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Haskell Quiz/Numeric Maze/Solution Ninju

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I haven't yet added any optimization, because I wanted to keep the program as simple (and therefore readable) as possible, but I might add some later.
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[[Category:Haskell Quiz solutions|Numeric Maze]]
   
 
<haskell>
 
<haskell>
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import System.Environment
 
import System.Environment
 
import Data.List
 
import Data.List
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  +
data Operator = AddTwo | Double | Halve
   
 
main :: IO ()
 
main :: IO ()
 
main = do args <- getArgs
 
main = do args <- getArgs
if length args == 2
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if length args == 2
then do let [a,b] = map read args
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then let [a,b] = map read args
putStrLn $ show (solve a b)
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in print $ solve a b
 
else putStrLn "Usage: solve START TARGET"
 
else putStrLn "Usage: solve START TARGET"
return ()
 
 
data Operation = AddTwo Integer | Double Integer | Halve Integer
 
   
valid :: Operation -> Bool
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apply :: Operator -> Integer -> Integer
valid (Halve x) = x `mod` 2 == 0
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apply AddTwo x = x + 2
valid _ = True
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apply Double x = x * 2
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apply Halve x = x `div` 2
   
apply :: Operation -> Integer
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valid :: Operator -> Integer -> Bool
apply (AddTwo x) = x + 2
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valid Halve x = even x
apply (Double x) = x * 2
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valid _ _ = True
apply (Halve x) = x `div` 2
 
   
 
solve :: Integer -> Integer -> [Integer]
 
solve :: Integer -> Integer -> [Integer]
solve a b = solve' [[a]] b
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solve a b = solve' [[a]] b [a]
where
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solve' paths target = case find ((== target) . last) paths of
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solve' :: [[Integer]] -> Integer -> [Integer] -> [Integer]
Just path -> path
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solve' paths target seen = case find ((== target) . last) paths of
Nothing -> solve' (concatMap buildPathsFrom paths) target
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Just path -> path
buildPathsFrom path = [ path ++ [apply (op (last path))] | op <- [AddTwo, Double, Halve], valid (op (last path)) ]
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Nothing -> let newPaths = filter ((`notElem` seen) . last) $ concatMap buildPathsFrom paths
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newSeen = seen ++ map last newPaths
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in solve' newPaths target newSeen
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buildPathsFrom :: [Integer] -> [[Integer]]
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buildPathsFrom path = let n = last path
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in [ path ++ [ apply operator n ] | operator <- [AddTwo, Double, Halve], valid operator n ]
 
</haskell>
 
</haskell>

Latest revision as of 08:23, 27 November 2009


module Main where
import System.Environment
import Data.List
 
data Operator = AddTwo | Double | Halve
 
main :: IO ()
main = do args <- getArgs
          if length args == 2
            then let [a,b] = map read args
                 in print $ solve a b 
            else putStrLn "Usage: solve START TARGET"
 
apply :: Operator -> Integer -> Integer 
apply AddTwo x = x + 2 
apply Double x = x * 2 
apply Halve x = x `div` 2
 
valid :: Operator -> Integer -> Bool 
valid Halve x = even x
valid _ _ = True
 
solve :: Integer -> Integer -> [Integer]
solve a b = solve' [[a]] b [a] 
 
solve' :: [[Integer]] -> Integer -> [Integer] -> [Integer]
solve' paths target seen =  case find ((== target) . last) paths of
                                Just path -> path
                                Nothing -> let newPaths = filter ((`notElem` seen) . last) $ concatMap buildPathsFrom paths
                                               newSeen = seen ++ map last newPaths
                                           in solve' newPaths target newSeen
 
 
buildPathsFrom :: [Integer] -> [[Integer]] 
buildPathsFrom path = let n = last path
                      in [ path ++ [ apply operator n ] | operator <- [AddTwo, Double, Halve], valid operator n ]