Superación de límites

PorJosé A. Alonso 14-diciembre-201821-diciembre-2018

Una sucesión de puntuaciones se puede representar mediante una lista de números. Por ejemplo, [7,5,9,9,4,5,4,2,5,9,12,1]. En la lista anterior, los puntos en donde se alcanzan un nuevo máximo son 7, 9 y 12 (porque son mayores que todos sus anteriores) y en donde se alcanzan un nuevo mínimo son 7, 5, 4, 2 y 1 (porque son menores que todos sus anteriores). Por tanto, el máximo se ha superado 2 veces y el mínimo 4 veces.

Definir las funciones

   nuevosMaximos :: [Int] -> [Int]
   nuevosMinimos :: [Int] -> [Int]
   nRupturas     :: [Int] -> (Int,Int)

nuevosMaximos :: [Int] -> [Int]

nuevosMinimos :: [Int] -> [Int]

nRupturas :: [Int] -> (Int,Int)

tales que

(nuevosMaximos xs) es la lista de los nuevos máximos de xs. Por ejemplo,

     nuevosMaximos [7,5,9,9,4,5,4,2,5,9,12,1]  ==  [7,9,12]

1	nuevosMaximos [7,5,9,9,4,5,4,2,5,9,12,1] == [7,9,12]

(nuevosMinimos xs) es la lista de los nuevos mínimos de xs. Por ejemplo,

     nuevosMinimos [7,5,9,9,4,5,4,2,5,9,12,1]  ==  [7,5,4,2,1]

1	nuevosMinimos [7,5,9,9,4,5,4,2,5,9,12,1] == [7,5,4,2,1]

(nRupturas xs) es el par formado por el número de veces que se supera el máximo y el número de veces que se supera el mínimo en xs. Por ejemplo,

     nRupturas [7,5,9,9,4,5,4,2,5,9,12,1]  ==  (2,4)

1	nRupturas [7,5,9,9,4,5,4,2,5,9,12,1] == (2,4)

Soluciones

import Data.List (group, inits)

nuevosMaximos :: [Int] -> [Int]
nuevosMaximos xs = map head (group (map maximum xss))
  where xss = tail (inits xs)

nuevosMinimos :: [Int] -> [Int]
nuevosMinimos xs = map head (group (map minimum xss))
  where xss = tail (inits xs)

nRupturas :: [Int] -> (Int,Int)
nRupturas [] = (0,0)
nRupturas xs =
  ( length (nuevosMaximos xs) - 1
  , length (nuevosMinimos xs) - 1)

import Data.List (group, inits)

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos xs = map head (group (map maximum xss))

where xss = tail (inits xs)

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos xs = map head (group (map minimum xss))

where xss = tail (inits xs)

nRupturas :: [Int] -> (Int,Int)

nRupturas [] = (0,0)

nRupturas xs =

( length (nuevosMaximos xs) - 1

, length (nuevosMinimos xs) - 1)

Pensamiento

«Todo necio confunde valor y precio.» ~ Antonio Machado.

6 Comentarios

nuevosMaximos :: [Int] -> [Int]
nuevosMaximos [] = []
nuevosMaximos xs = head xs : aux xs (head xs)
  where aux [] _ = []
        aux (x:xs) v | x > v     = x : aux xs x
                     | otherwise = aux xs v

nuevosMinimos :: [Int] -> [Int]
nuevosMinimos [] = []
nuevosMinimos xs = head xs : aux xs (head xs)
  where aux [] _ = []
        aux (x:xs) v | x < v     = x : aux xs x
                     | otherwise = aux xs v

nRupturas     :: [Int] -> (Int,Int)
nRupturas [] = (0,0)
nRupturas xs = (f (nuevosMaximos xs), f (nuevosMinimos xs))
  where f ys = length ys - 1

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos [] = []

nuevosMaximos xs = head xs : aux xs (head xs)

where aux [] _ = []

aux (x:xs) v | x > v = x : aux xs x

| otherwise = aux xs v

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos [] = []

nuevosMinimos xs = head xs : aux xs (head xs)

where aux [] _ = []

aux (x:xs) v | x < v = x : aux xs x

| otherwise = aux xs v

nRupturas :: [Int] -> (Int,Int)

nRupturas [] = (0,0)

nRupturas xs = (f (nuevosMaximos xs), f (nuevosMinimos xs))

where f ys = length ys - 1

Responder

import Data.List
 
nuevosMaximos :: [Int] -> [Int]
nuevosMaximos xs =
  nub (map maximum [take n xs | (n,_) <- zip [1..] xs])
 
nuevosMinimos :: [Int] -> [Int]
nuevosMinimos xs =
  nub (map minimum [take n xs | (n,_) <- zip [1..] xs])
 
nRupturas :: [Int] -> (Int, Int)
nRupturas xs =
  (l (nuevosMaximos xs), l (nuevosMinimos xs))
  where l xs = length xs -1

import Data.List

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos xs =

nub (map maximum [take n xs | (n,_) <- zip [1..] xs])

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos xs =

nub (map minimum [take n xs | (n,_) <- zip [1..] xs])

nRupturas :: [Int] -> (Int, Int)

nRupturas xs =

(l (nuevosMaximos xs), l (nuevosMinimos xs))

where l xs = length xs -1

Responder

nuevosMaximos :: [Int] -> [Int]
nuevosMaximos xs =
  [x | (x,y) <- zip xs [1..length xs],
       and [x > z | z <- take (y-1) xs]]
 
nuevosMinimos :: [Int] -> [Int]
nuevosMinimos xs =
  [x | (x,y) <- zip xs [1..length xs],
       and [ x < z | z <- take (y-1) xs]]
 
nRupturas :: [Int] -> (Int,Int)
nRupturas xs =
  (length (nuevosMaximos xs) - 1,
   length (nuevosMinimos xs) - 1)

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos xs =

[x | (x,y) <- zip xs [1..length xs],

and [x > z | z <- take (y-1) xs]]

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos xs =

[x | (x,y) <- zip xs [1..length xs],

and [ x < z | z <- take (y-1) xs]]

nRupturas :: [Int] -> (Int,Int)

nRupturas xs =

(length (nuevosMaximos xs) - 1,

length (nuevosMinimos xs) - 1)

Responder

import Data.List (nub)
nuevosMaximos :: [Int] -> [Int]
nuevosMaximos (x:xs) = quitaMaxFalso  (nub (filter (>=x) (x:xs)))x
  where quitaMaxFalso [] a  = [] 
        quitaMaxFalso (x:xs) a | x < a = quitaMaxFalso xs a
                               | otherwise = x:quitaMaxFalso xs x

nuevosMinimos :: [Int] -> [Int]
nuevosMinimos (x:xs) = quitaMinFalso  (nub (filter (<=x) (x:xs)))x
  where quitaMinFalso [] a  = [] 
        quitaMinFalso (x:xs) a | x > a = quitaMinFalso xs a
                               | otherwise = x:quitaMinFalso xs x

nRupturas     :: [Int] -> (Int,Int)
nRupturas xs = (length (nuevosMaximos xs) -1, length (nuevosMinimos xs) -1)

import Data.List (nub)

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos (x:xs) = quitaMaxFalso (nub (filter (>=x) (x:xs)))x

where quitaMaxFalso [] a = []

quitaMaxFalso (x:xs) a | x < a = quitaMaxFalso xs a

| otherwise = x:quitaMaxFalso xs x

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos (x:xs) = quitaMinFalso (nub (filter (<=x) (x:xs)))x

where quitaMinFalso [] a = []

quitaMinFalso (x:xs) a | x > a = quitaMinFalso xs a

| otherwise = x:quitaMinFalso xs x

nRupturas :: [Int] -> (Int,Int)

nRupturas xs = (length (nuevosMaximos xs) -1, length (nuevosMinimos xs) -1)

Responder

nuevosMaximos :: [Int] -> [Int]
nuevosMaximos [] = []
nuevosMaximos (x:xs) =  x : (nuevosMaximos (dropWhile (<=x) xs))
 
nuevosMinimos :: [Int] -> [Int]
nuevosMinimos [] = []
nuevosMinimos (x:xs) = x : (nuevosMinimos (dropWhile (>=x) xs))
 
nRupturas :: [Int] -> (Int,Int)
nRupturas xs =
  (length (nuevosMaximos xs) - 1,
   length (nuevosMinimos xs) - 1)

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos [] = []

nuevosMaximos (x:xs) = x : (nuevosMaximos (dropWhile (<=x) xs))

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos [] = []

nuevosMinimos (x:xs) = x : (nuevosMinimos (dropWhile (>=x) xs))

nRupturas :: [Int] -> (Int,Int)

nRupturas xs =

(length (nuevosMaximos xs) - 1,

length (nuevosMinimos xs) - 1)

Responder

nuevosMaximos :: [Int] -> [Int]
nuevosMaximos [] = []
nuevosMaximos (x:xs) = x:filter (>x) (nuevosMaximos xs)

nuevosMinimos :: [Int] -> [Int]
nuevosMinimos [] = []
nuevosMinimos (x:xs) = x:filter (<x) (nuevosMinimos xs)

nRupturas :: [Int] -> (Int,Int)
nRupturas xs = (m,n)
 where m = (length . nuevosMaximos) xs - 1
       n = (length . nuevosMinimos) xs - 1

nuevosMaximos :: [Int] -> [Int]

nuevosMaximos [] = []

nuevosMaximos (x:xs) = x:filter (>x) (nuevosMaximos xs)

nuevosMinimos :: [Int] -> [Int]

nuevosMinimos [] = []

nuevosMinimos (x:xs) = x:filter (<x) (nuevosMinimos xs)

nRupturas :: [Int] -> (Int,Int)

nRupturas xs = (m,n)

where m = (length . nuevosMaximos) xs - 1

n = (length . nuevosMinimos) xs - 1

Responder

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