Detects simple sequences in a list of numbers. Only capable of determining liner addition/subtraction sequences.

SequencesDetector.scala

object Worksheet {

	val t = List(25, 21, 17, 13, 9)           //> t  : List[Int] = List(25, 21, 17, 13, 9)

	sealed abstract class SequenceType(dif: Int)
	case class Addition(dif: Int) extends SequenceType(dif)
	case class Subtraction(dif: Int) extends SequenceType(dif)
	case class Multiplication(dif: Int) extends SequenceType(dif)
	case class Division(dif: Int) extends SequenceType(dif)
	case class Invalid extends SequenceType(0)

	def analyzeSequence(seq: List[Int]): Option[Int => Int] = {
		val List(n1, n2) = seq.take(2)
		var ops = List(Addition(n2 - n1),
									 Subtraction(n2 - n1),
									 Multiplication(n1 * n2),
									 Division(n1 / n2))

		seq.drop(2).foldLeft(n2) { (prev, cur) =>
			ops = ops.map(op => {
				op match {
					case op: Addition => {
						val dif = cur - prev;
						if (dif == op.dif && dif > 0) Addition(dif) else Invalid()
					}
					case op: Subtraction => {
						val dif = cur - prev;
						if (dif == op.dif && dif < 0) Subtraction(dif) else Invalid()
					}
					case op: Multiplication => Invalid()
					case op: Division => Invalid()
					case op: Invalid => Invalid()
				}
			})
			cur
		}

		ops.filter(x => x match {
			case op: Invalid => false
			case _ => true
		}).headOption match {
			case Some(op) => {
				val generatorFunc = (n: Int) => {
					n match {
						case 0 => 0
						case 1 => n1
						case x if (n > 1) => {
							val x = op.asInstanceOf[Subtraction]
							x.dif * (n - 1) + n1
						}
					}
				}
				Some(generatorFunc)
			}
			case None => None
		}
	}                                         //> analyzeSequence: (seq: List[Int])Option[Int => Int]

	val gen = analyzeSequence(t).get          //> gen  : Int => Int = <function1>
	for (i <- 1 to 5) println(gen(i))         //> 25
                                                  //| 21
                                                  //| 17
                                                  //| 13
                                                  //| 9
}