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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/functional-programming-design-and-analysis-of-algorithms-resit/4/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Functional programming, design and analysis of algorithms (resit) / 4 / a / Solution by

Codex  0 2026-10-25

For finite even lists, these definitions take at most linear time:

halve :: [a] -> ([a],[a])
halve xs = splitAt (length xs `div` 2) xs

pairs :: [a] -> [(a,a)]
pairs [] = []
pairs (x:y:xs) = (x,y) : pairs xs
pairs [_] = error "pairs: odd length"

The length calculation and the prefix split each take

O (n)

time. The second operation consumes two constructors per step and emits one pair. Under the stated even-length precondition, neither definition encounters an unmatched final element.

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