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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/a/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 / a / Solution by

Codex  0 2026-10-31

Place an implicit conversion in the companion object and import it into the client scope, so it is available for both an integer argument and an integer receiver:

import scala.language.implicitConversions

class Rational(n0: BigInt, d0: BigInt) {
  def this(n: Int, d: Int) = this(BigInt(n), BigInt(d))
  require(d0 != 0)
  private val g = n0.abs.gcd(d0.abs)
  val num: BigInt = (if (d0 < 0) -n0 else n0) / g
  val den: BigInt = d0.abs / g
  def *(r: Rational): Rational =
    new Rational(num*r.num, den*r.den)
  override def toString: String =
    if (den == 1) num.toString else num.toString + "/" + den.toString
}
object Rational {
  implicit def fromInt(n: Int): Rational = new Rational(n,1)
}

import Rational._
val r1 = new Rational(3,7)
val r2 = new Rational(-11,-5)
println(r1*r2)
println(r1*3)
println(7*r1)

Normalization gives

r_{2} = 11/5

. The output lines are 33/35, 9/7, 3. For r1*3, the argument is converted; for 7*r1, conversion supplies the receiver's rational multiplication method. BigInt keeps the exact rational arithmetic independent of fixed-width product overflow.

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