object CumulativeOps {
  def cumSum[A](xs: Seq[A])(implicit num: Numeric[A]): Seq[A] = {
    xs.tail.scanLeft(xs.head)(num.plus)
  }

  def cumDiff[A](xs: Seq[A])(implicit num: Numeric[A]): Seq[A] = {
    val total = xs.sum
    xs.scanLeft(total)(num.minus).dropRight(1)
  }

  def cumMultiplication[A](xs: Seq[A])(implicit num: Numeric[A]): Seq[A] = {
    xs.tail.scanLeft(xs.head)(num.times)
  }
}

class CumulativeOpsTest extends WordSpec with Matchers {
  "CumulativeOps" should {

    "calculate cumulative sum of Ints" in {
      CumulativeOps.cumSum(Vector(1, 2, 4, 7, 3, 4)) should
        contain theSameElementsInOrderAs (Seq(1, 3, 7, 14, 17, 21))
    }

    "calculate cumulative sum of Doubles" in {
      CumulativeOps.cumSum(Vector(1.25, 2, 4.25, 7.5, 3.25, 4.75)) should
        contain theSameElementsInOrderAs (Vector(1.25, 3.25, 7.5, 15.0, 18.25, 23.0))
    }

    "calculate cumulative diff of Ints" in {
      CumulativeOps.cumDiff(Vector(1, 2, 4, 7, 3, 4)) should
        contain theSameElementsInOrderAs (Vector(21, 20, 18, 14, 7, 4))
    }

    "calculate cumulative diff of Doubles" in {
      CumulativeOps.cumDiff(Vector(1.25, 2.5, 4, 7.25, 3, 4)) should
        contain theSameElementsInOrderAs (Vector(22.0, 20.75, 18.25, 14.25, 7.0, 4.0))
    }

    "calculate cumulative multiplication of Ints" in {
      CumulativeOps.cumMultiplication((List(2, 3, 7, 14, 17, 21))) should
        contain theSameElementsInOrderAs (Vector(2, 6, 42, 588, 9996, 209916))
    }

    "calculate cumulative multiplication of Doubles" in {
      CumulativeOps.cumMultiplication((List(0.99, 0.83, 0.74, 0.5, 0.5, 0.5))) should
        contain theSameElementsInOrderAs (Vector(0.99, 0.8217, 0.608058, 0.304029, 0.1520145, 0.07600725))
    }
  }
}