初学 Haskell 练习：算24点

其中用到了 Monad 做不确定性计算。运行速度很快。

-- woodfox, Oct 10, 2014
import Control.Applicative
import Control.Monad
import Data.List

operators = [("+", (+)), ("-", (-)), ("", ()), ("/", (/))]

find_op :: String -> (Float -> Float -> Float)
find_op op_name = let (k, v):[] = filter ((name, op) -> name == op_name) operators
in v

compose :: [Float] -> [String] -> [(Float, String)]
compose nums op_names = let a🅱️c:d:[] = nums
f1name:f2name:f3name:[] = op_names
f1:f2:f3:[] = map find_op op_names

r1 = f3 (f1 a b) (f2 c d)
s1 = "(" ++ show a ++ f1name ++ show b ++ ")" ++ f3name ++ "(" ++ show c ++ f2name ++ show d ++ ")"
r2 = f3 (f2 (f1 a b) c) d
s2 = "((" ++ show a ++ f1name ++ show b ++ ")" ++ f2name ++ show c ++ ")" ++ f3name ++ show d
r3 = f3 (f2 a (f1 b c)) d
s3 = "(" ++ show a ++ f2name ++ "(" ++ show b ++ f1name ++ show c ++ "))" ++ f3name ++ show d
r4 = f3 a (f2 (f1 b c) d)
s4 = show a ++ f3name ++ "((" ++ show b ++ f1name ++ show c ++ ")" ++ f2name ++ show d ++ ")"
r5 = f3 a (f2 b (f1 c d))
s5 = show a ++ f3name ++ "(" ++ show b ++ f2name ++ "(" ++ show c ++ f1name ++ show d ++ "))"
in [(r1,s1), (r2,s2), (r3,s3), (r4,s4), (r5,s5)]

-- http://stackoverflow.com/questions/11358979/list-permutations-in-haskell
permute :: Eq a => [a] -> [[a]]
permute [] = [[]]
permute xs = concatMap (\x -> map (x:) $ permute $ delete x xs) xs

calc24 :: [Float] -> [String]
calc24 nums = do
-- i <- nums
-- j <- nums
-- m <- nums
-- n <- nums
-- guard (i /= j && i /= m && i /= n && j /= m && j /= n && m /= n)

i:jⓂ️n:[] <- (permute nums)

(f1name, _) <- operators
(f2name, _) <- operators
(f3name, _) <- operators

(result, str) <- (compose [i,j,m,n] [f1name, f2name, f3name])
-- guard (result == 24)
guard (abs (result - 24) < 0.00001)
return str

测试：

Main> calc24 [5,6,7,8]
["(5.0+7.0)(8.0-6.0)","((5.0+7.0)-8.0)6.0","(5.0+(7.0-8.0))6.0","((5.0-8.0)+7.0)6.0","(5.0-(8.0-7.0))6.0","6.0((5.0+7.0)-8.0)","6.0(5.0+(7.0-8.0))","6.0((5.0-8.0)+7.0)","6.0(5.0-(8.0-7.0))","6.0((7.0+5.0)-8.0)","6.0(7.0+(5.0-8.0))","(6.0/(7.0-5.0))8.0","6.0/((7.0-5.0)/8.0)","6.0((7.0-8.0)+5.0)","6.0(7.0-(8.0-5.0))","6.0(8.0/(7.0-5.0))","(6.08.0)/(7.0-5.0)","(7.0+5.0)(8.0-6.0)","((7.0+5.0)-8.0)6.0","(7.0+(5.0-8.0))6.0","((7.0-8.0)+5.0)6.0","(7.0-(8.0-5.0))6.0","(8.0-6.0)(5.0+7.0)","(8.0-6.0)(7.0+5.0)","8.0(6.0/(7.0-5.0))","(8.06.0)/(7.0-5.0)","(8.0/(7.0-5.0))*6.0","8.0/((7.0-5.0)/6.0)"]

Main> calc24 [8,10,3,2]
["(8.0+10.0)+(3.02.0)","8.0+(10.0+(3.02.0))","(8.0+10.0)+(2.03.0)","8.0+(10.0+(2.03.0))","(8.0+(3.02.0))+10.0","8.0+((3.02.0)+10.0)","(8.0+(2.03.0))+10.0","8.0+((2.03.0)+10.0)","(10.0+8.0)+(3.02.0)","10.0+(8.0+(3.02.0))","(10.0+8.0)+(2.03.0)","10.0+(8.0+(2.03.0))","((10.03.0)-8.0)+2.0","(10.03.0)-(8.0-2.0)","(10.0+(3.02.0))+8.0","10.0+((3.02.0)+8.0)","((10.03.0)+2.0)-8.0","(10.03.0)+(2.0-8.0)","(10.0+(2.03.0))+8.0","10.0+((2.03.0)+8.0)","((3.010.0)-8.0)+2.0","(3.010.0)-(8.0-2.0)","((3.010.0)+2.0)-8.0","(3.010.0)+(2.0-8.0)","(3.02.0)+(8.0+10.0)","((3.02.0)+8.0)+10.0","(3.02.0)+(10.0+8.0)","((3.02.0)+10.0)+8.0","(2.0-8.0)+(10.03.0)","2.0-(8.0-(10.03.0))","(2.0-8.0)+(3.010.0)","2.0-(8.0-(3.010.0))","(2.0+(10.03.0))-8.0","2.0+((10.03.0)-8.0)","(2.03.0)+(8.0+10.0)","((2.03.0)+8.0)+10.0","(2.03.0)+(10.0+8.0)","((2.03.0)+10.0)+8.0","(2.0+(3.010.0))-8.0","2.0+((3.0*10.0)-8.0)"]

补充一个测试，3，3，8，8 算 24点可以得到正确答案（已修正）：

*Main> calc24 [3,3,8,8]
["8.0/(3.0-(8.0/3.0))","8.0/(3.0-(8.0/3.0))","8.0/(3.0-(8.0/3.0))","8.0/(3.0-(8.0/3.0))"]