用 Haskell 的 list comprehension 來解某數學愛好者社團的某題目 (https://www.facebook.com/photo.php?fbid=2475098332534617)

README.md

用 Haskell 的 list comprehension 來解某數學愛好者社團的某題目。

執行結果

$ ghc -o solution solution.hs && ./solution
[[D,A,D,B,B,D,C,C,D,C]]

有段時間沒寫 Haskell 了所以寫法可能很糟。

solution.hs

data Answer = A | B | C | D deriving (Eq, Show)

solution :: [[Answer]]
solution =
  [ all_answers
  | let possible_answers = [A, B, C, D]
  , a01 <- possible_answers
  , a02 <- possible_answers
  , a03 <- possible_answers
  , a04 <- possible_answers
  , a05 <- possible_answers
  , a06 <- possible_answers
  , a07 <- possible_answers
  , a08 <- possible_answers
  , a09 <- possible_answers
  , a10 <- possible_answers
  , let all_answers = [a01, a02, a03, a04, a05, a06, a07, a08, a09, a10]
  -- Condition 1
  , length (filter (== A) all_answers) == 1
  , length (filter (== B) all_answers) == 2
  , length (filter (== C) all_answers) == 3
  , length (filter (== D) all_answers) == 4
  -- Condition 2
  , a02 /= a04
  , a02 /= a06
  , a02 /= a08
  , a04 /= a06
  , a04 /= a08
  , a06 /= a08
  -- Condition 3
  , a03 == a06
  -- Condition 4
  , (length (filter (== a06) all_answers))
    > (length (filter (== a08) all_answers))
  -- Condition 5
  , a05 == a04
  -- Condition 6
  , a06 == a09
  -- Condition 7: 這個條件跟條件一等價，故不列出
  -- Condition 8: 這題不構成任何制約條件
  -- Condition 9
  , a09 /= a02
  , a09 /= a05
  , a09 /= a07
  -- 「當初出題者對於第 9 題的確是希望只有一個答案，即是第 2、5、7 題三項均不同」故增加以下三行
  , a02 /= a05
  , a02 /= a07
  , a05 /= a07
  -- Condition 10
  , a10 == a08
  ]

main :: IO ()
main = print solution