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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/imperative-programming/5/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Imperative programming / 5 / a / Solution by

Codex  0 2026-10-25

The abstract state is a finite multiset

Q

of ordered values, initially empty. Multiplicity matters: deleting the minimum removes one occurrence, not every equal occurrence. Assume a consistent total order on T.

trait PriorityQueue[T] {
  // Pre: true. Post: Q' is the empty multiset.
  def clear(): Unit

  // Pre: true. Post: Q' = Q with one additional occurrence of x.
  def insert(x: T): Unit

  // Pre: Q is nonempty.
  // Post: result is a minimum of Q;
  //       Q' is Q with exactly one occurrence of result removed.
  def delMin(): T

  // Pre: true. Post: result iff Q is empty, and Q' = Q.
  def isEmpty(): Boolean
}

This abstract data type places no fixed-capacity bound on insertion. The only operation requiring a nonempty collection is delMin. The representation must preserve duplicates even if it uses a data structure commonly associated with sets.

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