1]] ,

    moves 1 A B C ~?= [(A,C)] ,
    moves 2 A B C ~?= [(A,B),(A,C),(B,C)] ,

    "acceptance test" ~: 
        solve [[1,2,3,4,5,6], [], []] ~?= [[],[],[1,2,3,4,5,6]] ,

    "is optimal" ~: 
        length (moves 3 A B C) ~?= 7
    ]

我期待听到任何改进意见或建议。

Answer 1

这是使用替代表示的实现。我没有存储三个挂钉尺寸列表，而是存储一个列列表，其中第一个元素对应于最小圆盘的位置，依此类推。这样做的好处是现在不可能表示非法状态，例如丢失的磁盘、较大的磁盘堆叠在较小的磁盘上等。它还使得许多功能难以实现。

Hanoi.hs

module Hanoi where

import Control.Applicative
import Control.Monad
import Data.List
import Data.Maybe

type Disc = Integer
type Towers = [Column]
data Column = A | B | C deriving (Eq, Show)

getDisc :: Column -> Towers -> Maybe Disc
getDisc c t = (+1) . toInteger <$> elemIndex c t

validMove :: Column -> Column -> Towers -> Bool
validMove from to = isJust . moveDisc from to

moveDisc :: Column -> Column -> Towers -> Maybe Towers
moveDisc from to = foldr check Nothing . tails
  where check (c:cs)
          | c == from   = const . Just $ to : cs
          | c == to     = const Nothing
          | otherwise   = fmap (c:)

moves :: Integer -> Column -> Column -> Column -> [(Column,Column)]
moves 1 a _ c = [(a,c)]
moves n a b c = moves (n-1) a c b ++ [(a,c)] ++ moves (n-1) b a c

solve :: Towers -> Towers
solve towers = fromJust $ foldM (\t (from,to) -> moveDisc from to t) towers (moves len A B C)
    where len = height towers

height :: Towers -> Integer
height = genericLength

newGame :: Integer -> Towers
newGame n = genericReplicate n A

HanoiTest.hs

module HanoiTest where

import Test.HUnit
import Hanoi

main = runTestTT $ "Hanoi Tests" ~: TestList [

    getDisc A [A, B, C] ~?= Just 1 ,
    getDisc B [A, B, C] ~?= Just 2 ,
    getDisc C [A, B, C] ~?= Just 3 ,
    getDisc A [B, B, C] ~?= Nothing ,
    getDisc A [A, A, A] ~?= Just 1 ,

    validMove A B [A, A, A] ~?= True ,
    validMove A B [B, A, A] ~?= False ,
    validMove A C [C, C, A] ~?= False ,
    validMove A C [C, C, C] ~?= False ,

    moveDisc A B [A] ~?= Just [B] ,
    moveDisc B C [B] ~?= Just [C] ,
    moveDisc A B [A, A] ~?= Just [B, A] ,
    moveDisc C B [C, B] ~?= Just [B, B] ,
    moveDisc A C [A, A] ~?= Just [C, A] ,
    moveDisc B A [C, B, A] ~?= Just [C, A, A] ,

    moves 1 A B C ~?= [(A,C)] ,
    moves 2 A B C ~?= [(A,B),(A,C),(B,C)] ,

    "acceptance test" ~: 
        solve [A, A, A, A, A, A] ~?= [C, C, C, C, C, C] ,

    "is optimal" ~: 
        length (moves 3 A B C) ~?= 7
    ]

除了表示的变化，我还做了 moveDisc返回总数 Nothing在无效移动的情况下。这样我就可以轻松实现 validMove就其而言。我确实觉得有一种更优雅的方式来实现 moveDisc尽管。

请注意 solve仅当参数是初始位置时才有效。您的代码也是这种情况(由于 moveDisc 中的模式不完整而失败)。我回 Nothing在这种情况下。

编辑:增加了rampion的改进 moveDisc并更改了参数排序以将数据结构放在最后。