p93.hs

module P93 where

data Expr = Operator Op
          | Value Rational
          deriving (Show, Eq)

data Op = Plus | Minus | Mul | Div deriving (Show, Eq, Enum, Bounded)

puzzle nums = [s1 ++ " = " ++ s2
               | (p1, p2) <- split nums
               , (s1,v1) <- genEq1 p1 Nothing
               , (s2, v2) <- genEq1 p2 Nothing,
               v1 == v2]

split :: [Rational] -> [([Rational], [Rational])]
split nums = [(take n nums, drop n nums) | n <- [1 .. length nums - 1]]

genEq1 :: [Rational] -> Maybe Op -> [(String, Rational)]
genEq1 [] _ = error "Cannot operate on empty list"
genEq1 [n] _ = [(showValue n, n)]
genEq1 ns parentOp = [
    (wrap parentOp op $ s1 ++ showOp op ++ s2, applyOp op v1 v2)
    | (p1, p2) <- split ns
    , op <- [Plus .. Div]
    , (s1, v1) <- genEq1 p1 (Just op)
    , (s2, v2) <- genEq1 p2 (Just op)
    ]

wrap :: Maybe Op -> Op -> String -> String
wrap Nothing _ s = s
wrap (Just Plus) _ s = s
wrap (Just Minus) Mul s = s
wrap (Just Minus) Div s = s
wrap (Just Mul) Mul s = s
wrap _ _ s = wrap' s
wrap' s = "(" ++ s ++ ")"

applyOp Plus = (+)
applyOp Minus = (-)
applyOp Mul = (*)
applyOp Div = (/)

showOp Plus = "+"
showOp Minus = "-"
showOp Mul = "*"
showOp Div = "/"


showValue :: Rational -> String
showValue v = if toRational truncated == v
              then show truncated
              else show $ fromRational v
  where truncated = ceiling $ fromRational v