99 questions/Solutions/3

(*) 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_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''' xs n = head . drop (n - 1) $ xs

or elementAt_w' correctly in point-free style:

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