Máximo de una función

3 Comentarios

1. Haskell

   max_gC :: Integer -> Integer max_gC n | n < 0 = 0 | otherwise = last [l | (l,m) <- valores n, m == maximum [r | (s,r) <- valores n]] valores n = zip [0..n] [g y | y <- [0..n]] max_gR :: Integer -> Integer max_gR n | n < 0 = 0 | n < 10 || g n >= 81 = n | otherwise = max_gR (n-1) -- Comprobar con QuickCheck que la función max_g es equivalente a la -- función f definida por f :: Integer -> Integer f n | n < 0 = 0 | n >= 10 && n < 81 = 9 | otherwise = n prop_max_gC n = max_gC n == f n prop_max_gR n = max_gR n == f n -- comprobaciones -- *Main> quickCheck prop_max_gC -- +++ OK, passed 100 tests. -- *Main> quickCheck prop_max_gR -- +++ OK, passed 100 tests.

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   max_gC :: Integer -> Integer max_gC n     | n < 0 = 0     | otherwise = last [l | (l,m) <- valores n,                              m == maximum [r | (s,r) <- valores n]]   valores n =  zip [0..n] [g y | y <- [0..n]]   max_gR :: Integer -> Integer max_gR n | n < 0 = 0          | n < 10 || g n >= 81 = n          | otherwise = max_gR (n-1)   -- Comprobar con QuickCheck que la función max_g es equivalente a la -- función f definida por     f :: Integer -> Integer f n | n < 0             = 0     | n >= 10 && n < 81 = 9     | otherwise         = n   prop_max_gC n = max_gC n == f n prop_max_gR n = max_gR n == f n   -- comprobaciones --  *Main> quickCheck prop_max_gC --  +++ OK, passed 100 tests.   --  *Main> quickCheck prop_max_gR --  +++ OK, passed 100 tests.

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2. — Por comprensión:

   Haskell

   max_g :: Integer -> Integer max_g n | n <= 0 = 0 | otherwise = last [x| x <- [0..n], g x == m n] m :: Integer -> Integer m n = maximum [g y| y <- [0..n]] -- Comprobar con QuickCheck que la función max_g es equivalente a la -- función f definida por : f :: Integer -> Integer f n | n < 0 = 0 | n >= 10 && n < 81 = 9 | otherwise = n prop_g_f :: Integer -> Bool prop_g_f n = max_g n == f n -- La comprobación es: -- *Main> quickCheck prop_g_f -- +++ OK, passed 100 tests.

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   max_g :: Integer -> Integer max_g n | n <= 0    = 0         | otherwise = last [x| x <- [0..n], g x == m n]   m :: Integer -> Integer m n = maximum [g y| y <- [0..n]]   -- Comprobar con QuickCheck que la función max_g es equivalente a la -- función f definida por :   f :: Integer -> Integer f n | n < 0             = 0     | n >= 10 && n < 81 = 9     | otherwise         = n   prop_g_f :: Integer -> Bool prop_g_f n = max_g n == f n   -- La comprobación es: --    *Main> quickCheck prop_g_f --    +++ OK, passed 100 tests.

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3. Haskell

   g :: Integer -> Integer g n = if n < 10 then n*n else n maximoR f a b = aux a (a+1) (f a) where aux y x m | x > b = y | f x > m = aux x (x+1) (f x) | otherwise = aux y (x+1) m max_gR n = maximoR g 0 n maximoC f a b = head [x | x <-[a..b], f x == m] where m = maximum [f x | x <-[a..b]] max_gC n | n < 0 = 0 | otherwise = maximoC g 0 n f :: Integer -> Integer f n | n < 0 = 0 | n >= 10 && n < 81 = 9 | otherwise = n prop n = max_gR n == y && max_gC n == y where y = f n -- quickCheck prop -- +++ OK, passed 100 tests.

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   g :: Integer -> Integer g n = if n < 10 then n*n else n   maximoR f a b = aux a (a+1) (f a)     where aux y x m | x > b     = y                     | f x > m   = aux x (x+1) (f x)                     | otherwise = aux y (x+1) m   max_gR n = maximoR g 0 n   maximoC f a b = head [x | x <-[a..b], f x == m]     where m = maximum [f x | x <-[a..b]]   max_gC n | n < 0     = 0          | otherwise = maximoC g 0 n   f :: Integer -> Integer f n | n < 0             = 0     | n >= 10 && n < 81 = 9     | otherwise         = n     prop n = max_gR n == y && max_gC n == y     where y = f n   -- quickCheck prop -- +++ OK, passed 100 tests.

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