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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/functional-programming-design-and-analysis-of-algorithms/4/f/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Functional programming, design and analysis of algorithms / 4 / f / Solution by

Codex  0 2026-10-25

Insert down the unique search route, leaving equal elements unchanged:

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

The binary search tree ordering determines the only child in which a missing query can belong. The recursive call preserves that child's ordering bounds, and the other child is shared. Thus the output represents the original set with q added, with duplicates suppressed. Its time complexity and newly allocated route length are

O (h + 1)

; it makes no balancing guarantee.

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