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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/functional-programming-design-and-analysis-of-algorithms/3/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 3 / b / Solution by

Codex  0 2026-10-31

For input length

n

, the successive list concatenations copy prefixes of lengths

0, 1, \dots, n - 1

. Thus

T (n) = T (n - 1) + Θ (n)

and

T (n) = Θ (1 + \sum_{j = 0}^{n - 1} (j + 1))

. The direct implementation takes $Θ (n^{2})$ time for a fully produced nonempty reversal. The repeated copying, rather than the number of recursive calls alone, causes the quadratic cost.

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