Menor contenedor de primos

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1. Haskell

   import Data.Numbers.Primes (primes) import Data.List (inits) menorContenedor :: Int -> Int menorContenedor n = head [x | x <- [1..], menorContenedorAux x n] menorContenedorAux :: Int -> Int -> Bool menorContenedorAux n a = and [ elem x (map listaDeIntToInt (subcadenas (digitosInt n))) | x <- take a primes] digitosInt :: Int -> [Int] digitosInt n = [read [x] | x <- show n] subcadenas :: [Int] -> [[Int]] subcadenas [] = [] subcadenas (x:xs) = [x:y | y <- inits xs] ++ subcadenas xs listaDeIntToInt :: [Int] -> Int listaDeIntToInt xs = sum [a*(10^b) | (a,b) <- zip (reverse (separaCifras xs)) [0..]] separaCifras :: [Int] -> [Int] separaCifras [] = [] separaCifras (x:xs) = digitosInt x ++ separaCifras xs

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   import Data.Numbers.Primes (primes) import Data.List (inits) menorContenedor :: Int -> Int menorContenedor n = head [x | x <- [1..], menorContenedorAux x n] menorContenedorAux :: Int -> Int -> Bool menorContenedorAux n a =   and [ elem x (map listaDeIntToInt (subcadenas (digitosInt n)))       | x <- take a primes] digitosInt :: Int -> [Int] digitosInt n = [read [x] | x <- show n]   subcadenas :: [Int] -> [[Int]] subcadenas []     = [] subcadenas (x:xs) = [x:y | y <- inits xs] ++ subcadenas xs listaDeIntToInt :: [Int] -> Int listaDeIntToInt xs =   sum [a*(10^b) | (a,b) <- zip (reverse (separaCifras xs)) [0..]]   separaCifras :: [Int] -> [Int] separaCifras []     = [] separaCifras (x:xs) = digitosInt x ++ separaCifras xs

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2. Haskell

   import Data.Numbers.Primes (primes, isPrime) -- 1º DEFINICIÓN (poco eficiente) menorContenedor :: Int -> Int menorContenedor 0 = 1 menorContenedor x = head [fromIntegral n | n <- [2..] , and [ elem y (contiene n) | y <- (take x primes)]] contiene :: Integer -> [Integer] contiene x = [ y | y <- (agrupa x) , isPrime y == True] agrupa :: Integer -> [Integer] agrupa x = [ joiner ys | ys <- (agrupalist x)] agrupalist :: Integer -> [[Integer]] agrupalist x = [ xs | xs <- agrupalist2 [1..(length (show x))] x] agrupalist2 :: [Int] -> Integer -> [[Integer]] agrupalist2 [] _ = [] agrupalist2 (x:xs) n = agrupaR x (digitos n) ++ agrupalist2 xs n digitos :: Integer -> [Integer] digitos n = [read [x] | x <- show n] agrupaR :: Int -> [a] -> [[a]] agrupaR _ [] = [] agrupaR n xs | n > (length xs) = [] agrupaR n xs = take n xs : agrupaR n (drop 1 xs) joiner :: [Integer] -> Integer joiner (x:xs) = read (concat (map show (x:xs))) -------------------------------------------------------------------------------- -- 2º DEFINICIÓN (más eficiente) menorContenedor2 :: Int -> Integer menorContenedor2 0 = 1 menorContenedor2 x = (joiner(eliminaigual1 (dig (listafinal7 (listafinal2 (take x primes)))))) listafinal7 :: [Integer] -> [Integer] listafinal7 xs | listafinal5 xs == [] = xs | otherwise = listafinal7 (listafinal6 xs) listafinal6 :: [Integer] -> [Integer] listafinal6 xs = (take (head (listafinal5 xs) -1 ) xs) ++ (drop (head (listafinal5 xs)) xs) listafinal5 :: [Integer] -> [Int] listafinal5 xs = [ y | (x,y)<- zip (listafinal4 xs) [1..], x > 1] listafinal4 :: [Integer] -> [Int] listafinal4 xs = [ (aparece (show x) (agrupaR (length (show x)) (show(joiner(eliminaigual1(dig(listafinal (xs)))))))) | x <- xs] listafinal3 :: [Integer] -> String listafinal3 [] = [] listafinal3 xs = (show(joiner(eliminaigual1(dig(listafinal xs))))) aparece :: Eq a => [a] -> [[a]] -> Int aparece [] _ = 0 aparece _ [] = 0 aparece xs (ys:yss) | xs == ys = 1 + aparece xs yss | otherwise = aparece xs yss listafinal2 :: [Integer] -> [Integer] listafinal2 (xs) = reverse(eliminacero(ordena(m(listafinal xs)))) listafinal :: [Integer] -> [Integer] listafinal [] = [] listafinal xs = [ x | x <- xs , (elem (show x) (pertenece4 xs)) == False] pertenece4 :: [Integer] -> [String] pertenece4 [] = [] pertenece4 xs = pertenece3 xs ++ pertenece3 (drop (length (sacar xs)) xs) pertenece3 :: [Integer] -> [String] pertenece3 [] = [] pertenece3 xs = [ ys | ys <- lista2 xs, pertenece2 ys (lista xs) /= [] ] pertenece2 :: String -> [String] -> String pertenece2 _ [] = [] pertenece2 xs (ys:yss) | xs == ys = xs | otherwise = pertenece2 xs yss lista :: [Integer] -> [String] lista xs | and [(length (show x)) == (length (show (head xs))) | x <- xs] == True = [] | otherwise = (agrupaR (length(show (head (sacar xs)))) (show (joiner(drop (length (sacar xs)) xs)))) lista2 :: [Integer] -> [String] lista2 (xs) = (agrupaR1 (length(show (head (sacar xs)))) (sacar2 xs)) agrupaR1 :: Int -> [a] -> [[a]] agrupaR1 _ [] = [] agrupaR1 n xs | n > (length xs) = [] agrupaR1 n xs = take n xs : agrupaR1 n (drop n xs) sacar2 :: [Integer] -> [Char] sacar2 xs = [ a | a <- (show (joiner(sacar (xs))))] sacar :: [Integer] -> [Integer] sacar xs = [ x | x <- xs, length (show x) == length (show (head xs))] eliminaigual1 :: [Integer] -> [Integer] eliminaigual1 xs | eliminaigual2 xs == [] = xs | otherwise = eliminaigual1 ((take (head (eliminaigual2 xs) -1 ) xs) ++ (drop (head (eliminaigual2 xs)) xs) ) eliminaigual2 :: [Integer] -> [Int] eliminaigual2 xs = [fromIntegral x | x <- igualposicion xs , elem (x-1) (igualposicion xs) && elem (x+1) (igualposicion xs)] igualposicion :: [Integer] -> [Integer] igualposicion xs = [ n | (a,n) <- zip xs [1..] , elem a (tresiguales xs), a==1] tresiguales :: [Integer] -> [Integer] tresiguales xs | length xs < 3 = [] tresiguales (x:y:z:xs) | x==y && y==z = x : tresiguales (y:z:xs) | otherwise = tresiguales (y:z:xs) dig :: [Integer] -> [Integer] dig xs = digitos (joiner(eliminacero(ordena( m xs)))) eliminacero :: [Integer] -> [Integer] eliminacero [] = [] eliminacero (x:xs) | rem x 10 /= 0 = x : eliminacero xs | otherwise = eliminacero ((div x 10):xs) ordena :: Ord a => [a] -> [a] ordena [] = [] ordena (x:xs) = ordena menores ++ [x] ++ ordena mayores where menores = [y | y <- xs, y <= x] mayores = [y | y <- xs, y > x] l :: [Integer] -> Int l xs = length (show (last xs)) l2 :: [Integer] -> [Int] l2 xs = [ (l xs) - (length (show x)) | x <- xs] m :: [Integer] -> [Integer] m xs = [ x*(10^y) |(x,y) <- zip xs (l2 xs)] ------------------------------------------------------------------------- -- EFICIENCIA: --λ> menorContenedor 6 --113257 --(42.52 secs, 32,629,175,072 bytes) --λ> menorContenedor2 6 --113257 --(0.02 secs, 3,014,392 bytes) --λ> menorContenedor 30 --10110310710911317192329414347535961677379838997 --( ≈ 1.2036108604497068e35 años) --λ> menorContenedor2 30 --10110310710911317192329414347535961677379838997 --(4.61 secs, 1,127,487,392 bytes) -- Tengo dudas en el caso menorContenedor 0 ¿0 o 1?

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   import Data.Numbers.Primes (primes, isPrime)   -- 1º DEFINICIÓN (poco  eficiente)     menorContenedor :: Int -> Int menorContenedor 0 = 1 menorContenedor x = head [fromIntegral  n | n <- [2..] ,                            and [ elem y (contiene n) | y <- (take x primes)]]   contiene :: Integer -> [Integer] contiene x = [ y | y <- (agrupa x) , isPrime y == True]   agrupa :: Integer -> [Integer] agrupa x = [ joiner ys | ys <- (agrupalist x)]   agrupalist :: Integer -> [[Integer]] agrupalist x = [ xs | xs <- agrupalist2 [1..(length (show x))] x]   agrupalist2 :: [Int] -> Integer -> [[Integer]] agrupalist2 [] _ = [] agrupalist2 (x:xs) n = agrupaR x (digitos n) ++ agrupalist2 xs n   digitos :: Integer -> [Integer] digitos n = [read [x] | x <- show n]   agrupaR :: Int -> [a] -> [[a]] agrupaR _ [] = [] agrupaR n xs | n > (length xs) = [] agrupaR n xs = take n xs : agrupaR n (drop 1 xs)   joiner :: [Integer] -> Integer joiner (x:xs) = read (concat (map show (x:xs)))   --------------------------------------------------------------------------------   -- 2º DEFINICIÓN (más eficiente)   menorContenedor2 :: Int -> Integer menorContenedor2 0 = 1 menorContenedor2 x = (joiner(eliminaigual1                      (dig (listafinal7 (listafinal2 (take x primes))))))   listafinal7 :: [Integer] -> [Integer] listafinal7 xs | listafinal5 xs == [] = xs                | otherwise = listafinal7 (listafinal6 xs)   listafinal6 :: [Integer] -> [Integer] listafinal6 xs = (take (head (listafinal5 xs) -1 ) xs) ++                 (drop  (head (listafinal5 xs)) xs)   listafinal5 :: [Integer] -> [Int] listafinal5 xs = [ y | (x,y)<- zip (listafinal4 xs) [1..], x > 1]   listafinal4 :: [Integer] -> [Int] listafinal4 xs = [ (aparece (show x) (agrupaR (length (show x))             (show(joiner(eliminaigual1(dig(listafinal (xs)))))))) | x <- xs]   listafinal3 :: [Integer] -> String listafinal3 [] = [] listafinal3 xs = (show(joiner(eliminaigual1(dig(listafinal xs)))))   aparece :: Eq a => [a] -> [[a]] -> Int aparece [] _ = 0 aparece _ [] = 0 aparece xs (ys:yss) | xs == ys = 1 + aparece xs yss                     | otherwise = aparece xs yss                        listafinal2 :: [Integer] -> [Integer] listafinal2 (xs) = reverse(eliminacero(ordena(m(listafinal xs))))                           listafinal :: [Integer] -> [Integer] listafinal [] = [] listafinal xs = [ x | x <- xs , (elem (show x) (pertenece4 xs)) == False]   pertenece4 :: [Integer] -> [String] pertenece4 [] = [] pertenece4 xs = pertenece3 xs ++ pertenece3 (drop (length (sacar xs)) xs)   pertenece3 :: [Integer] -> [String] pertenece3 [] = [] pertenece3 xs = [ ys | ys <- lista2 xs, pertenece2 ys (lista xs) /= [] ]   pertenece2 :: String -> [String]  -> String pertenece2 _ [] = [] pertenece2 xs (ys:yss) | xs == ys = xs                        | otherwise = pertenece2 xs yss                          lista :: [Integer] -> [String] lista xs | and [(length (show x)) == (length (show (head xs)))  | x <- xs]           == True = []          | otherwise = (agrupaR (length(show (head (sacar xs))))            (show (joiner(drop (length (sacar xs)) xs))))   lista2 :: [Integer] -> [String] lista2 (xs) = (agrupaR1 (length(show (head (sacar xs)))) (sacar2 xs))   agrupaR1 :: Int -> [a] -> [[a]] agrupaR1 _ [] = [] agrupaR1 n xs | n > (length xs) = [] agrupaR1 n xs = take n xs : agrupaR1 n (drop n xs)   sacar2 :: [Integer] -> [Char] sacar2 xs = [ a | a <- (show (joiner(sacar (xs))))]   sacar :: [Integer] -> [Integer] sacar xs = [ x | x <- xs, length (show x) == length (show (head xs))]   eliminaigual1 :: [Integer] -> [Integer] eliminaigual1 xs | eliminaigual2 xs == [] = xs                  | otherwise = eliminaigual1                  ((take (head (eliminaigual2 xs) -1 ) xs) ++                 (drop  (head (eliminaigual2 xs)) xs) )    eliminaigual2 :: [Integer] -> [Int] eliminaigual2 xs = [fromIntegral x | x <- igualposicion xs ,                     elem (x-1) (igualposicion xs)                     &&  elem (x+1) (igualposicion xs)]   igualposicion :: [Integer] -> [Integer] igualposicion xs = [ n | (a,n) <- zip xs [1..] , elem a (tresiguales xs), a==1]   tresiguales :: [Integer] -> [Integer] tresiguales xs | length xs < 3 = [] tresiguales (x:y:z:xs) | x==y && y==z = x : tresiguales (y:z:xs)                            | otherwise =  tresiguales (y:z:xs)       dig :: [Integer] -> [Integer] dig xs = digitos (joiner(eliminacero(ordena( m xs))))     eliminacero :: [Integer] -> [Integer] eliminacero [] = [] eliminacero (x:xs) | rem x 10 /= 0 = x : eliminacero xs                    | otherwise = eliminacero ((div x 10):xs)   ordena :: Ord a => [a] -> [a] ordena [] = [] ordena (x:xs) =  ordena menores ++ [x] ++ ordena mayores     where menores = [y | y <- xs, y <= x]           mayores = [y | y <- xs, y >  x]            l :: [Integer] -> Int l xs = length (show (last  xs))   l2 :: [Integer] -> [Int] l2 xs = [ (l xs) - (length (show x)) | x <- xs]   m :: [Integer] -> [Integer] m xs = [ x*(10^y) |(x,y) <- zip xs (l2 xs)]   -------------------------------------------------------------------------   -- EFICIENCIA:     --λ> menorContenedor 6 --113257 --(42.52 secs, 32,629,175,072 bytes) --λ> menorContenedor2 6 --113257 --(0.02 secs, 3,014,392 bytes)   --λ> menorContenedor 30 --10110310710911317192329414347535961677379838997 --( ≈ 1.2036108604497068e35 años) --λ> menorContenedor2 30 --10110310710911317192329414347535961677379838997 --(4.61 secs, 1,127,487,392 bytes)         -- Tengo dudas en el caso menorContenedor 0 ¿0 o 1?

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