Divisibles por el primero

PorJosé A. Alonso 30-octubre-201427-diciembre-2014

Enunciado

-- Definir la función
--    divisiblesPorPrimero :: [Int] -> Bool
-- tal que (divisibles xs) se verifica si todos los elementos positivos
-- de xs son divisibles por el primero. Por ejemplo,
--    divisiblesPorPrimero [2,6,-3,0,18,-17,10]  ==  True
--    divisiblesPorPrimero [-13]                 ==  True
--    divisiblesPorPrimero [-3,6,1,-3,9,18]      ==  False
--    divisiblesPorPrimero [5,-2,-6,3]           ==  False
--    divisiblesPorPrimero []                    ==  False
--    divisiblesPorPrimero [0,2,4]               ==  False

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-- Definir la función

-- divisiblesPorPrimero :: [Int] -> Bool

-- tal que (divisibles xs) se verifica si todos los elementos positivos

-- de xs son divisibles por el primero. Por ejemplo,

-- divisiblesPorPrimero [2,6,-3,0,18,-17,10] == True

-- divisiblesPorPrimero [-13] == True

-- divisiblesPorPrimero [-3,6,1,-3,9,18] == False

-- divisiblesPorPrimero [5,-2,-6,3] == False

-- divisiblesPorPrimero [] == False

-- divisiblesPorPrimero [0,2,4] == False

Soluciones

-- 1ª definición (por comprensión)
divisiblesPorPrimero1 :: [Int] -> Bool
divisiblesPorPrimero1 []     = False
divisiblesPorPrimero1 (0:_)  = False
divisiblesPorPrimero1 (x:xs) = and [y `rem` x == 0 | y <- xs, y > 0]

-- 2ª definición (por recursión)
divisiblesPorPrimero2 :: [Int] -> Bool
divisiblesPorPrimero2 []     = False
divisiblesPorPrimero2 (0:_)  = False
divisiblesPorPrimero2 (x:xs) = aux xs
    where aux [] = True
          aux (y:ys) | y > 0     = y `rem` x == 0 && aux ys
                     | otherwise = aux ys

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-- 1ª definición (por comprensión)

divisiblesPorPrimero1 :: [Int] -> Bool

divisiblesPorPrimero1 [] = False

divisiblesPorPrimero1 (0:_) = False

divisiblesPorPrimero1 (x:xs) = and [y `rem` x == 0 | y <- xs, y > 0]

-- 2ª definición (por recursión)

divisiblesPorPrimero2 :: [Int] -> Bool

divisiblesPorPrimero2 [] = False

divisiblesPorPrimero2 (0:_) = False

divisiblesPorPrimero2 (x:xs) = aux xs

where aux [] = True

aux (y:ys) | y > 0 = y `rem` x == 0 && aux ys

| otherwise = aux ys

8 Comentarios

divisiblesPorPrimero [] = False
divisiblesPorPrimero (x:xs) 
    | x /= 0 = and [rem (y) (x) == 0 | y <- (filter (>0) xs)]
    | x == 0 = False

primero (x:xs) = x

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divisiblesPorPrimero [] = False

divisiblesPorPrimero (x:xs)

| x /= 0 = and [rem (y) (x) == 0 | y <- (filter (>0) xs)]

| x == 0 = False

primero (x:xs) = x

José A. Alonso dice:

30-octubre-2014 a las 22:40

La definición se puede simplificar usando ecuaciones sin guardas.

Responder

divisiblesPorPrimero :: [Int]->Bool
divisiblesPorPrimero xs
    | xs == [] || x==0 = False
    | otherwise = and [y `mod` x == 0| y <- xs, y >= 0]
    where x = head xs

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divisiblesPorPrimero :: [Int]->Bool

divisiblesPorPrimero xs

| xs == [] || x==0 = False

| otherwise = and [y `mod` x == 0| y <- xs, y >= 0]

where x = head xs

José A. Alonso dice:

30-octubre-2014 a las 22:41

La definición se puede simplificar usando ecuaciones sin guardas.

Responder

divisiblesPorPrimero :: [Int] -> Bool
divisiblesPorPrimero []     = False
divisiblesPorPrimero (0:xs) = False
divisiblesPorPrimero (x:xs) = and [rem n x == 0 | n <- xs, n >= 0]

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divisiblesPorPrimero :: [Int] -> Bool

divisiblesPorPrimero [] = False

divisiblesPorPrimero (0:xs) = False

divisiblesPorPrimero (x:xs) = and [rem n x == 0 | n <- xs, n >= 0]

divisiblesPorPrimero :: [Int] -> Bool
divisiblesPorPrimero []     = False
divisiblesPorPrimero (0:xs) = False
divisiblesPorPrimero (x:xs) = and [mod y x == 0| y <- (x:xs), y>0

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divisiblesPorPrimero :: [Int] -> Bool

divisiblesPorPrimero [] = False

divisiblesPorPrimero (0:xs) = False

divisiblesPorPrimero (x:xs) = and [mod y x == 0| y <- (x:xs), y>0

divisiblesPorPrimero :: [Int] -> Bool
divisiblesPorPrimero []     = False
divisiblesPorPrimero (0:_)  = False
divisiblesPorPrimero (x:xs) = and [mod y x == 0| y <- xs, y > 0]

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divisiblesPorPrimero :: [Int] -> Bool

divisiblesPorPrimero [] = False

divisiblesPorPrimero (0:_) = False

divisiblesPorPrimero (x:xs) = and [mod y x == 0| y <- xs, y > 0]

divisiblesPorPrimero :: [Int] -> Bool
divisiblesPorPrimero [] = False
divisiblesPorPrimero (0:_) = False
divisiblesPorPrimero (x:xs) = and [y `mod` x == 0 | y <- filter (>0) xs]

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divisiblesPorPrimero :: [Int] -> Bool

divisiblesPorPrimero [] = False

divisiblesPorPrimero (0:_) = False

divisiblesPorPrimero (x:xs) = and [y `mod` x == 0 | y <- filter (>0) xs]

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