DouKaku? 4742 shiro: ナイーブに全探索。 opparse...(小町算)

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ナイーブに全探索。

opparseで演算子順位文法を使って式をRPNに変換し、calcで計算してます。

opsの定義を変えれば演算子を増やしたり優先順位を買えたりできます。同じ優先度の演算子は左結合。

import Numeric

data Item a b = Value a | Op (a->a->a) b [Char]

cat a b = a*10+b

ops :: [Item Double Integer]
ops = [Op cat 2 "", Op (+) 0 "+", Op (-) 0 "-", Op (*) 1 "*", Op (/) 1 "/"]
 
opparse [] _ vs = reverse vs
opparse (op:ops) (i:is) vs = opparse ops is $ push op (Value i) vs

push op@(Op o p _) v (op'@(Op o' p' _):vs)
  | (p <= p') = (op:v:op':vs)
  | otherwise = (op':push op v vs)
push op v vs = op:v:vs

calc [a] [] = a
calc ns ((Value a):vs) = calc (a:ns) vs
calc (a:b:ns) ((Op op _ _):vs) = calc ((op b a):ns) vs
calc _ _ = error "invalid stack state"

showFormula ops = "1" ++ rec [2..] ops where
   rec _ [] = ""
   rec (i:is) ((Op _ _ n):ops) = n ++ (showInt . round) i (rec is ops)

genops 0 = [[]]
genops n = [o:os | o <- map (ops!!) [0..4], os <- genops (n-1)]

komachi n = [ops | ops <- genops n, test 100 ops] where
   test sum ops = abs (sum - (calc [] $ opparse ops [2..] [Value 1])) <= 1.0e-10

main = putStr $ unlines $ map showFormula $ komachi 8

高階関数と有理数を使って書き直してみました。
一部私好みに書き換えています。

import Ratio

data Item a b c = Value a | Op (b->b->b) c String

cat a b = a*10+b

ops :: [Item Integer Rational Integer]
ops = [Op cat 2 "", Op (+) 0 "+", Op (-) 0 "-", Op (*) 1 "*", Op (/) 1 "/"]

opparse ops = reverse $ foldl push [Value 1] (zip ops $ map Value [2..])

push (op'@(Op o' p' _):vs) opv@(op@(Op o p _), v)
  | p <= p' = op:v:op':vs
  | otherwise = op':push vs opv
push vs (op, v) = op:v:vs

calc vs = head $ foldl g [] vs where
  g ns (Value a) = a%1:ns
  g (a:b:ns) (Op op _ _) = op b a:ns
  g _ _ = error "invalid stack state"

showFormula ops = concat $ ["1"] ++ zipWith (\(Op _ _ n) i -> n ++ show i) ops [2..]

genops n = sequence $ replicate n ops

komachi n = filter (test 100) $ genops n where
   test sum ops = sum == (calc $ opparse ops)

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