module Golf where

-- Exercise 1

-- Explanation:
-- takeNth takes the nth value of a list without crashing. First, it drops all
-- the first `n - 1` elements from the list. Then, it takes the desired element.
-- This function is total and can be thought of as the total version of the
-- partial function `!!`.
takeNth :: [a] -> Int -> [a]
takeNth l n = take 1 $ drop (n-1) l

-- Explanation:
-- skips first maps all values in `nl`, defined as all values from 1 to the
-- length of the list (excluded), to `concatMap`, which is the same as `concat
-- (map ...)`. `concatMap` maps again the same array, this time multiplied by
-- each value `n` coming from the outer map, to takeNth of the given list `l`
-- and concatenates the result.
skips :: [a] -> [[a]]
skips [] = []
skips l = map (\n -> concatMap (takeNth l . (*n)) nl) nl
    where
        len = length l
        nl = [1..len]