# 99 questions/Solutions/3

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< 99 questions | Solutions(Difference between revisions)

(Copied solution from 99 questions/1 to 10) |
(Commented on bug in one of the solutions.) |
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(13 intermediate revisions by 9 users not shown) | |||

Line 13: | Line 13: | ||

<haskell> | <haskell> | ||

elementAt :: [a] -> Int -> a | elementAt :: [a] -> Int -> a | ||

− | elementAt list i = list !! (i-1) | + | elementAt list i = list !! (i-1) |

</haskell> | </haskell> | ||

Line 20: | Line 20: | ||

<haskell> | <haskell> | ||

elementAt' :: [a] -> Int -> a | elementAt' :: [a] -> Int -> a | ||

− | elementAt' (x:_) 1 = x | + | elementAt' (x:_) 1 = x |

− | elementAt' [] _ = error "Index out of bounds" | + | elementAt' [] _ = error "Index out of bounds" |

elementAt' (_:xs) k | elementAt' (_:xs) k | ||

− | + | | k < 1 = error "Index out of bounds" | |

− | + | | otherwise = elementAt' xs (k - 1) | |

+ | </haskell> | ||

+ | |||

+ | Alternative version: | ||

+ | |||

+ | <haskell> | ||

+ | elementAt'' :: [a] -> Int -> a | ||

+ | elementAt'' (x:_) 1 = x | ||

+ | elementAt'' (_:xs) i = elementAt'' xs (i - 1) | ||

+ | elementAt'' _ _ = error "Index out of bounds" | ||

+ | </haskell> | ||

+ | '''This does not work correctly on invalid indexes and infinite lists, e.g.:''' | ||

+ | <haskell> | ||

+ | elementAt'' [1..] 0 | ||

+ | </haskell> | ||

+ | |||

+ | A few more solutions using prelude functions: | ||

+ | |||

+ | <haskell> | ||

+ | elementAt'' xs n | length xs < n = error "Index out of bounds" | ||

+ | | otherwise = fst . last $ zip xs [1..n] | ||

+ | </haskell> | ||

+ | |||

+ | <haskell> | ||

+ | elementAt''' xs n = head $ foldr ($) xs | ||

+ | $ replicate (n - 1) tail | ||

+ | -- Negative indeces not handled correctly: | ||

+ | -- Main> elementAt''' "haskell" (-1) | ||

+ | -- 'h' | ||

+ | </haskell> | ||

+ | |||

+ | <haskell> | ||

+ | elementAt_w' xs n = last . take n $ xs -- wrong | ||

+ | -- Main> map (elementAt_w' [1..4]) [1..10] | ||

+ | -- [1,2,3,4,4,4,4,4,4,4] | ||

+ | </haskell> | ||

+ | |||

+ | <haskell> | ||

+ | elementAt_w'' xs n = head . reverse . take n $ xs -- wrong | ||

+ | -- Main> map (elementAt_w'' [1..4]) [1..10] | ||

+ | -- [1,2,3,4,4,4,4,4,4,4] | ||

+ | </haskell> | ||

+ | |||

+ | <haskell> | ||

+ | elementAt_w''' xs n = head . drop (n - 1) $ xs -- wrong | ||

+ | -- Main> map (elementAt_w''' [1..4]) [0..10] | ||

+ | -- [1,1,2,3,4,*** Exception: Prelude.head: empty list | ||

+ | </haskell> | ||

+ | |||

+ | or <hask>elementAt_w'</hask> correctly in point-free style: | ||

+ | <haskell> | ||

+ | elementAt_w'pf = (last .) . take . (+ 1) | ||

+ | </haskell> | ||

+ | |||

+ | Pedantic note: the above definition of <hask>elementAt_w'pf</hask> does not conform to the order of arguments specified by the question, but the following does: | ||

+ | <haskell> | ||

+ | elementAt_w'pf' = flip $ (last .) . take . (+ 1) | ||

</haskell> | </haskell> |

## Revision as of 17:25, 18 April 2013

(*) Find the K'th element of a list. The first element in the list is number 1.

This is (almost) the infix operator !! in Prelude, which is defined as:

(!!) :: [a] -> Int -> a (x:_) !! 0 = x (_:xs) !! n = xs !! (n-1)

Except this doesn't quite work, because !! is zero-indexed, and element-at should be one-indexed. So:

elementAt :: [a] -> Int -> a elementAt list i = list !! (i-1)

Or without using the infix operator:

elementAt' :: [a] -> Int -> a elementAt' (x:_) 1 = x elementAt' [] _ = error "Index out of bounds" elementAt' (_:xs) k | k < 1 = error "Index out of bounds" | otherwise = elementAt' xs (k - 1)

Alternative version:

elementAt'' :: [a] -> Int -> a elementAt'' (x:_) 1 = x elementAt'' (_:xs) i = elementAt'' xs (i - 1) elementAt'' _ _ = error "Index out of bounds"

**This does not work correctly on invalid indexes and infinite lists, e.g.:**

elementAt'' [1..] 0

A few more solutions using prelude functions:

elementAt'' xs n | length xs < n = error "Index out of bounds" | otherwise = fst . last $ zip xs [1..n]

elementAt''' xs n = head $ foldr ($) xs $ replicate (n - 1) tail -- Negative indeces not handled correctly: -- Main> elementAt''' "haskell" (-1) -- 'h'

elementAt_w' xs n = last . take n $ xs -- wrong -- Main> map (elementAt_w' [1..4]) [1..10] -- [1,2,3,4,4,4,4,4,4,4]

elementAt_w'' xs n = head . reverse . take n $ xs -- wrong -- Main> map (elementAt_w'' [1..4]) [1..10] -- [1,2,3,4,4,4,4,4,4,4]

elementAt_w''' xs n = head . drop (n - 1) $ xs -- wrong -- Main> map (elementAt_w''' [1..4]) [0..10] -- [1,1,2,3,4,*** Exception: Prelude.head: empty list

elementAt_w'

elementAt_w'pf = (last .) . take . (+ 1)

elementAt_w'pf

elementAt_w'pf' = flip $ (last .) . take . (+ 1)