如何在 Haskell 中创建函数 minimax？答案

【问题标题】：How to create function minimax in Haskell?如何在 Haskell 中创建函数 minimax？
【发布时间】：2018-09-28 17:24:12
【问题描述】：

我一直在努力在 Haskell 中创建一个极小极大函数，但在 SO 上找不到任何好的替代方案，因此我问：

我想创建以下函数：

minimax :: Player -> Rose Board -> Rose Int

我想要一棵整数玫瑰树，它们必须是 1、0 或 -1（对于轮到的玩家来说，移动可以是好的、中性的或坏的。

(root :> leaves)               -- constructor of a Rose
(board :> boards)              -- constructor of a Rose Board
(Int :> Ints)                  -- constructor of a Rose Int

我写了函数 hasWinner, minimum' 和 maximum' 让事情变得更容易：

hasWinner :: Board -> Maybe Player

minimum' :: [Int] -> Int
minimum' (x:xs) | x == -1 = -1
                | otherwise = minimum' xs

maximum' :: [Int] -> Int
maximum' (x:xs) | x == 1 = 1
                | otherwise = maximum' xs

此外，我认为我的基本情况如下：

minimax player (board :> []) = (0 :> [])

目前这是我所在的位置：

minimax player (board :> boards)| maximum' [(isWinner player b (minimax' player)) | (b :> bs) <- boards] == 1 = _
                                | minimum' [(isWinner player b (minimax' player)) | (b :> bs) <- boards] == -1 = _
                                | otherwise = _
                 where   minimax' player     | player == P1 = P2
                                             | otherwise = P1
                         isWinner p1 board p2    | hasWinner board == Just p1 = 1
                                                 | hasWinner board == Just p2 = -1
                                                 | otherwise = 0

我似乎无法弄清楚当我找到一个赢了、输了或没有任何后果的棋盘时会发生什么。那么如何使用正确的 Rose Board 再次调用 minimax 函数呢？

非常感谢任何帮助！

拉蒙

【问题讨论】：

标签： haskell minimax

【解决方案1】：

我实际上发现了另一篇讨论我在这里遇到的同样问题的帖子：Haskell Recursive Minimax Tree

答案如下：

minimax :: Player -> Rose Board -> Rose Int
minimax p (r :> [])   | hasWinner r == Just P1 = 1    :> []
                      | hasWinner r == Just P2 = (-1) :> []
                      | otherwise              = 0    :> []
minimax P1 (r :> rs) = maximum (map root xs) :> xs
    where xs = map (minimax (nextPlayer P1)) rs

minimax P2 (r :> rs) = minimum (map root xs) :> xs
    where xs = map (minimax (nextPlayer P2)) rs

我希望这至少可以在将来对其他人有所帮助。此答案中使用的功能是：

root :: Rose a -> a
root (a :> bs) = a 

nextPlayer :: Player -> Player
nextPlayer P1 = P2
nextPlayer P2 = P1

hasWinner :: Board -> Maybe Player

minimum :: Ord a => [a] -> a
maximum :: Ord a => [a] -> a

干杯！

【讨论】：