Subnúmeros pares

PorJosé A. Alonso 18-abril-201725-abril-2017

Los subnúmeros de un número x son los números que se pueden formar con dígitos de x en posiciones consecutivas. Por ejemplo, el número 254 tiene 6 subnúmeros: 2, 5, 4, 25, 54 y 254.

Definir las funciones

   subnumeros       :: Integer -> [Integer]
   nSubnumerosPares :: Integer -> Integer

1 2	subnumeros :: Integer -> [Integer] nSubnumerosPares :: Integer -> Integer

tales que

(subnumerosPares x) es la lista de los subnúmeros pares de x. Por ejemplo,

     subnumerosPares 254   ==  [2,254,54,4]
     subnumerosPares 154   ==  [154,54,4]
     subnumerosPares 15    ==  []

subnumerosPares 254 == [2,254,54,4]

subnumerosPares 154 == [154,54,4]

subnumerosPares 15 == []

(nSubnumerosPares x) es la cantidad de subnúmeros pares de x. Por ejemplo,

     nSubnumerosPares 254   ==  4
     nSubnumerosPares2 (4^(10^6))  ==  90625258498

1 2	nSubnumerosPares 254 == 4 nSubnumerosPares2 (4^(10^6)) == 90625258498

Soluciones

import Data.List ( genericLength
                 , inits
                 , tails
                 )

subnumerosPares :: Integer -> [Integer]
subnumerosPares n =
  filter even (subnumeros n)

-- (subnumeros n) es la lista de los subnúmeros de n. Por ejemplo,
--    subnumeros 254  ==  [2,25,5,254,54,4]
subnumeros :: Integer -> [Integer]
subnumeros n =
  [read x | x <- sublistas (show n)]

-- (sublistas xs) es la lista de las sublistas de xs. Por ejemplo, 
--    sublistas "abc"  ==  ["a","ab","b","abc","bc","c"]
sublistas :: [a] -> [[a]]
sublistas xs =
  concat [init (tails ys) | ys <- tail (inits xs)]

-- 1ª definición
-- =============

nSubnumerosPares :: Integer -> Integer
nSubnumerosPares =
  genericLength . subnumerosPares

-- 2ª definición
-- =============

nSubnumerosPares2 :: Integer -> Integer
nSubnumerosPares2 =
  sum . posicionesDigitosPares 

-- (posicionesDigitosPares x) es la lista de las posiciones de los
-- dígitos pares de x. Por ejemplo,
--    posicionesDigitosPares 254  ==  [1,3]
posicionesDigitosPares :: Integer -> [Integer]
posicionesDigitosPares x =
  [n | (n,y) <- zip [1..] (show x)
     , y `elem` "02468"]

-- Comparación de eficiencia
--    λ> nSubnumerosPares (2^(10^3))
--    22934
--    (2.83 secs, 3,413,414,872 bytes)
--    λ> nSubnumerosPares2 (2^(10^3))
--    22934
--    (0.01 secs, 0 bytes)

import Data.List ( genericLength

, inits

, tails

)

subnumerosPares :: Integer -> [Integer]

subnumerosPares n =

filter even (subnumeros n)

-- (subnumeros n) es la lista de los subnúmeros de n. Por ejemplo,

-- subnumeros 254 == [2,25,5,254,54,4]

subnumeros :: Integer -> [Integer]

subnumeros n =

[read x | x <- sublistas (show n)]

-- (sublistas xs) es la lista de las sublistas de xs. Por ejemplo,

-- sublistas "abc" == ["a","ab","b","abc","bc","c"]

sublistas :: [a] -> [[a]]

sublistas xs =

concat [init (tails ys) | ys <- tail (inits xs)]

-- 1ª definición

-- =============

nSubnumerosPares :: Integer -> Integer

nSubnumerosPares =

genericLength . subnumerosPares

-- 2ª definición

-- =============

nSubnumerosPares2 :: Integer -> Integer

nSubnumerosPares2 =

sum . posicionesDigitosPares

-- (posicionesDigitosPares x) es la lista de las posiciones de los

-- dígitos pares de x. Por ejemplo,

-- posicionesDigitosPares 254 == [1,3]

posicionesDigitosPares :: Integer -> [Integer]

posicionesDigitosPares x =

[n | (n,y) <- zip [1..] (show x)

, y `elem` "02468"]

-- Comparación de eficiencia

-- λ> nSubnumerosPares (2^(10^3))

-- 22934

-- (2.83 secs, 3,413,414,872 bytes)

-- λ> nSubnumerosPares2 (2^(10^3))

-- 22934

-- (0.01 secs, 0 bytes)

5 Comentarios

import Data.List
import Data.Char

subnumerosPares :: Integer -> [Integer]
subnumerosPares =  filter even . map read . subConsecutivos . show 

subConsecutivos :: String -> [String]
subConsecutivos []     = []
subConsecutivos (x:xs) = scanl (\x y -> x ++ [y]) [x] xs ++ subConsecutivos xs 
                   
nSubnumerosPares :: Integer -> Integer
nSubnumerosPares = genericLength . subnumerosPares

nSubnumerosPares2 :: Integer -> Integer
nSubnumerosPares2 = sum . map fst . filter (even . snd) . zip [1..] . map digitToInt .  show

import Data.List

import Data.Char

subnumerosPares :: Integer -> [Integer]

subnumerosPares = filter even . map read . subConsecutivos . show

subConsecutivos :: String -> [String]

subConsecutivos [] = []

subConsecutivos (x:xs) = scanl (\x y -> x ++ [y]) [x] xs ++ subConsecutivos xs

nSubnumerosPares :: Integer -> Integer

nSubnumerosPares = genericLength . subnumerosPares

nSubnumerosPares2 :: Integer -> Integer

nSubnumerosPares2 = sum . map fst . filter (even . snd) . zip [1..] . map digitToInt . show

Responder

import Data.List
subnumerosPares :: Integer -> [Integer]
subnumerosPares x = filter (even) (subnumeros x)

nSubnumerosPares :: Integer -> Integer
nSubnumerosPares = genericLength.subnumerosPares

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

subnumeros :: Integer -> [Integer]
subnumeros x = map digitToNumber (pepa (digitos x))

pepa [x] = [[x]]
pepa (x:xs) = [take n (x:xs) | n <- [1..length (x:xs)]] ++ pepa xs

digitToNumber [] = 0
digitToNumber [0] = 0
digitToNumber (x:xs) = x*10^(length(x:xs)-1)+(digitToNumber xs)

import Data.List

subnumerosPares :: Integer -> [Integer]

subnumerosPares x = filter (even) (subnumeros x)

nSubnumerosPares :: Integer -> Integer

nSubnumerosPares = genericLength.subnumerosPares

digitos :: Integer -> [Integer]

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

subnumeros :: Integer -> [Integer]

subnumeros x = map digitToNumber (pepa (digitos x))

pepa [x] = [[x]]

pepa (x:xs) = [take n (x:xs) | n <- [1..length (x:xs)]] ++ pepa xs

digitToNumber [] = 0

digitToNumber [0] = 0

digitToNumber (x:xs) = x*10^(length(x:xs)-1)+(digitToNumber xs)

Responder

import Data.Char


subnumerosPares :: Integer -> [Integer]
subnumerosPares x = map read $ concat $ aux [] (show x)
    where aux _ [] = []
          aux xs (y:ys) | even (digitToInt y) = (f (reverse xs) y):aux (y:xs) ys
                        | otherwise = aux (y:xs) ys
          f [] t = [[t]]
          f p@(c:cs) t = (p++[t]):f cs t

nSubnumerosPares :: Integer -> Integer
nSubnumerosPares x = aux (show x) 1
      where aux [] _ = 0
            aux (y:ys) n | even (digitToInt y) = n + aux ys (n+1)
                         | otherwise = aux ys (n+1)

import Data.Char

subnumerosPares :: Integer -> [Integer]

subnumerosPares x = map read $ concat $ aux [] (show x)

where aux _ [] = []

aux xs (y:ys) | even (digitToInt y) = (f (reverse xs) y):aux (y:xs) ys

| otherwise = aux (y:xs) ys

f [] t = [[t]]

f p@(c:cs) t = (p++[t]):f cs t

nSubnumerosPares :: Integer -> Integer

nSubnumerosPares x = aux (show x) 1

where aux [] _ = 0

aux (y:ys) n | even (digitToInt y) = n + aux ys (n+1)

| otherwise = aux ys (n+1)

Responder

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

c :: [String] -> [String]
c [] = []
c xs |length xs == 1 = []
     |otherwise = concat (take 2 xs) : c(drop 1 xs)

subnumeros :: Integer -> [Integer]
subnumeros x = map (read) (show x : (c z) ++ z)
  where z = map show (f x)

subnumerosPares :: Integer -> [Integer]
subnumerosPares x = filter (even) (subnumeros x)
 
nSubnumerosPares :: Integer -> Integer
nSubnumerosPares = genericLength.subnumerosPares

f :: Integer -> [Integer]

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

c :: [String] -> [String]

c [] = []

c xs |length xs == 1 = []

|otherwise = concat (take 2 xs) : c(drop 1 xs)

subnumeros :: Integer -> [Integer]

subnumeros x = map (read) (show x : (c z) ++ z)

where z = map show (f x)

subnumerosPares :: Integer -> [Integer]

subnumerosPares x = filter (even) (subnumeros x)

nSubnumerosPares :: Integer -> Integer

nSubnumerosPares = genericLength.subnumerosPares

Responder

import Data.List

subnumerosPares :: Integer -> [Integer]
subnumerosPares x = filter (even) (map (read) (subConsecutivo xs))
 where
  xs = show x


subConsecutivo (x:xs) = filter (/=[]) (nub (aux (x:xs)))
 where aux [] = [[]]
       aux (x:xs) = inits (x:xs) ++ aux xs

       
nSubnumerosPares :: Integer -> Integer
nSubnumerosPares = genericLength.subnumerosPares

import Data.List

subnumerosPares :: Integer -> [Integer]

subnumerosPares x = filter (even) (map (read) (subConsecutivo xs))

where

xs = show x

subConsecutivo (x:xs) = filter (/=[]) (nub (aux (x:xs)))

where aux [] = [[]]

aux (x:xs) = inits (x:xs) ++ aux xs

nSubnumerosPares :: Integer -> Integer

nSubnumerosPares = genericLength.subnumerosPares

Responder

Subnúmeros pares

Soluciones

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