[Scala] Rational+

某所の宿題メモ(No.8 まで)。

class Rational(n: Int, d: Int) { 
  require(d != 0)
  private val g = gcd(n.abs, d.abs)
  private def gcd(a: Int, b: Int): Int = 
    if (b == 0) a else gcd(b, a % b)

  // 4. denom > 0 となるように
  val numer: Int = if(d > 0) n / g else -n / g
  val denom: Int = if(d > 0) d / g else -d / g

  def this(n: Int) = this(n, 1)

  override def toString = numer + " / " + denom
  
  def + (that: Rational): Rational = 
    new Rational(
      numer * that.denom + that.numer * denom,
      denom * that.denom
  )

  // 2. 単項演算子 -
  def unary_- = new Rational(-numer, denom)
  // 2. unary_- を使って - をリライト
  def - (that: Rational): Rational = this + (- that)
 
  def * (that: Rational): Rational =
    new Rational(numer * that.numer, denom * that.denom)
 
  // 3. inv (逆数)
  def inv = { 
    require(numer != 0)
    new Rational(denom, numer)
  }
  // 3. inv を使って / をリライト
  def / (that: Rational):Rational = this * that.inv
 
  // 6. < の定義
  def < (that: Rational) = 
    this.numer * that.denom < that.numer * this.denom
 
  // 7. toDoubleメソッドの定義
  def toDouble = numer.toDouble / denom.toDouble
}

object Rational { 
  // 1. implicit def
  implicit def intToRational(x:Int) = new Rational(x)

  // 8. 循環小数 -> Rational 変換関数
  // どこに置くか迷ったけど、一応ここに。
  // もっと効率よく書けそうだけど...
  val periodReg = """(\d+)\.(\d*)\{(\d+)\}""".r
  def period2Rational(period: String):Rational =
    period match { 
      case periodReg(a,b,c) => {
        val intPart = a.toInt
        val nonRepeatPart = 
          if(b == "") new Rational(0) 
          else new Rational(b.toInt, Math.pow(10.0, b.length).toInt)
        val repeatPart = 
          new Rational(c.toInt, (Math.pow(10.0, c.length)-1).toInt) / Math.pow(10.0, b.length).toInt
        intPart + nonRepeatPart + repeatPart
      }
      case _ => error("Invalid argument: " + period)
    }
}

No.8 は こちらサイト を参考にしました。無限等比級数と考えるんですね。昔習ったような気もする。

scala> Rational.period2Rational("0.{3}") 
res3: Rational = 1 / 3
scala> 1.0 / 3.0
res4: Double = 0.3333333333333333

scala> Rational.period2Rational("0.2{142857}")
res5: Rational = 3 / 14
scala> 3.0 / 14.0
res6: Double = 0.21428571428571427

scala> Rational.period2Rational("0.153{42}")
res9: Rational = 5063 / 33000
scala> 5063.0 / 33000.0
res10: Double = 0.15342424242424244

No.9 はまた今度(たぶん)。