Último dígito no nulo del factorial

PorJosé A. Alonso 14-noviembre-201425-abril-2021

Enunciado

-- El factorial de 7 es
--    7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040
-- por tanto, el último dígito no nulo del factorial de 7 es 4.
-- 
-- Definir la función
--    ultimoNoNuloFactorial :: Integer -> Integer
-- tal que (ultimoNoNuloFactorial n) es el último dígito no nulo del
-- factorial de n. Por ejemplo,
--    ultimoNoNuloFactorial  7  == 4
--    ultimoNoNuloFactorial 10  == 8
--    ultimoNoNuloFactorial 12  == 6
--    ultimoNoNuloFactorial 97  == 2
--    ultimoNoNuloFactorial  0  == 1
--
-- Comprobar con QuickCheck que si n es mayor que 4, entonces el último
-- dígito no nulo del factorial de n es par.

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-- El factorial de 7 es

-- 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040

-- por tanto, el último dígito no nulo del factorial de 7 es 4.

--

-- Definir la función

-- ultimoNoNuloFactorial :: Integer -> Integer

-- tal que (ultimoNoNuloFactorial n) es el último dígito no nulo del

-- factorial de n. Por ejemplo,

-- ultimoNoNuloFactorial 7 == 4

-- ultimoNoNuloFactorial 10 == 8

-- ultimoNoNuloFactorial 12 == 6

-- ultimoNoNuloFactorial 97 == 2

-- ultimoNoNuloFactorial 0 == 1

--

-- Comprobar con QuickCheck que si n es mayor que 4, entonces el último

-- dígito no nulo del factorial de n es par.

Soluciones

import Test.QuickCheck

ultimoNoNuloFactorial :: Integer -> Integer
ultimoNoNuloFactorial n = ultimoNoNulo (factorial n)

-- (ultimoNoNulo n) es el último dígito no nulo de n. Por ejemplo,
--    ultimoNoNulo 5040  ==  4
ultimoNoNulo :: Integer -> Integer
ultimoNoNulo n | m /= 0    = m
               | otherwise = ultimoNoNulo (n `div` 10)
               where m = n `rem` 10

-- 2ª definición (por comprensión)
ultimoNoNulo2 :: Integer -> Integer
ultimoNoNulo2 n = read [head (dropWhile (=='0') (reverse (show n)))]

-- (factorial n) es el factorial de n. Por ejemplo,
--    factorial 7  ==  5040
factorial :: Integer -> Integer
factorial n = product [1..n]


-- La propiedad es
prop_ultimoNoNuloFactorial :: Integer -> Property
prop_ultimoNoNuloFactorial n = 
    n > 4 ==> even (ultimoNoNuloFactorial n)
                  
-- La comprobación es
--    ghci> quickCheck prop_ultimoNoNuloFactorial
--    +++ OK, passed 100 tests.

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import Test.QuickCheck

ultimoNoNuloFactorial :: Integer -> Integer

ultimoNoNuloFactorial n = ultimoNoNulo (factorial n)

-- (ultimoNoNulo n) es el último dígito no nulo de n. Por ejemplo,

-- ultimoNoNulo 5040 == 4

ultimoNoNulo :: Integer -> Integer

ultimoNoNulo n | m /= 0 = m

| otherwise = ultimoNoNulo (n `div` 10)

where m = n `rem` 10

-- 2ª definición (por comprensión)

ultimoNoNulo2 :: Integer -> Integer

ultimoNoNulo2 n = read [head (dropWhile (=='0') (reverse (show n)))]

-- (factorial n) es el factorial de n. Por ejemplo,

-- factorial 7 == 5040

factorial :: Integer -> Integer

factorial n = product [1..n]

-- La propiedad es

prop_ultimoNoNuloFactorial :: Integer -> Property

prop_ultimoNoNuloFactorial n =

n > 4 ==> even (ultimoNoNuloFactorial n)

-- La comprobación es

-- ghci> quickCheck prop_ultimoNoNuloFactorial

-- +++ OK, passed 100 tests.

4 Comentarios

ultimoNoNuloFactorial :: Integer -> Integer
ultimoNoNuloFactorial n = last (filter (/=0) (digitosC (factorial n))) 

factorial :: Integer -> Integer
factorial n = product [1..n]

digitosC :: Integer -> [Integer]
digitosC n = [read [x] | x <- show n]

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ultimoNoNuloFactorial :: Integer -> Integer

ultimoNoNuloFactorial n = last (filter (/=0) (digitosC (factorial n)))

factorial :: Integer -> Integer

factorial n = product [1..n]

digitosC :: Integer -> [Integer]

digitosC n = [read [x] | x <- show n]

ultimoNoNuloFactorial :: Integer -> Integer
ultimoNoNuloFactorial n = 
   head [read [x]| x<- (reverse (show (factorial n))), x /= '0']

factorial :: Integer -> Integer
factorial n = product [1..n]

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ultimoNoNuloFactorial :: Integer -> Integer

ultimoNoNuloFactorial n =

head [read [x]| x<- (reverse (show (factorial n))), x /= '0']

factorial :: Integer -> Integer

factorial n = product [1..n]

ultimoNoNuloFactorial :: Integer -> Integer
ultimoNoNuloFactorial n = read [head (dropWhile (== '0') (reverse (show (factorial n))))]

prop :: Integer-> Property
prop n = n> 4 ==> even (ultimoNoNuloFactorial n)

-- La comprobación es: 
--    *Main> quickCheck prop
--    +++ OK, passed 100 tests.

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ultimoNoNuloFactorial :: Integer -> Integer

ultimoNoNuloFactorial n = read [head (dropWhile (== '0') (reverse (show (factorial n))))]

prop :: Integer-> Property

prop n = n> 4 ==> even (ultimoNoNuloFactorial n)

-- La comprobación es:

-- *Main> quickCheck prop

-- +++ OK, passed 100 tests.

ultimoNoNuloFactorial :: Integer -> Integer
ultimoNoNuloFactorial x = last (filter (/=0) (digitos (factorial x)))

digitos :: Integer -> [Integer]
digitos n = [read [x] | x <- show n]

factorial :: Integer -> Integer
factorial n = product [1..n]

prop :: Integer -> Bool
prop x = x < 4 || even (ultimoNoNuloFactorial x)

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ultimoNoNuloFactorial :: Integer -> Integer

ultimoNoNuloFactorial x = last (filter (/=0) (digitos (factorial x)))

digitos :: Integer -> [Integer]

digitos n = [read [x] | x <- show n]

factorial :: Integer -> Integer

factorial n = product [1..n]

prop :: Integer -> Bool

prop x = x < 4 || even (ultimoNoNuloFactorial x)

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