99 questions/Solutions/57

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(**) Binary search trees (dictionaries)

Use the predicate add/3, developed in chapter 4 of the course, to write a predicate to construct a binary search tree from a list of integer numbers.

add :: Ord a => a -> Tree a -> Tree a
add x Empty            = Branch x Empty Empty
add x t@(Branch y l r) = case compare x y of
                            LT -> Branch y (add x l) r
                            GT -> Branch y l (add x r)
                            EQ -> t

construct xs = foldl (flip add) Empty xs

Here, the definition of construct is trivial, because the pattern of accumulating from the left is captured by the standard function foldl.