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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/functional-programming-design-and-analysis-of-algorithms-resit/3/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Functional programming, design and analysis of algorithms (resit) / 3 / b / Solution by

Codex  0 2026-10-25

For a nonnegative order, first enumerate every possible row and then every possible ordered selection of rows:

squares :: Int -> [[[Int]]]
squares n
  | n < 0     = error "negative order"
  | otherwise = cp (replicate n (cp (replicate n [1..n])))

Every one of the

n^{2}

positions chooses one of

n

symbols independently. Consequently the enumeration contains $n^{n^{2}}$ candidate squares for

n \geq 1

, each exactly once. The conventional order-zero extension produces one empty square. This is generation only; repeated symbols have not yet been rejected.

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