Múltiplos con ceros y unos

5 Comentarios

1. No se me ocurre ninguna forma mejor que revisar linealmente.

   Haskell

   import Test.QuickCheck -- Naturales con sólo los dígitos 0 y/o 1 bins :: [ℤ] bins = g 1 [0] where g k xs = let ys = map (k+) xs in ys ⧺ g (10 * k) (xs ⧺ ys) -- Aquellos múltiplos de `n` multiplosCon1y0 :: ℤ → [ℤ] multiplosCon1y0 n = [b | b ← bins, b `mod` n ≡ 0] {- > head (multiplosCon1y0 1234658) ≡ 110101101101000000110 True (5.91 secs, 669,436,136 bytes) > quickCheckWith (stdArgs { maxSuccess = 10000 }) (¬ ∘ null ∘ multiplosCon1y0 ∘ (1+) ∘ abs) +++ OK, passed 10000 tests. (4.61 secs, 290,609,368 bytes) -}

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   import Test.QuickCheck   -- Naturales con sólo los dígitos 0 y/o 1 bins :: [ℤ] bins = g 1 [0] where g k xs = let ys = map (k+) xs                               in  ys ⧺ g (10 * k) (xs ⧺ ys)   -- Aquellos múltiplos de `n` multiplosCon1y0 :: ℤ → [ℤ] multiplosCon1y0 n = [b | b ← bins, b `mod` n ≡ 0]     {- > head (multiplosCon1y0 1234658) ≡ 110101101101000000110 True (5.91 secs, 669,436,136 bytes) > quickCheckWith (stdArgs { maxSuccess = 10000 }) (¬ ∘ null ∘ multiplosCon1y0 ∘ (1+) ∘ abs) +++ OK, passed 10000 tests. (4.61 secs, 290,609,368 bytes) -}

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2. Haskell

   import Test.QuickCheck multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 x = [q | q <- cerosYunos, q `rem` x == 0] cerosYunos :: [Integer] cerosYunos = 1 : concat [ [10*x,10*x+1]| x <- cerosYunos] comprobacion :: Positive Integer -> Bool comprobacion (Positive x) = not $ null $ multiplosCon1y0 x -- *Main> quickCheck comprobacion -- +++ OK, passed 100 tests.

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   import Test.QuickCheck     multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 x = [q | q <- cerosYunos, q `rem` x == 0]     cerosYunos :: [Integer] cerosYunos = 1 : concat [ [10*x,10*x+1]| x <- cerosYunos]     comprobacion :: Positive Integer -> Bool comprobacion (Positive x) = not $ null $ multiplosCon1y0 x   -- *Main> quickCheck comprobacion -- +++ OK, passed 100 tests.

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3. Haskell

   multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 n = [n*x | x <- [1..], todos1y0 (n*x)] where todos1y0 n = all (\x -> elem x ['0','1']) (show n)

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   multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 n = [n*x | x <- [1..], todos1y0 (n*x)]      where todos1y0 n = all (\x -> elem x ['0','1']) (show n)

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4. Haskell

   La solución es tan ineficiente que no termina de cargar el QuickCheck. multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 n = [n*x | x <- [1..], null [y | y <- digitos (n*x), y /= 0, y /= 1]] digitos :: Integer -> [Integer] digitos n = [read [d] | d <- show n] prop_multiplosCon1y0 :: Integer -> Property prop_multiplosCon1y0 n = n > 0 ==> not (null (multiplosCon1y0 n))

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   La solución es tan ineficiente que no termina de cargar el QuickCheck. multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 n = [n*x | x <- [1..], null [y | y <- digitos (n*x), y /= 0, y /= 1]]   digitos :: Integer -> [Integer] digitos n = [read [d] | d <- show n]   prop_multiplosCon1y0 :: Integer -> Property prop_multiplosCon1y0 n = n > 0 ==> not (null (multiplosCon1y0 n))

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   1. Haskell

      --La solución es tan ineficiente que no termina de cargar el QuickCheck. multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 n = [n*x | x <- [1..], null [y | y <- digitos (n*x), y /= 0, y /= 1]] prop_multiplosCon1y0 :: Integer -> Property prop_multiplosCon1y0 n = n > 0 ==> not (null (multiplosCon1y0 n))

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      --La solución es tan ineficiente que no termina de cargar el QuickCheck. multiplosCon1y0 :: Integer -> [Integer] multiplosCon1y0 n = [n*x | x <- [1..], null [y | y <- digitos (n*x), y /= 0, y /= 1]]   prop_multiplosCon1y0 :: Integer -> Property prop_multiplosCon1y0 n = n > 0 ==> not (null (multiplosCon1y0 n))

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