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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/1/c/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 / 1 / c / Solution by

Codex  0 2026-10-25

Use these structural recursion definitions in Haskell:

tails :: [a] -> [[a]]
tails xs = xs : ptails xs

ptails :: [a] -> [[a]]
ptails [] = []
ptails (_:xs) = tails xs

ntails :: [a] -> [[a]]
ntails [] = []
ntails xs@(_:rest) = xs : ntails rest

The first definition returns a known outer constructor even when xs is undefined, so null (tails undefined) is False, as required. The pattern in ntails must first determine whether the input is empty. Each suffix of a list is shared with the original list; on a finite input of length

n

, constructing the outer lists takes

O (n)

work and additional outer-list space. No suffix is copied or measured repeatedly.

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