Add rotations to Util

src/Util.md

@@ -51,6 +51,29 @@ contains x (y :: xs) =
     else contains x xs
 ```
 
+### rotations
+
+Provides all the 'rotations' of a list.
+
+Example:
+
+```
+rotations [1, 2, 3] == [[1, 2, 3], [3, 1, 2], [2, 3, 1]]
+```
+
+```idris
+export
+rotations : List a -> List (List a) 
+rotations xs = rotations' (length xs) xs []
+  where
+    rotations' : Nat -> List a -> (acc : List (List a)) -> List (List a)
+    rotations' 0 xs acc = acc
+    rotations' (S k) [] acc = acc
+    rotations' (S k) (x :: xs) acc = 
+      let next = xs ++ [x]
+      in rotations' k next (next :: acc)
+```
+
 ## Vectors
 
 Define some operations for pairs of numbers, treating them roughly like vectors