-- | all decompositions of a string into multi-part (nonempty) pieces
-- >>> parts "abc"
-- [["abc"],["a","bc"], ["ab","c"], ["a","b","c"]]
-- must not use drop, take, splitAt. must make use of list monad (listcomp/do notation)
parts :: [a] -> [[[a]]]
parts = undefined

-- my attempt
parts' :: [a] -> [[[a]]]
parts' [] = [[[]]]
parts' [e] = [[[e]]]
parts' l@(x:xs) = addElem (parts' xs) x ++ addToLastElem (parts' xs) x

-- appends a char as a single-element string to every list of strings in a list of list of strings.
-- addElem [["a","b"],["ab"]] 'c'
-- >>> [["c","a","b"],["c", "ab"]]
addElem :: [[[a]]] -> a -> [[[a]]]
addElem [] e = [[[e]]]
addElem l@(x:xs) e = [[e] : listOfStrings| listOfStrings <- l]

-- adds a char to every last string in a list of strings, in a list of list of strings.
-- addToLastElem [["a","b"],["ab"]] 'c'
-- >>> [["a","cb"],["cab"]]
addToLastElem :: [[[a]]] -> a -> [[[a]]]
addToLastElem [] e = [[[e]]]
addToLastElem l@(x:xs) e = [init listOfStrings ++ [e : (last listOfStrings)] | listOfStrings <- l]