# Haskell Quiz/Maximum Sub-Array/Solution Jkramar

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< Haskell Quiz | Maximum Sub-Array(Difference between revisions)

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[[Category:Haskell Quiz solutions|Maximum Sub-Array]] | [[Category:Haskell Quiz solutions|Maximum Sub-Array]] | ||

− | + | This includes a solution to the "extra credit" problem of finding the maximum subrectangle. | |

<haskell> | <haskell> | ||

− | maxSubArray xs = | + | import Data.List |

+ | |||

+ | maxSubArray' :: (Ord a, Num a) => [a] -> (a, (Int, Int)) | ||

+ | maxSubArray' xs = maximum$zipWith diff sumswithpos$scanl1 min sumswithpos where | ||

sumswithpos = zip (scanl (+) 0 xs) [0..] | sumswithpos = zip (scanl (+) 0 xs) [0..] | ||

− | diff | + | diff (a,ai) (b,bi) = (a-b,(ai,bi)) |

− | (from,to) = | + | |

+ | maxSubArray :: (Ord a, Num a) => [a] -> [a] | ||

+ | maxSubArray xs = drop from$take to xs where (_, (to, from)) = maxSubArray' xs | ||

+ | |||

+ | maxSubRect' :: (Ord a, Num a) => [[a]] -> ((a, (Int, Int)), (Int, Int)) | ||

+ | maxSubRect' as = maximum rectsums where | ||

+ | sums ((c,b):rs) = [(maxSubArray'$zipWith (-) b' b, (c',c))|(c',b') <- rs] | ||

+ | rectsums = concatMap sums$init$tails$zip [0..]$transpose$map (scanl (+) 0) as | ||

+ | |||

+ | maxSubRect :: (Ord a, Num a) => [[a]] -> [[a]] | ||

+ | maxSubRect as = map (drop y1.take y2)$drop x1$take x2 as where | ||

+ | ((_,(x2,x1)),(y2,y1)) = maxSubRect' as | ||

+ | </haskell> | ||

+ | And now with a gratuitous monad, which actually ends up decreasing the type-safety: | ||

+ | <haskell> | ||

+ | import Data.Monoid | ||

+ | import Data.Function (on) | ||

+ | import Data.List | ||

+ | import Control.Applicative | ||

+ | import Control.Monad | ||

+ | import Data.Ord (comparing) | ||

+ | |||

+ | data TakeNote n a = TakeNote !n !a deriving (Show, Read) | ||

+ | note (TakeNote n _) = n | ||

+ | dropNote (TakeNote _ a) = a | ||

+ | instance (Eq a) => Eq (TakeNote n a) where (==) = (==) `on` dropNote | ||

+ | instance (Ord a) => Ord (TakeNote n a) where compare = comparing dropNote | ||

+ | instance (Monoid n) => Monad (TakeNote n) where | ||

+ | return = TakeNote mempty | ||

+ | TakeNote n a >>= f = TakeNote (mappend n m) b where TakeNote m b = f a | ||

+ | instance Functor (TakeNote n) where fmap f (TakeNote n a) = TakeNote n$f a | ||

+ | instance (Monoid n) => Applicative (TakeNote n) where pure = return; (<*>) = ap | ||

+ | |||

+ | number :: [a] -> [TakeNote [Int] a] | ||

+ | number = zipWith TakeNote (pure<$>[0..]) | ||

+ | |||

+ | psum :: (Num a) => [a] -> [a] | ||

+ | psum = scanl (+) 0 | ||

+ | |||

+ | maxSubArray' :: (Ord a, Num a) => [a] -> TakeNote [Int] a | ||

+ | maxSubArray' xs = maximum$zipWith (liftA2 (-)) psums$scanl1 min psums where | ||

+ | psums = number$psum xs | ||

+ | |||

+ | maxSubArray' :: (Ord a, Num a) => [a] -> [a] | ||

+ | maxSubArray xs = drop from$take to xs where [to, from] = note$maxSubArray' xs | ||

+ | |||

+ | maxSubRect' :: (Ord a, Num a) => [[a]] -> TakeNote [Int] a | ||

+ | maxSubRect' as = maximum$concatMap sums$tails$number$transpose$psum<$>as where | ||

+ | sums (r:rs) = [maxSubArray'=<<liftA2 (zipWith (-)) r' r|r'<-rs]; sums [] = [] | ||

+ | |||

+ | maxSubRect :: (Ord a, Num a) => [[a]] -> [[a]] | ||

+ | maxSubRect as = map (drop y1.take y2)$drop x1$take x2 as where | ||

+ | [y2,y1,x2,x1] = note$maxSubRect' as | ||

</haskell> | </haskell> |

## Latest revision as of 18:47, 21 February 2010

This includes a solution to the "extra credit" problem of finding the maximum subrectangle.

import Data.List maxSubArray' :: (Ord a, Num a) => [a] -> (a, (Int, Int)) maxSubArray' xs = maximum$zipWith diff sumswithpos$scanl1 min sumswithpos where sumswithpos = zip (scanl (+) 0 xs) [0..] diff (a,ai) (b,bi) = (a-b,(ai,bi)) maxSubArray :: (Ord a, Num a) => [a] -> [a] maxSubArray xs = drop from$take to xs where (_, (to, from)) = maxSubArray' xs maxSubRect' :: (Ord a, Num a) => [[a]] -> ((a, (Int, Int)), (Int, Int)) maxSubRect' as = maximum rectsums where sums ((c,b):rs) = [(maxSubArray'$zipWith (-) b' b, (c',c))|(c',b') <- rs] rectsums = concatMap sums$init$tails$zip [0..]$transpose$map (scanl (+) 0) as maxSubRect :: (Ord a, Num a) => [[a]] -> [[a]] maxSubRect as = map (drop y1.take y2)$drop x1$take x2 as where ((_,(x2,x1)),(y2,y1)) = maxSubRect' as

And now with a gratuitous monad, which actually ends up decreasing the type-safety:

import Data.Monoid import Data.Function (on) import Data.List import Control.Applicative import Control.Monad import Data.Ord (comparing) data TakeNote n a = TakeNote !n !a deriving (Show, Read) note (TakeNote n _) = n dropNote (TakeNote _ a) = a instance (Eq a) => Eq (TakeNote n a) where (==) = (==) `on` dropNote instance (Ord a) => Ord (TakeNote n a) where compare = comparing dropNote instance (Monoid n) => Monad (TakeNote n) where return = TakeNote mempty TakeNote n a >>= f = TakeNote (mappend n m) b where TakeNote m b = f a instance Functor (TakeNote n) where fmap f (TakeNote n a) = TakeNote n$f a instance (Monoid n) => Applicative (TakeNote n) where pure = return; (<*>) = ap number :: [a] -> [TakeNote [Int] a] number = zipWith TakeNote (pure<$>[0..]) psum :: (Num a) => [a] -> [a] psum = scanl (+) 0 maxSubArray' :: (Ord a, Num a) => [a] -> TakeNote [Int] a maxSubArray' xs = maximum$zipWith (liftA2 (-)) psums$scanl1 min psums where psums = number$psum xs maxSubArray' :: (Ord a, Num a) => [a] -> [a] maxSubArray xs = drop from$take to xs where [to, from] = note$maxSubArray' xs maxSubRect' :: (Ord a, Num a) => [[a]] -> TakeNote [Int] a maxSubRect' as = maximum$concatMap sums$tails$number$transpose$psum<$>as where sums (r:rs) = [maxSubArray'=<<liftA2 (zipWith (-)) r' r|r'<-rs]; sums [] = [] maxSubRect :: (Ord a, Num a) => [[a]] -> [[a]] maxSubRect as = map (drop y1.take y2)$drop x1$take x2 as where [y2,y1,x2,x1] = note$maxSubRect' as