shorten first exercise solution

1 files changed, 15 insertions, 18 deletions

diff --git a/lec03/Golf.hs b/lec03/Golf.hs
index eb69136..b89aa57 100644
--- a/lec03/Golf.hs
+++ b/lec03/Golf.hs
@@ -3,25 +3,22 @@ module Golf where
 -- Exercise 1
 
 -- Explanation:
--- takeEvery takes all elements with index equal or multiple of a given
--- positive number, index 0 exluded. In the first two cases, it checks whether
--- the list is empty or the number is zero, and returns an empty list if so. In
--- the next case, which is the most general, it defines l2 and l3, which are
--- respectively the list without the first n-1 and n elements. Then it takes
--- the fist element out of l2, which, relative to the list, has an index
--- multiple of (or equal to) the given number, and then recursively call the
--- function itself on l3 so that it drops another (n-1) elements and takes the
--- one whose index is multiple of the number, etc.
-takeEvery :: [a] -> Int -> [a]
-takeEvery [] _ = []
-takeEvery _ 0 = []
-takeEvery l n = take 1 l2 ++ takeEvery l3 n
-    where
-        l2 = drop (n-1) l
-        l3 = drop 1 l2
+-- 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 calls takeEvery for every number from 1 to the length of the list - 1.
+-- 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 (takeEvery l) [1..length l]
+skips l = map (\n -> concatMap (takeNth l . (*n)) nl) nl
+    where
+        len = length l
+        nl = [1..len]