# 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_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```
or
elementAt_w'
correctly in point-free style:
`elementAt_w'pf = (last .) . take . (+ 1)`