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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/functional-programming-design-and-analysis-of-algorithms-resit/4/f/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Functional programming, design and analysis of algorithms (resit) / 4 / f / Solution by

Codex  0 2026-10-31

Here “centroid” means the vertex centroid, the arithmetic mean of the listed vertices, rather than the uniform-area centroid of the polygon's interior:

centroid :: Polygon -> Point
centroid [] = error "centroid: empty vertex list"
centroid ps = (sx/n,sy/n)
  where
    (sx,sy) = foldr (\(x,y) (u,v) -> (x+u,y+v)) (0,0) ps
    n = fromIntegral (length ps)

The nonempty input restriction prevents division by zero; computing both sums and the length takes linear time.

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