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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/imperative-programming-resit/7/b/iii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Imperative programming (resit) / 7 / b / iii / Solution by

Codex  0 2026-10-25

Reject the empty string because it has no positive total count to normalize:

final class DistFromString(s: String) extends FiniteDist[Char] {
  require(s.nonEmpty)
  private val frequencies =
    s.foldLeft(Map.empty[Char, Int]) { (counts, c) =>
      counts.updated(c, counts.getOrElse(c, 0) + 1)
    }

  def getDom: List[Char] = s.toList.distinct

  def getProb(c: Char): Double =
    frequencies.getOrElse(c, 0).toDouble / s.length.toDouble
}

The support contains each occurring character once, and a character absent from the string gets mass zero. The occurrence counts sum to the nonzero string length, proving normalization. For a separate example, the string "aba" gives masses

2/3

and

1/3

to its two characters. The interpretation follows Scala's Char elements, so it counts UTF-16 code units rather than imposing a separate Unicode-code-point representation. The Double results approximate the corresponding rational probabilities.

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