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-- Ex. 1

insertall :: a -> [a] -> [[a]]
insertall a bs = insertnext a [] bs

insertnext :: a -> [a] -> [a] -> [[a]]
insertnext a pre []       = [(pre ++ [a])]
insertnext a pre (p:post) = (pre ++ [a] ++ (p:post)):
                            (insertnext a (pre ++ [p]) post)

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-- Ex. 2

transpose :: [[a]] -> [[a]]
transpose ([]:_) = []
transpose as     = (map head as):(transpose (map tail as))

mult :: (Num a) => [[a]] -> [[a]] -> [[a]]
mult as bs = let ts = transpose bs
             in map (inject ts) as

inject :: (Num a) => [[a]] -> [a] -> [a]
inject bs a = [sum (vectorprod a b) | b <- bs ]

vectorprod :: (Num a) => [a] -> [a] -> [a]
vectorprod [] [] = []
vectorprod (a:as) (b:bs) = (a*b):(vectorprod as bs)


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-- Ex. 3

riffle :: [Int] -> [Int]
riffle as = myzip evens odds where
    evens = filter even as
    odds  = filter odd as

myzip :: [a] -> [a] -> [a]
myzip as [] = []
myzip [] bs = []
myzip (a:as) (b:bs) = a:b:(myzip as bs)

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-- Ex. 4

sortit :: [Int] -> [Int]
sortit [] = []
sortit as = [a | a <- as, a == m] ++ sortit [a | a <- as, a /= m] where
    m = minimum as

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