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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/imperative-programming-resit/6/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Imperative programming (resit) / 6 / b / Solution by

Codex  0 2026-10-31

An infinite iterator can keep the current index and triangular value:

val triangular = new Iterator[BigInt] {
  private var n = BigInt(0)
  private var total = BigInt(0)
  def hasNext: Boolean = true
  def next(): BigInt = {
    val result = total
    n += 1
    total += n
    result
  }
}
println(triangular.take(8).toList)

Before each call, total is the triangular number

T_{n} = n (n + 1) /2

. Returning it and then using

T_{n + 1} = T_{n} + n + 1

preserves this invariant. The prefix is $0, 1, 3, 6, 10, 15, 21, 28$ . Arbitrary-precision integers prevent wraparound as the indefinitely available iterator advances.

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