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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/functional-programming-design-and-analysis-of-algorithms/3/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Functional programming, design and analysis of algorithms / 3 / a / Solution by

Codex  0 2026-10-31

Using only list comprehensions:

type Matrix a = [[a]]
type Grid = Matrix Int

choicesComp :: Grid -> Matrix [Int]
choicesComp rows =
  [[[d | d <- [1..9], n == 0 || d == n] | n <- row] | row <- rows]

The input contract restricts each cell to zero or a digit from one to nine. A definition using standard list functions is:

choicesMap :: Grid -> Matrix [Int]
choicesMap = map (map choice)
  where
    choice :: Int -> [Int]
    choice 0 = [1..9]
    choice n = [n]

choices :: Grid -> Matrix [Int]
choices = choicesMap

Both preserve the row structure and construct the initial constraint domains of the Sudoku problem. The alternative names let both definitions coexist; either can supply choices.

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