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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/imperative-programming-resit/6/b/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Imperative programming (resit) / 6 / b / i / Solution by

Codex  0 2026-10-25

Use a fixed-size count array and protected hooks defining a stable character-to-slot mapping. The default hooks count the ASCII lowercase interval. The document must start empty, and all subsequent edits must pass through the mixin methods, as they do for new DocImp with CharCountPlugin.

trait CharCountPlugin extends Doc {
  protected def firstCounted: Char = 'a'
  protected def numberCounted: Int = 26
  protected def slot(ch: Char): Int = {
    val k = ch.toInt - firstCounted.toInt
    if (0 <= k && k < numberCounted) k else -1
  }
  private lazy val totals = Array.fill(numberCounted)(0)

  abstract override def insert(pos: Int, ch: Char): Unit = {
    val k = slot(ch)
    super.insert(pos, ch)
    if (k >= 0) totals(k) += 1
  }

  abstract override def delete(pos: Int): Char = {
    val removed = super.delete(pos)
    val k = slot(removed)
    if (k >= 0) totals(k) -= 1
    removed
  }

  def count(ch: Char): Int = {
    val k = slot(ch)
    require(k >= 0, "character is outside the counted alphabet")
    totals(k)
  }
}

The additional representation invariant is that each array slot equals the number of corresponding characters in the current document. Initially all counts are zero. Each successful underlying edit changes exactly one relevant count, while a failed position check throws before any count is changed. Returning the actual deleted character lets deletion adjust the correct slot.

count takes $O (1)$ time for the fixed alphabet, as do the mixin's additions to edit cost. The lazy array avoids reading subclass-overridden size hooks during trait construction; the hooks must remain stable. An extension can override the interval hooks, or override slot with another fixed finite mapping. This is stackable modification by a trait: abstract override permits the method to call the next implementation of super, supplied here by DocImp.^[ref]

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