Números de Harshad hereditarios

12 Comentarios

1. Haskell

   numeroHHD :: Int -> Bool numeroHHD n | k == 1 = True | n `mod` k == 0 = numeroHHD (n `div` 10) | otherwise = False where k = (length . show) n maxNumeroHHD :: Int maxNumeroHHD = head $ filter numeroHHD [999,998..100]

   1 2 3 4 5 6 7 8

   numeroHHD :: Int -> Bool numeroHHD n | k == 1          = True             | n `mod` k == 0  = numeroHHD (n `div` 10)             | otherwise       = False   where k = (length . show) n   maxNumeroHHD :: Int maxNumeroHHD = head $ filter numeroHHD [999,998..100]

   Responder

   1. La definición no es correcta. Por ejemplo,

      Haskell

      λ> numeroHHD 14 True

      1 2	λ> numeroHHD 14 True

      pero 14 no es un número de Harshad porque no es divisible por 5.

      Responder

      1. Tienes toda la razón. La solución está incorrecta.

         Responder

2. Haskell

   numeroHHD :: Int -> Bool numeroHHD n | n < 10 = True | otherwise = (mod n (sum (digitos n)) == 0) && numeroHHD (div n 10) digitos :: Int -> [Int] digitos n = [read [x] | x <- show n] maxNumeroHHD :: Int -> Int maxNumeroHHD n = head (filter (numeroHHD) [n-1,n-2..1]) -- maxNumeroHHD 999 = 902

   1 2 3 4 5 6 7 8 9 10 11 12 13

   numeroHHD :: Int -> Bool numeroHHD n   | n < 10 = True   | otherwise = (mod n (sum (digitos n)) == 0) &&                 numeroHHD (div n 10)   digitos :: Int -> [Int] digitos n = [read [x] | x <- show n]   maxNumeroHHD :: Int -> Int maxNumeroHHD n = head (filter (numeroHHD) [n-1,n-2..1]) -- maxNumeroHHD 999 = 902

   Responder

3. Haskell

   numeroHHD :: Int -> Bool numeroHHD n = check y y xs where (x:xs) = show n y = read [x] check :: Int -> Int -> String -> Bool check n s [] = n `mod` s == 0 check n s (x:xs) | n `mod` s == 0 = check (10*n+y) (s+y) xs | otherwise = False where y = read [x] maximoHHD :: Int maximoHHD = head $ filter numeroHHD [999,998..1]

   1 2 3 4 5 6 7 8 9 10 11 12

   numeroHHD :: Int -> Bool numeroHHD n = check y y xs   where (x:xs) = show n         y = read [x]         check :: Int -> Int -> String -> Bool         check n s  []    = n `mod` s == 0         check n s (x:xs) | n `mod` s == 0 = check (10*n+y) (s+y) xs                          | otherwise      = False           where y = read [x]   maximoHHD :: Int maximoHHD = head $ filter numeroHHD [999,998..1]

   Responder

4. Haskell

   sumaDigitos :: Integer -> Integer sumaDigitos n | mod n 10 == n = n | otherwise = (read [last (show n)]::Integer) + sumaDigitos (div n 10) isHarshad :: Integer -> Bool isHarshad n = mod n (sumaDigitos n) == 0 numeroHHD :: Integer -> Bool numeroHHD n | mod n 10 == n = isHarshad n | otherwise = isHarshad n && numeroHHD (div n 10)

   1 2 3 4 5 6 7 8 9 10

   sumaDigitos :: Integer -> Integer sumaDigitos n | mod n 10 == n = n               | otherwise = (read [last (show n)]::Integer) + sumaDigitos (div n 10)   isHarshad :: Integer -> Bool isHarshad n = mod n (sumaDigitos n) == 0   numeroHHD :: Integer -> Bool numeroHHD n | mod n 10 == n = isHarshad n             | otherwise = isHarshad n && numeroHHD (div n 10)

   Responder

   1. Haskell

      -- Versión 2.0 numeroHHDA4 :: Integer -> Bool numeroHHDA4 n | n < 10 = isHarshad n | otherwise = isHarshad n && numeroHHDA4 (div n 10) isHarshad :: Integer -> Bool isHarshad n = mod n (sumaDigitos n) == 0 sumaDigitos :: Integer -> Integer sumaDigitos n | n < 10 = n | otherwise = (read [head s]) + sumaDigitos (read (tail s)) where s = show n

      1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

      -- Versión 2.0 numeroHHDA4 :: Integer -> Bool numeroHHDA4 n   |  n < 10 = isHarshad n   | otherwise = isHarshad n && numeroHHDA4 (div n 10)   isHarshad :: Integer -> Bool isHarshad n = mod n (sumaDigitos n) == 0   sumaDigitos :: Integer -> Integer sumaDigitos n   | n < 10 = n   | otherwise = (read [head s]) + sumaDigitos (read (tail s))     where s = show n

      Responder

5. Haskell

   import Data.List numeroH :: Int -> Bool numeroH n = n `mod` (sum [ (read [a]) :: Int | a <- show n]) == 0 numeroHHD :: Int -> Bool numeroHHD n = and (map (numeroH) [ (read a) :: Int | a <- (inits (show n)\\[[]])]) mayorNumeroHHD :: Int -> Int mayorNumeroHHD n = maximum [ a | a <- [10 ^ (n-1)..10 ^ n - 1 ] , numeroHHD a] -- El resultado es: -- *Main> mayorNumeroHHD 3 -- 902

   1 2 3 4 5 6 7 8 9 10 11 12 13 14

   import Data.List   numeroH :: Int -> Bool numeroH n = n `mod` (sum [ (read [a]) :: Int | a <- show n]) == 0   numeroHHD :: Int -> Bool numeroHHD n  = and (map (numeroH) [ (read a) :: Int | a <- (inits (show n)\\[[]])])   mayorNumeroHHD :: Int -> Int mayorNumeroHHD n = maximum [ a | a <- [10 ^ (n-1)..10 ^ n - 1 ]                                , numeroHHD a] -- El resultado es: -- *Main> mayorNumeroHHD 3 -- 902

   Responder

   1. Haskell

      -- Corregido import Data.List numeroH :: Int -> Bool numeroH n = n `mod` (sum [ read [a] | a <- show n]) == 0 numeroHHD :: Int -> Bool numeroHHD n = and (map (numeroH) [ read a | a <- tail (inits (show n))]) suma :: [Integer] -> Integer suma xs = foldl' (+) (0) xs mayorNumeroHHD :: Int -> Int mayorNumeroHHD n = maximum [ a | a <- [10 ^ (n-1)..10 ^ n - 1 ] , numeroHHD a] -- El resultado es: -- *Main> mayorNumeroHHD 3 -- 902

      1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

      -- Corregido   import Data.List   numeroH :: Int -> Bool numeroH n = n `mod` (sum [ read [a] | a <- show n]) == 0   numeroHHD :: Int -> Bool numeroHHD n  = and (map (numeroH) [ read a | a <- tail (inits (show n))]) suma :: [Integer] -> Integer suma xs = foldl' (+) (0) xs   mayorNumeroHHD :: Int -> Int mayorNumeroHHD n = maximum [ a | a <- [10 ^ (n-1)..10 ^ n - 1 ]                                , numeroHHD a] -- El resultado es: -- *Main> mayorNumeroHHD 3 -- 902

      Responder

      1. Haskell

         --Mejorada/Corregida import Data.List numeroH :: Int -> Bool numeroH n = n `mod` (sum [ read[a] | a <- show n]) == 0 numeroHHD :: Int -> Bool numeroHHD n = and (map numeroH [ read a | a <- tail (inits (show n))]) mayorNumeroHHD :: Int -> Int mayorNumeroHHD n = head [ a | a <- [ 10 ^ n -1 , 10 ^ n - 2..10 ^ (n - 1) ] , numeroHHD a] -- El resultado es: -- *Main> mayorNumeroHHD 3 -- 902

         1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

         --Mejorada/Corregida   import Data.List   numeroH :: Int -> Bool numeroH n = n `mod` (sum [ read[a] | a <- show n]) == 0   numeroHHD :: Int -> Bool numeroHHD n  = and (map numeroH [ read a | a <- tail (inits (show n))])   mayorNumeroHHD :: Int -> Int mayorNumeroHHD n = head [ a | a <- [ 10 ^ n -1 , 10 ^ n - 2..10 ^ (n - 1) ]                             , numeroHHD a] -- El resultado es: -- *Main> mayorNumeroHHD 3 -- 902

         Responder

6. Haskell

   esNH :: Integer -> Bool esNH n = rem n (sum [read [x] | x <- show n]) == 0 numeroHHD :: Integer -> Bool numeroHHD 0 = True numeroHHD n = esNH n && numeroHHD (div n 10) mayorHHD3 :: Integer mayorHHD3 = last [x | x <- [1..999], numeroHHD x] -- El resultado es: 902

   1 2 3 4 5 6 7 8 9 10 11

   esNH :: Integer -> Bool esNH n = rem n (sum [read [x] | x <- show n]) == 0   numeroHHD :: Integer -> Bool numeroHHD 0 = True numeroHHD n = esNH n && numeroHHD (div n 10)   mayorHHD3 :: Integer mayorHHD3 = last [x | x <- [1..999], numeroHHD x]   -- El resultado es: 902

   Responder

7. Haskell

   import Data.List (inits) numeroHHD :: Int -> Bool numeroHHD n = and [aux xs | xs <- inits (show n), length xs > 1] where suma xs = sum [read [c]| c <- xs] aux xs = read xs `mod` suma xs == 0 maxNumeroHHD :: Int maxNumeroHHD = head $ filter numeroHHD [999,998..100]

   1 2 3 4 5 6 7 8 9

   import Data.List (inits)   numeroHHD :: Int -> Bool numeroHHD n = and [aux xs | xs <- inits (show n), length xs > 1]   where suma xs = sum [read [c]| c <- xs]         aux xs = read xs `mod` suma xs == 0   maxNumeroHHD :: Int maxNumeroHHD = head $ filter numeroHHD [999,998..100]

   Responder