Probablity.scala

import scala.collection.mutable

/**
 * User: Oleg
 * Date: 1/12/14
 * Time: 3:32 AM
 */
object Probability {
  def main(args: Array[String]) {
    println(prob[Int, Double](.5, .8, 13, 10, 0))
    println(prob[BigInt, BigDecimal](.5, .8, 13, 10, 0))
  }

  object prob {
    def apply[N, R](p: R, q: R, x: N, y: N, used: N)(implicit f: Fractional[R], num: Numeric[N]) =
      new Calculation(p, q)(f, num)(x, y, used)
    class Calculation[N, R](p: R, q: R)(implicit f: Fractional[R], num: Numeric[N]) {

      import f._

      val `-1` = num.fromInt(-1)
      val `0` = num.zero
      val cache = mutable.Map.empty[(N,N,N),R]

      def apply(x: N, y: N, used: N): R = cache.getOrElseUpdate((x, y, used),(x, y, used) match {
        case (`0`, `0`, _) => one
        case (_, `-1`, _) | (`-1`, _, _) => zero
        case (_, _, `0`) => apply(x --, y, `0`) * p + apply(x, y --, `0`) * (one - p)
        case _ => apply(x --, y, used --) * q + apply(x, y --, used --) * (one - q)
      })
      implicit class NumericExtra(t: N) {

        import num._

        def -- = t - one
      }
    }
  }
}