DA: Inquiisition constellation puzzle solver

ConstellationSolver.scala

// Astrarium constellation puzzle solver for DA: Inquisition. Just assign numeric labels to the stars, and record 
// the connections between them in the "edges" container.

object ConstellationSolver extends App {

	type Edge = (Int, Int)

	def E(i : Int, f : Int) = (i, f)

	def orderEdges(edges : Set[Edge]) : Set[Seq[Edge]] = {
		def rec(remaining : Set[Edge], sofar : Seq[Edge]) : Set[Seq[Edge]] = {
			if (remaining.isEmpty) {
				Set(sofar)
			} else {
				val connectedEdges = remaining.filter {
					case edge@(first, second) ⇒ connected(sofar.last, edge)
				}
				connectedEdges.flatMap {
					case edge@(first, second) ⇒ rec(remaining - edge, sofar :+ edge)
				}
			}
		}
		edges.flatMap(edge ⇒ rec(edges - edge, Seq(edge)))
	}

	def connected(edge : Edge, other : Edge) =
		edge._1 == other._1 || edge._2 == other._2 || edge._1 == other._2 || edge._2 == other._1

	val edges = Set(
		E(1, 2), E(2, 3), E(3, 4), E(4, 5), E(5, 6),
		E(6, 7), E(7, 8), E(8, 9), E(9, 10), E(10, 11),
		E(11, 12), E(12, 13), E(13, 14), E(4, 15), E(4, 17),
		E(15, 16), E(16, 11), E(17, 11)
	)

	val orders = orderEdges(edges)
	println(orders.head)

}